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6,001 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.6096 c | A clock moving at velocity v = 0.6096 c relative to an inertial observer measures a proper time interval Δτ = 1.001 s. The observer measures a dilated interval Δt = γ Δτ = 1.263 s, where γ = 1 / sqrt(1 − v²/c²) = 1.262. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,002 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.1964 c | A clock moving at velocity v = 0.1964 c relative to an inertial observer measures a proper time interval Δτ = 9.746 s. The observer measures a dilated interval Δt = γ Δτ = 9.94 s, where γ = 1 / sqrt(1 − v²/c²) = 1.02. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,003 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.7528 c | A clock moving at velocity v = 0.7528 c relative to an inertial observer measures a proper time interval Δτ = 3.183 s. The observer measures a dilated interval Δt = γ Δτ = 4.836 s, where γ = 1 / sqrt(1 − v²/c²) = 1.519. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,004 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.2052 c | A clock moving at velocity v = 0.2052 c relative to an inertial observer measures a proper time interval Δτ = 5.764 s. The observer measures a dilated interval Δt = γ Δτ = 5.889 s, where γ = 1 / sqrt(1 − v²/c²) = 1.022. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,005 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.5949 c | A clock moving at velocity v = 0.5949 c relative to an inertial observer measures a proper time interval Δτ = 0.7884 s. The observer measures a dilated interval Δt = γ Δτ = 0.9808 s, where γ = 1 / sqrt(1 − v²/c²) = 1.244. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,006 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.1417 c | A clock moving at velocity v = 0.1417 c relative to an inertial observer measures a proper time interval Δτ = 3.115 s. The observer measures a dilated interval Δt = γ Δτ = 3.147 s, where γ = 1 / sqrt(1 − v²/c²) = 1.01. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,007 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.7465 c | A clock moving at velocity v = 0.7465 c relative to an inertial observer measures a proper time interval Δτ = 7.548 s. The observer measures a dilated interval Δt = γ Δτ = 11.35 s, where γ = 1 / sqrt(1 − v²/c²) = 1.503. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,008 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.876 c | A clock moving at velocity v = 0.876 c relative to an inertial observer measures a proper time interval Δτ = 0.7966 s. The observer measures a dilated interval Δt = γ Δτ = 1.652 s, where γ = 1 / sqrt(1 − v²/c²) = 2.074. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,009 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.7059 c | A clock moving at velocity v = 0.7059 c relative to an inertial observer measures a proper time interval Δτ = 9.352 s. The observer measures a dilated interval Δt = γ Δτ = 13.2 s, where γ = 1 / sqrt(1 − v²/c²) = 1.412. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,010 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.8398 c | A clock moving at velocity v = 0.8398 c relative to an inertial observer measures a proper time interval Δτ = 5.461 s. The observer measures a dilated interval Δt = γ Δτ = 10.06 s, where γ = 1 / sqrt(1 − v²/c²) = 1.842. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,011 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.8704 c | A clock moving at velocity v = 0.8704 c relative to an inertial observer measures a proper time interval Δτ = 6.579 s. The observer measures a dilated interval Δt = γ Δτ = 13.36 s, where γ = 1 / sqrt(1 − v²/c²) = 2.031. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,012 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.1854 c | A clock moving at velocity v = 0.1854 c relative to an inertial observer measures a proper time interval Δτ = 4.036 s. The observer measures a dilated interval Δt = γ Δτ = 4.108 s, where γ = 1 / sqrt(1 − v²/c²) = 1.018. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,013 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.8912 c | A clock moving at velocity v = 0.8912 c relative to an inertial observer measures a proper time interval Δτ = 3.119 s. The observer measures a dilated interval Δt = γ Δτ = 6.875 s, where γ = 1 / sqrt(1 − v²/c²) = 2.204. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,014 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.8463 c | A clock moving at velocity v = 0.8463 c relative to an inertial observer measures a proper time interval Δτ = 0.9297 s. The observer measures a dilated interval Δt = γ Δτ = 1.745 s, where γ = 1 / sqrt(1 − v²/c²) = 1.877. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,015 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.3833 c | A clock moving at velocity v = 0.3833 c relative to an inertial observer measures a proper time interval Δτ = 7.411 s. The observer measures a dilated interval Δt = γ Δτ = 8.024 s, where γ = 1 / sqrt(1 − v²/c²) = 1.083. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,016 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.2164 c | A clock moving at velocity v = 0.2164 c relative to an inertial observer measures a proper time interval Δτ = 0.9432 s. The observer measures a dilated interval Δt = γ Δτ = 0.966 s, where γ = 1 / sqrt(1 − v²/c²) = 1.024. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,017 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.903 c | A clock moving at velocity v = 0.903 c relative to an inertial observer measures a proper time interval Δτ = 0.0401 s. The observer measures a dilated interval Δt = γ Δτ = 0.09332 s, where γ = 1 / sqrt(1 − v²/c²) = 2.327. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,018 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.8577 c | A clock moving at velocity v = 0.8577 c relative to an inertial observer measures a proper time interval Δτ = 0.4252 s. The observer measures a dilated interval Δt = γ Δτ = 0.8271 s, where γ = 1 / sqrt(1 − v²/c²) = 1.945. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,019 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.7881 c | A clock moving at velocity v = 0.7881 c relative to an inertial observer measures a proper time interval Δτ = 4.06 s. The observer measures a dilated interval Δt = γ Δτ = 6.595 s, where γ = 1 / sqrt(1 − v²/c²) = 1.624. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,020 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.1909 c | A clock moving at velocity v = 0.1909 c relative to an inertial observer measures a proper time interval Δτ = 1.588 s. The observer measures a dilated interval Δt = γ Δτ = 1.618 s, where γ = 1 / sqrt(1 − v²/c²) = 1.019. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,021 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.8987 c | A clock moving at velocity v = 0.8987 c relative to an inertial observer measures a proper time interval Δτ = 8.95 s. The observer measures a dilated interval Δt = γ Δτ = 20.41 s, where γ = 1 / sqrt(1 − v²/c²) = 2.28. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,022 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.3104 c | A clock moving at velocity v = 0.3104 c relative to an inertial observer measures a proper time interval Δτ = 3.341 s. The observer measures a dilated interval Δt = γ Δτ = 3.514 s, where γ = 1 / sqrt(1 − v²/c²) = 1.052. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,023 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.2574 c | A clock moving at velocity v = 0.2574 c relative to an inertial observer measures a proper time interval Δτ = 9.182 s. The observer measures a dilated interval Δt = γ Δτ = 9.502 s, where γ = 1 / sqrt(1 − v²/c²) = 1.035. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,024 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.6956 c | A clock moving at velocity v = 0.6956 c relative to an inertial observer measures a proper time interval Δτ = 1.039 s. The observer measures a dilated interval Δt = γ Δτ = 1.446 s, where γ = 1 / sqrt(1 − v²/c²) = 1.392. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,025 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.7904 c | A clock moving at velocity v = 0.7904 c relative to an inertial observer measures a proper time interval Δτ = 4.703 s. The observer measures a dilated interval Δt = γ Δτ = 7.678 s, where γ = 1 / sqrt(1 − v²/c²) = 1.632. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,026 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.7194 c | A clock moving at velocity v = 0.7194 c relative to an inertial observer measures a proper time interval Δτ = 1.267 s. The observer measures a dilated interval Δt = γ Δτ = 1.824 s, where γ = 1 / sqrt(1 − v²/c²) = 1.44. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,027 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.7272 c | A clock moving at velocity v = 0.7272 c relative to an inertial observer measures a proper time interval Δτ = 8.222 s. The observer measures a dilated interval Δt = γ Δτ = 11.98 s, where γ = 1 / sqrt(1 − v²/c²) = 1.457. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,028 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.6801 c | A clock moving at velocity v = 0.6801 c relative to an inertial observer measures a proper time interval Δτ = 2.386 s. The observer measures a dilated interval Δt = γ Δτ = 3.254 s, where γ = 1 / sqrt(1 − v²/c²) = 1.364. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,029 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.4467 c | A clock moving at velocity v = 0.4467 c relative to an inertial observer measures a proper time interval Δτ = 6.814 s. The observer measures a dilated interval Δt = γ Δτ = 7.616 s, where γ = 1 / sqrt(1 − v²/c²) = 1.118. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,030 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.8438 c | A clock moving at velocity v = 0.8438 c relative to an inertial observer measures a proper time interval Δτ = 5.767 s. The observer measures a dilated interval Δt = γ Δτ = 10.75 s, where γ = 1 / sqrt(1 − v²/c²) = 1.863. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,031 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.7204 c | A clock moving at velocity v = 0.7204 c relative to an inertial observer measures a proper time interval Δτ = 8.418 s. The observer measures a dilated interval Δt = γ Δτ = 12.14 s, where γ = 1 / sqrt(1 − v²/c²) = 1.442. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,032 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.5188 c | A clock moving at velocity v = 0.5188 c relative to an inertial observer measures a proper time interval Δτ = 2.379 s. The observer measures a dilated interval Δt = γ Δτ = 2.783 s, where γ = 1 / sqrt(1 − v²/c²) = 1.17. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,033 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.4653 c | A clock moving at velocity v = 0.4653 c relative to an inertial observer measures a proper time interval Δτ = 6.133 s. The observer measures a dilated interval Δt = γ Δτ = 6.928 s, where γ = 1 / sqrt(1 − v²/c²) = 1.13. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,034 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.4302 c | A clock moving at velocity v = 0.4302 c relative to an inertial observer measures a proper time interval Δτ = 8.25 s. The observer measures a dilated interval Δt = γ Δτ = 9.139 s, where γ = 1 / sqrt(1 − v²/c²) = 1.108. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,035 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.3488 c | A clock moving at velocity v = 0.3488 c relative to an inertial observer measures a proper time interval Δτ = 1.362 s. The observer measures a dilated interval Δt = γ Δτ = 1.453 s, where γ = 1 / sqrt(1 − v²/c²) = 1.067. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,036 | physics | relativity | time_dilation | 8 | worked_example | Time dilation at v = 0.9277 c | A clock moving at velocity v = 0.9277 c relative to an inertial observer measures a proper time interval Δτ = 4.115 s. The observer measures a dilated interval Δt = γ Δτ = 11.02 s, where γ = 1 / sqrt(1 − v²/c²) = 2.678. Time dilation is a direct consequence of the invariance of the spacetime interval. | Δt = γ Δτ; γ = 1 / sqrt(1 - v²/c²) | classical kinematics | Calculate the time-dilation factor and the dilated time interval. |
6,037 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 5.7834e-26 kg, speed 2.6943e+06 m/s | A free particle of mass 5.7834e-26 kg moving at speed 2.6943e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 4.2523e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,038 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 6.1639e-26 kg, speed 8.8958e+06 m/s | A free particle of mass 6.1639e-26 kg moving at speed 8.8958e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.2084e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,039 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 7.0691e-26 kg, speed 2.5507e+06 m/s | A free particle of mass 7.0691e-26 kg moving at speed 2.5507e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 3.6747e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,040 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 6.0526e-26 kg, speed 1.5525e+04 m/s | A free particle of mass 6.0526e-26 kg moving at speed 1.5525e+04 m/s has de Broglie wavelength λ = h / p = h / (m v) = 7.0515e-13 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,041 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 1.1462e-26 kg, speed 5.9078e+06 m/s | A free particle of mass 1.1462e-26 kg moving at speed 5.9078e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 9.7853e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,042 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 7.4679e-26 kg, speed 6.9133e+06 m/s | A free particle of mass 7.4679e-26 kg moving at speed 6.9133e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.2834e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,043 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 5.7662e-26 kg, speed 8.1446e+06 m/s | A free particle of mass 5.7662e-26 kg moving at speed 8.1446e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.4109e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,044 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 5.8021e-26 kg, speed 9.6718e+06 m/s | A free particle of mass 5.8021e-26 kg moving at speed 9.6718e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.1808e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,045 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 2.4879e-26 kg, speed 7.1110e+06 m/s | A free particle of mass 2.4879e-26 kg moving at speed 7.1110e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 3.7454e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,046 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 2.3086e-26 kg, speed 2.5007e+06 m/s | A free particle of mass 2.3086e-26 kg moving at speed 2.5007e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.1477e-14 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,047 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 4.6574e-27 kg, speed 7.2292e+05 m/s | A free particle of mass 4.6574e-27 kg moving at speed 7.2292e+05 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.9680e-13 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,048 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 3.9472e-26 kg, speed 9.6522e+06 m/s | A free particle of mass 3.9472e-26 kg moving at speed 9.6522e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.7391e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,049 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 2.7656e-26 kg, speed 1.1270e+06 m/s | A free particle of mass 2.7656e-26 kg moving at speed 1.1270e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 2.1259e-14 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,050 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 2.8276e-28 kg, speed 2.1028e+06 m/s | A free particle of mass 2.8276e-28 kg moving at speed 2.1028e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.1144e-12 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,051 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 1.1078e-26 kg, speed 6.9625e+06 m/s | A free particle of mass 1.1078e-26 kg moving at speed 6.9625e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 8.5904e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,052 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 4.1336e-26 kg, speed 3.4142e+06 m/s | A free particle of mass 4.1336e-26 kg moving at speed 3.4142e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 4.6950e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,053 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 4.4708e-26 kg, speed 1.4707e+06 m/s | A free particle of mass 4.4708e-26 kg moving at speed 1.4707e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.0077e-14 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,054 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 6.4797e-26 kg, speed 1.2333e+06 m/s | A free particle of mass 6.4797e-26 kg moving at speed 1.2333e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 8.2914e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,055 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 3.6876e-26 kg, speed 9.7725e+06 m/s | A free particle of mass 3.6876e-26 kg moving at speed 9.7725e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.8387e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,056 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 3.7873e-26 kg, speed 5.1891e+06 m/s | A free particle of mass 3.7873e-26 kg moving at speed 5.1891e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 3.3716e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,057 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 2.7507e-26 kg, speed 6.6315e+06 m/s | A free particle of mass 2.7507e-26 kg moving at speed 6.6315e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 3.6324e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,058 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 8.5776e-26 kg, speed 1.4600e+06 m/s | A free particle of mass 8.5776e-26 kg moving at speed 1.4600e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 5.2910e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,059 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 3.8922e-26 kg, speed 1.8808e+06 m/s | A free particle of mass 3.8922e-26 kg moving at speed 1.8808e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 9.0514e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,060 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 6.6586e-26 kg, speed 9.4677e+06 m/s | A free particle of mass 6.6586e-26 kg moving at speed 9.4677e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.0511e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,061 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 2.4278e-26 kg, speed 4.8896e+06 m/s | A free particle of mass 2.4278e-26 kg moving at speed 4.8896e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 5.5818e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,062 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 2.7390e-26 kg, speed 4.9029e+05 m/s | A free particle of mass 2.7390e-26 kg moving at speed 4.9029e+05 m/s has de Broglie wavelength λ = h / p = h / (m v) = 4.9341e-14 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,063 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 3.0674e-28 kg, speed 4.6364e+06 m/s | A free particle of mass 3.0674e-28 kg moving at speed 4.6364e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 4.6592e-13 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,064 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 6.1414e-27 kg, speed 8.8895e+06 m/s | A free particle of mass 6.1414e-27 kg moving at speed 8.8895e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.2137e-14 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,065 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 5.9602e-27 kg, speed 4.5880e+06 m/s | A free particle of mass 5.9602e-27 kg moving at speed 4.5880e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 2.4231e-14 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,066 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 2.8908e-26 kg, speed 4.1346e+06 m/s | A free particle of mass 2.8908e-26 kg moving at speed 4.1346e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 5.5437e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,067 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 8.8131e-26 kg, speed 1.4078e+06 m/s | A free particle of mass 8.8131e-26 kg moving at speed 1.4078e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 5.3404e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,068 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 2.7934e-26 kg, speed 4.2621e+06 m/s | A free particle of mass 2.7934e-26 kg moving at speed 4.2621e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 5.5655e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,069 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 1.3777e-27 kg, speed 7.8572e+06 m/s | A free particle of mass 1.3777e-27 kg moving at speed 7.8572e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 6.1210e-14 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,070 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 5.2960e-26 kg, speed 5.8653e+06 m/s | A free particle of mass 5.2960e-26 kg moving at speed 5.8653e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 2.1332e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,071 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 3.4785e-26 kg, speed 6.4429e+06 m/s | A free particle of mass 3.4785e-26 kg moving at speed 6.4429e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 2.9566e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,072 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 4.4935e-26 kg, speed 6.8846e+06 m/s | A free particle of mass 4.4935e-26 kg moving at speed 6.8846e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 2.1419e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,073 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 2.7562e-26 kg, speed 4.7689e+06 m/s | A free particle of mass 2.7562e-26 kg moving at speed 4.7689e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 5.0411e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,074 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 3.9060e-26 kg, speed 1.6054e+06 m/s | A free particle of mass 3.9060e-26 kg moving at speed 1.6054e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.0567e-14 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,075 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 2.2057e-26 kg, speed 9.0482e+06 m/s | A free particle of mass 2.2057e-26 kg moving at speed 9.0482e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 3.3200e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,076 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 1.7156e-27 kg, speed 2.3450e+06 m/s | A free particle of mass 1.7156e-27 kg moving at speed 2.3450e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.6471e-13 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,077 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 4.8591e-26 kg, speed 2.1895e+06 m/s | A free particle of mass 4.8591e-26 kg moving at speed 2.1895e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 6.2281e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,078 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 9.4852e-26 kg, speed 5.0975e+06 m/s | A free particle of mass 9.4852e-26 kg moving at speed 5.0975e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.3704e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,079 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 9.3398e-26 kg, speed 1.0991e+06 m/s | A free particle of mass 9.3398e-26 kg moving at speed 1.0991e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 6.4546e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,080 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 7.2125e-26 kg, speed 5.2208e+06 m/s | A free particle of mass 7.2125e-26 kg moving at speed 5.2208e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.7597e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,081 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 6.8991e-26 kg, speed 2.7188e+06 m/s | A free particle of mass 6.8991e-26 kg moving at speed 2.7188e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 3.5325e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,082 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 6.5830e-26 kg, speed 7.9948e+06 m/s | A free particle of mass 6.5830e-26 kg moving at speed 7.9948e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.2590e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,083 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 7.4641e-26 kg, speed 2.0398e+05 m/s | A free particle of mass 7.4641e-26 kg moving at speed 2.0398e+05 m/s has de Broglie wavelength λ = h / p = h / (m v) = 4.3521e-14 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,084 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 5.6716e-26 kg, speed 8.8482e+06 m/s | A free particle of mass 5.6716e-26 kg moving at speed 8.8482e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.3204e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,085 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 2.4123e-26 kg, speed 2.8289e+06 m/s | A free particle of mass 2.4123e-26 kg moving at speed 2.8289e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 9.7098e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,086 | physics | quantum | de_broglie | 7 | worked_example | de Broglie wavelength of particle mass 8.0971e-26 kg, speed 7.5776e+06 m/s | A free particle of mass 8.0971e-26 kg moving at speed 7.5776e+06 m/s has de Broglie wavelength λ = h / p = h / (m v) = 1.0799e-15 m, where h is Planck's constant. This relation underlies the wave-particle duality of matter and is confirmed by electron diffraction experiments. | λ = h / p | wave_speed; classical momentum | Compute the de Broglie wavelength of a massive particle. |
6,087 | chemistry | stoichiometry | mole_concept | 3 | worked_example | Moles of Fe2O3 from mass 85.6 g | The molar mass of Fe2O3 is 159.7 g/mol. A sample of mass 85.6 g therefore contains n = m / M = 85.6 / 159.7 = 0.536 mol. The mole is the SI unit for amount of substance and links macroscopic mass to number of entities via Avogadro's constant. | n = m / M | atomic masses; chemical formulas | Convert between mass and moles for a pure compound. |
6,088 | chemistry | stoichiometry | mole_concept | 3 | worked_example | Moles of CuSO4 from mass 79.92 g | The molar mass of CuSO4 is 159.6 g/mol. A sample of mass 79.92 g therefore contains n = m / M = 79.92 / 159.6 = 0.5007 mol. The mole is the SI unit for amount of substance and links macroscopic mass to number of entities via Avogadro's constant. | n = m / M | atomic masses; chemical formulas | Convert between mass and moles for a pure compound. |
6,089 | chemistry | stoichiometry | mole_concept | 3 | worked_example | Moles of Fe2O3 from mass 92.19 g | The molar mass of Fe2O3 is 159.7 g/mol. A sample of mass 92.19 g therefore contains n = m / M = 92.19 / 159.7 = 0.5773 mol. The mole is the SI unit for amount of substance and links macroscopic mass to number of entities via Avogadro's constant. | n = m / M | atomic masses; chemical formulas | Convert between mass and moles for a pure compound. |
6,090 | chemistry | stoichiometry | mole_concept | 3 | worked_example | Moles of CaCO3 from mass 97.75 g | The molar mass of CaCO3 is 100.1 g/mol. A sample of mass 97.75 g therefore contains n = m / M = 97.75 / 100.1 = 0.9766 mol. The mole is the SI unit for amount of substance and links macroscopic mass to number of entities via Avogadro's constant. | n = m / M | atomic masses; chemical formulas | Convert between mass and moles for a pure compound. |
6,091 | chemistry | stoichiometry | mole_concept | 3 | worked_example | Moles of H2O from mass 14.99 g | The molar mass of H2O is 18.02 g/mol. A sample of mass 14.99 g therefore contains n = m / M = 14.99 / 18.02 = 0.8323 mol. The mole is the SI unit for amount of substance and links macroscopic mass to number of entities via Avogadro's constant. | n = m / M | atomic masses; chemical formulas | Convert between mass and moles for a pure compound. |
6,092 | chemistry | stoichiometry | mole_concept | 3 | worked_example | Moles of H2O from mass 32.8 g | The molar mass of H2O is 18.02 g/mol. A sample of mass 32.8 g therefore contains n = m / M = 32.8 / 18.02 = 1.821 mol. The mole is the SI unit for amount of substance and links macroscopic mass to number of entities via Avogadro's constant. | n = m / M | atomic masses; chemical formulas | Convert between mass and moles for a pure compound. |
6,093 | chemistry | stoichiometry | mole_concept | 3 | worked_example | Moles of Fe2O3 from mass 42.03 g | The molar mass of Fe2O3 is 159.7 g/mol. A sample of mass 42.03 g therefore contains n = m / M = 42.03 / 159.7 = 0.2632 mol. The mole is the SI unit for amount of substance and links macroscopic mass to number of entities via Avogadro's constant. | n = m / M | atomic masses; chemical formulas | Convert between mass and moles for a pure compound. |
6,094 | chemistry | stoichiometry | mole_concept | 3 | worked_example | Moles of NH3 from mass 0.2459 g | The molar mass of NH3 is 17.03 g/mol. A sample of mass 0.2459 g therefore contains n = m / M = 0.2459 / 17.03 = 0.01444 mol. The mole is the SI unit for amount of substance and links macroscopic mass to number of entities via Avogadro's constant. | n = m / M | atomic masses; chemical formulas | Convert between mass and moles for a pure compound. |
6,095 | chemistry | stoichiometry | mole_concept | 3 | worked_example | Moles of C6H12O6 from mass 18.82 g | The molar mass of C6H12O6 is 180.2 g/mol. A sample of mass 18.82 g therefore contains n = m / M = 18.82 / 180.2 = 0.1045 mol. The mole is the SI unit for amount of substance and links macroscopic mass to number of entities via Avogadro's constant. | n = m / M | atomic masses; chemical formulas | Convert between mass and moles for a pure compound. |
6,096 | chemistry | stoichiometry | mole_concept | 3 | worked_example | Moles of H2SO4 from mass 72.12 g | The molar mass of H2SO4 is 98.07 g/mol. A sample of mass 72.12 g therefore contains n = m / M = 72.12 / 98.07 = 0.7353 mol. The mole is the SI unit for amount of substance and links macroscopic mass to number of entities via Avogadro's constant. | n = m / M | atomic masses; chemical formulas | Convert between mass and moles for a pure compound. |
6,097 | chemistry | stoichiometry | mole_concept | 3 | worked_example | Moles of CH4 from mass 25.19 g | The molar mass of CH4 is 16.04 g/mol. A sample of mass 25.19 g therefore contains n = m / M = 25.19 / 16.04 = 1.57 mol. The mole is the SI unit for amount of substance and links macroscopic mass to number of entities via Avogadro's constant. | n = m / M | atomic masses; chemical formulas | Convert between mass and moles for a pure compound. |
6,098 | chemistry | stoichiometry | mole_concept | 3 | worked_example | Moles of H2SO4 from mass 58.66 g | The molar mass of H2SO4 is 98.07 g/mol. A sample of mass 58.66 g therefore contains n = m / M = 58.66 / 98.07 = 0.5981 mol. The mole is the SI unit for amount of substance and links macroscopic mass to number of entities via Avogadro's constant. | n = m / M | atomic masses; chemical formulas | Convert between mass and moles for a pure compound. |
6,099 | chemistry | stoichiometry | mole_concept | 3 | worked_example | Moles of CH4 from mass 67.02 g | The molar mass of CH4 is 16.04 g/mol. A sample of mass 67.02 g therefore contains n = m / M = 67.02 / 16.04 = 4.177 mol. The mole is the SI unit for amount of substance and links macroscopic mass to number of entities via Avogadro's constant. | n = m / M | atomic masses; chemical formulas | Convert between mass and moles for a pure compound. |
6,100 | chemistry | stoichiometry | mole_concept | 3 | worked_example | Moles of CuSO4 from mass 56.57 g | The molar mass of CuSO4 is 159.6 g/mol. A sample of mass 56.57 g therefore contains n = m / M = 56.57 / 159.6 = 0.3544 mol. The mole is the SI unit for amount of substance and links macroscopic mass to number of entities via Avogadro's constant. | n = m / M | atomic masses; chemical formulas | Convert between mass and moles for a pure compound. |
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