data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
math-ai/minervamath | [
{
"role": "user",
"content": "Determine the wavelength of $\\lambda_{K_{\\alpha}}$ for molybdenum (Mo). Please format your answer as $n \\times 10^x$ where $n$ is to 2 decimal places, in meters.\n\nLet's think step by step and output the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "7.25e-11"
} | {
"index": 200,
"split": "test",
"question": "Determine the wavelength of $\\lambda_{K_{\\alpha}}$ for molybdenum (Mo). Please format your answer as $n \\times 10^x$ where $n$ is to 2 decimal places, in meters."
} |
math-ai/minervamath | [
{
"role": "user",
"content": "Determine the second-nearest neighbor distance (in pm) for nickel (Ni) at $100^{\\circ} \\mathrm{C}$ if its density at that temperature is $8.83 \\mathrm{~g} / \\mathrm{cm}^{3}$. Please format your answer as $n \\times 10^x$ where $n$ is to 2 decimal places.\n\nLet's think step... | math | {
"style": "rule",
"ground_truth": "3.61e2"
} | {
"index": 201,
"split": "test",
"question": "Determine the second-nearest neighbor distance (in pm) for nickel (Ni) at $100^{\\circ} \\mathrm{C}$ if its density at that temperature is $8.83 \\mathrm{~g} / \\mathrm{cm}^{3}$. Please format your answer as $n \\times 10^x$ where $n$ is to 2 decimal places."
} |
math-ai/minervamath | [
{
"role": "user",
"content": "What is the working temperature for silica glass in Celsius?\n\nLet's think step by step and output the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1950"
} | {
"index": 202,
"split": "test",
"question": "What is the working temperature for silica glass in Celsius?"
} |
math-ai/minervamath | [
{
"role": "user",
"content": "What acceleration potential $V$ must be applied to electrons to cause electron diffraction on $\\{220\\}$ planes of gold $(\\mathrm{Au})$ at $\\theta=5^{\\circ}$ ? Format your answer as an integer, in Volts.\n\nLet's think step by step and output the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "2415"
} | {
"index": 203,
"split": "test",
"question": "What acceleration potential $V$ must be applied to electrons to cause electron diffraction on $\\{220\\}$ planes of gold $(\\mathrm{Au})$ at $\\theta=5^{\\circ}$ ? Format your answer as an integer, in Volts."
} |
math-ai/minervamath | [
{
"role": "user",
"content": "To increase its corrosion resistance, chromium $(\\mathrm{Cr})$ is diffused into steel at $980^{\\circ} \\mathrm{C}$. If during diffusion the surface concentration of chromium remains constant at $100 \\%$, how long will it take (in days) to achieve a $\\mathrm{Cr}$ concentrati... | math | {
"style": "rule",
"ground_truth": "6.4"
} | {
"index": 204,
"split": "test",
"question": "To increase its corrosion resistance, chromium $(\\mathrm{Cr})$ is diffused into steel at $980^{\\circ} \\mathrm{C}$. If during diffusion the surface concentration of chromium remains constant at $100 \\%$, how long will it take (in days) to achieve a $\\mathrm{Cr}$ c... |
math-ai/minervamath | [
{
"role": "user",
"content": "Subproblem 0: What is the working temperature for silica glass in Celsius?\n\n\nSolution: \\boxed{1950}.\n\nFinal answer: The final answer is 1950. I hope it is correct.\n\nSubproblem 1: What is the softening temperature for silica glass in Celsius?\n\n\nSolution: \\boxed{1700}... | math | {
"style": "rule",
"ground_truth": "1200"
} | {
"index": 205,
"split": "test",
"question": "Subproblem 0: What is the working temperature for silica glass in Celsius?\n\n\nSolution: \\boxed{1950}.\n\nFinal answer: The final answer is 1950. I hope it is correct.\n\nSubproblem 1: What is the softening temperature for silica glass in Celsius?\n\n\nSolution: \\b... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: Calculate the vacancy fraction in copper (Cu) in $\\mathrm{~cm}^{-3}$ at the following temperatures. Measurements have determined the values of the enthalpy of vacancy formation, $\\Delta \\mathrm{H}_{\\mathrm{V}}$, to be $1.03 \\mathrm{eV}$ and the entropic prefactor... | math | {
"style": "rule",
"ground_truth": "1.85e5"
} | {
"index": 206,
"split": "test",
"question": "Preamble: Calculate the vacancy fraction in copper (Cu) in $\\mathrm{~cm}^{-3}$ at the following temperatures. Measurements have determined the values of the enthalpy of vacancy formation, $\\Delta \\mathrm{H}_{\\mathrm{V}}$, to be $1.03 \\mathrm{eV}$ and the entropic... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: For aluminum at $300 \\mathrm{~K}$, \n\nCalculate the planar packing fraction (fractional area occupied by atoms) of the ( 110 ) plane. Please round your answer to 3 decimal places.\n\nLet's think step by step and output the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.554"
} | {
"index": 207,
"split": "test",
"question": "Preamble: For aluminum at $300 \\mathrm{~K}$, \n\nCalculate the planar packing fraction (fractional area occupied by atoms) of the ( 110 ) plane. Please round your answer to 3 decimal places."
} |
math-ai/minervamath | [
{
"role": "user",
"content": "Determine the inter-ionic equilibrium distance in meters between the sodium and chlorine ions in a sodium chloride molecule knowing that the bond energy is $3.84 \\mathrm{eV}$ and that the repulsive exponent is 8. Please format your answer as $n \\times 10^x$ where $n$ is to 1 ... | math | {
"style": "rule",
"ground_truth": "3.3e-10"
} | {
"index": 208,
"split": "test",
"question": "Determine the inter-ionic equilibrium distance in meters between the sodium and chlorine ions in a sodium chloride molecule knowing that the bond energy is $3.84 \\mathrm{eV}$ and that the repulsive exponent is 8. Please format your answer as $n \\times 10^x$ where $n... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: A formation energy of $2.0 \\mathrm{eV}$ is required to create a vacancy in a particular metal. At $800^{\\circ} \\mathrm{C}$ there is one vacancy for every 10,000 atoms.\n\nAt what temperature (in Celsius) will there be one vacancy for every 1,000 atoms? Format your ... | math | {
"style": "rule",
"ground_truth": "928"
} | {
"index": 209,
"split": "test",
"question": "Preamble: A formation energy of $2.0 \\mathrm{eV}$ is required to create a vacancy in a particular metal. At $800^{\\circ} \\mathrm{C}$ there is one vacancy for every 10,000 atoms.\n\nAt what temperature (in Celsius) will there be one vacancy for every 1,000 atoms? Fo... |
math-ai/minervamath | [
{
"role": "user",
"content": "For $\\mathrm{NaF}$ the repulsive (Born) exponent, $\\mathrm{n}$, is 8.7. Making use of data given in your Periodic Table, calculate the crystal energy ( $\\left.\\Delta \\mathrm{E}_{\\text {cryst }}\\right)$ in kJ/mole, to 1 decimal place.\n\nLet's think step by step and outpu... | math | {
"style": "rule",
"ground_truth": "927.5"
} | {
"index": 210,
"split": "test",
"question": "For $\\mathrm{NaF}$ the repulsive (Born) exponent, $\\mathrm{n}$, is 8.7. Making use of data given in your Periodic Table, calculate the crystal energy ( $\\left.\\Delta \\mathrm{E}_{\\text {cryst }}\\right)$ in kJ/mole, to 1 decimal place."
} |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: Calculate the molecular weight in g/mole (to 2 decimal places) of each of the substances listed below.\n\nSubproblem 0: $\\mathrm{NH}_{4} \\mathrm{OH}$\n\n\nSolution: $\\mathrm{NH}_{4} \\mathrm{OH}$ :\n$5 \\times 1.01=5.05(\\mathrm{H})$\n$1 \\times 14.01=14.01(\\mathr... | math | {
"style": "rule",
"ground_truth": "84.01"
} | {
"index": 211,
"split": "test",
"question": "Preamble: Calculate the molecular weight in g/mole (to 2 decimal places) of each of the substances listed below.\n\nSubproblem 0: $\\mathrm{NH}_{4} \\mathrm{OH}$\n\n\nSolution: $\\mathrm{NH}_{4} \\mathrm{OH}$ :\n$5 \\times 1.01=5.05(\\mathrm{H})$\n$1 \\times 14.01=14.... |
math-ai/minervamath | [
{
"role": "user",
"content": "In iridium (Ir), the vacancy fraction, $n_{v} / \\mathrm{N}$, is $3.091 \\times 10^{-5}$ at $12340^{\\circ} \\mathrm{C}$ and $5.26 \\times 10^{-3}$ at the melting point. Calculate the enthalpy of vacancy formation, $\\Delta \\mathrm{H}_{\\mathrm{v}}$. Round your answer to 1 dec... | math | {
"style": "rule",
"ground_truth": "1.5"
} | {
"index": 212,
"split": "test",
"question": "In iridium (Ir), the vacancy fraction, $n_{v} / \\mathrm{N}$, is $3.091 \\times 10^{-5}$ at $12340^{\\circ} \\mathrm{C}$ and $5.26 \\times 10^{-3}$ at the melting point. Calculate the enthalpy of vacancy formation, $\\Delta \\mathrm{H}_{\\mathrm{v}}$. Round your answe... |
math-ai/minervamath | [
{
"role": "user",
"content": "If no electron-hole pairs were produced in germanium (Ge) until the temperature reached the value corresponding to the energy gap, at what temperature (Celsius) would Ge become conductive? Please format your answer as $n \\times 10^x$ where n is to 1 decimal place. $\\left(\\m... | math | {
"style": "rule",
"ground_truth": "5.3e3"
} | {
"index": 213,
"split": "test",
"question": "If no electron-hole pairs were produced in germanium (Ge) until the temperature reached the value corresponding to the energy gap, at what temperature (Celsius) would Ge become conductive? Please format your answer as $n \\times 10^x$ where n is to 1 decimal place. $... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: A first-order chemical reaction is found to have an activation energy $\\left(E_{A}\\right)$ of 250 $\\mathrm{kJ} /$ mole and a pre-exponential (A) of $1.7 \\times 10^{14} \\mathrm{~s}^{-1}$.\n\nDetermine the rate constant at $\\mathrm{T}=750^{\\circ} \\mathrm{C}$. Ro... | math | {
"style": "rule",
"ground_truth": "28.8"
} | {
"index": 214,
"split": "test",
"question": "Preamble: A first-order chemical reaction is found to have an activation energy $\\left(E_{A}\\right)$ of 250 $\\mathrm{kJ} /$ mole and a pre-exponential (A) of $1.7 \\times 10^{14} \\mathrm{~s}^{-1}$.\n\nDetermine the rate constant at $\\mathrm{T}=750^{\\circ} \\math... |
math-ai/minervamath | [
{
"role": "user",
"content": "A cubic metal $(r=0.77 \\AA$ ) exhibits plastic deformation by slip along $<111>$ directions. Determine its planar packing density (atoms $/ \\mathrm{m}^{2}$) for its densest family of planes. Please format your answer as $n \\times 10^x$ where $n$ is to 2 decimal places.\n\nLe... | math | {
"style": "rule",
"ground_truth": "4.46e19"
} | {
"index": 215,
"split": "test",
"question": "A cubic metal $(r=0.77 \\AA$ ) exhibits plastic deformation by slip along $<111>$ directions. Determine its planar packing density (atoms $/ \\mathrm{m}^{2}$) for its densest family of planes. Please format your answer as $n \\times 10^x$ where $n$ is to 2 decimal pla... |
math-ai/minervamath | [
{
"role": "user",
"content": "Determine the total void volume $(\\mathrm{cm}^{3} / mole)$ for gold (Au) at $27^{\\circ} \\mathrm{C}$; make the hard-sphere approximation in your calculation. Note that the molar volume of gold (Au) is $10.3 \\mathrm{~cm}^{3} / \\mathrm{mole}$. Please round your answer to 2 de... | math | {
"style": "rule",
"ground_truth": "2.68"
} | {
"index": 216,
"split": "test",
"question": "Determine the total void volume $(\\mathrm{cm}^{3} / mole)$ for gold (Au) at $27^{\\circ} \\mathrm{C}$; make the hard-sphere approximation in your calculation. Note that the molar volume of gold (Au) is $10.3 \\mathrm{~cm}^{3} / \\mathrm{mole}$. Please round your answ... |
math-ai/minervamath | [
{
"role": "user",
"content": "Subproblem 0: What is the working temperature for silica glass in Celsius?\n\n\nSolution: \\boxed{1950}.\n\nFinal answer: The final answer is 1950. I hope it is correct.\n\nSubproblem 1: What is the softening temperature for silica glass in Celsius?\n\n\nSolution: \\boxed{1700}... | math | {
"style": "rule",
"ground_truth": "700"
} | {
"index": 217,
"split": "test",
"question": "Subproblem 0: What is the working temperature for silica glass in Celsius?\n\n\nSolution: \\boxed{1950}.\n\nFinal answer: The final answer is 1950. I hope it is correct.\n\nSubproblem 1: What is the softening temperature for silica glass in Celsius?\n\n\nSolution: \\b... |
math-ai/minervamath | [
{
"role": "user",
"content": "What is the maximum wavelength $(\\lambda)$ (in meters) of radiation capable of second order diffraction in platinum (Pt)? Please format your answer as $n \\times 10^x$ where $n$ is to 2 decimal places.\n\nLet's think step by step and output the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "2.26e-10"
} | {
"index": 218,
"split": "test",
"question": "What is the maximum wavelength $(\\lambda)$ (in meters) of radiation capable of second order diffraction in platinum (Pt)? Please format your answer as $n \\times 10^x$ where $n$ is to 2 decimal places."
} |
math-ai/minervamath | [
{
"role": "user",
"content": "What is the activation energy of a process which is observed to increase by a factor of three when the temperature is increased from room temperature $\\left(20^{\\circ} \\mathrm{C}\\right)$ to $40^{\\circ} \\mathrm{C}$ ? Round your answer to 1 decimal place, and express it in ... | math | {
"style": "rule",
"ground_truth": "41.9"
} | {
"index": 219,
"split": "test",
"question": "What is the activation energy of a process which is observed to increase by a factor of three when the temperature is increased from room temperature $\\left(20^{\\circ} \\mathrm{C}\\right)$ to $40^{\\circ} \\mathrm{C}$ ? Round your answer to 1 decimal place, and expr... |
math-ai/minervamath | [
{
"role": "user",
"content": "How much oxygen (in kg, to 3 decimal places) is required to completely convert 1 mole of $\\mathrm{C}_{2} \\mathrm{H}_{6}$ into $\\mathrm{CO}_{2}$ and $\\mathrm{H}_{2} \\mathrm{O}$ ?\n\nLet's think step by step and output the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.112"
} | {
"index": 220,
"split": "test",
"question": "How much oxygen (in kg, to 3 decimal places) is required to completely convert 1 mole of $\\mathrm{C}_{2} \\mathrm{H}_{6}$ into $\\mathrm{CO}_{2}$ and $\\mathrm{H}_{2} \\mathrm{O}$ ?"
} |
math-ai/minervamath | [
{
"role": "user",
"content": "Determine the differences in relative electronegativity $(\\Delta x$ in $e V)$ for the systems ${H}-{F}$ and ${C}-{F}$ given the following data:\n$\\begin{array}{cl}\\text { Bond Energy } & {kJ} / \\text { mole } \\\\ {H}_{2} & 436 \\\\ {~F}_{2} & 172 \\\\ {C}-{C} & 335 \\\\ {H... | math | {
"style": "rule",
"ground_truth": "0.54"
} | {
"index": 221,
"split": "test",
"question": "Determine the differences in relative electronegativity $(\\Delta x$ in $e V)$ for the systems ${H}-{F}$ and ${C}-{F}$ given the following data:\n$\\begin{array}{cl}\\text { Bond Energy } & {kJ} / \\text { mole } \\\\ {H}_{2} & 436 \\\\ {~F}_{2} & 172 \\\\ {C}-{C} & 3... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: The number of electron-hole pairs in intrinsic germanium (Ge) is given by:\n\\[\nn_{i}=9.7 \\times 10^{15} \\mathrm{~T}^{3 / 2} \\mathrm{e}^{-\\mathrm{E}_{g} / 2 \\mathrm{KT}}\\left[\\mathrm{cm}^{3}\\right] \\quad\\left(\\mathrm{E}_{\\mathrm{g}}=0.72 \\mathrm{eV}\\rig... | math | {
"style": "rule",
"ground_truth": "3.21e13"
} | {
"index": 222,
"split": "test",
"question": "Preamble: The number of electron-hole pairs in intrinsic germanium (Ge) is given by:\n\\[\nn_{i}=9.7 \\times 10^{15} \\mathrm{~T}^{3 / 2} \\mathrm{e}^{-\\mathrm{E}_{g} / 2 \\mathrm{KT}}\\left[\\mathrm{cm}^{3}\\right] \\quad\\left(\\mathrm{E}_{\\mathrm{g}}=0.72 \\mathr... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: For light with a wavelength $(\\lambda)$ of $408 \\mathrm{~nm}$ determine:\n\nSubproblem 0: the frequency in $s^{-1}$. Please format your answer as $n \\times 10^x$, where $n$ is to 3 decimal places. \n\n\nSolution: To solve this problem we must know the following rel... | math | {
"style": "rule",
"ground_truth": "2.45e6"
} | {
"index": 223,
"split": "test",
"question": "Preamble: For light with a wavelength $(\\lambda)$ of $408 \\mathrm{~nm}$ determine:\n\nSubproblem 0: the frequency in $s^{-1}$. Please format your answer as $n \\times 10^x$, where $n$ is to 3 decimal places. \n\n\nSolution: To solve this problem we must know the fol... |
math-ai/minervamath | [
{
"role": "user",
"content": "Calculate the volume in mL of $0.25 \\mathrm{M} \\mathrm{NaI}$ that would be needed to precipitate all the $\\mathrm{g}^{2+}$ ion from $45 \\mathrm{~mL}$ of a $0.10 \\mathrm{M} \\mathrm{Hg}\\left(\\mathrm{NO}_{3}\\right)_{2}$ solution according to the following reaction:\n\\[\n... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 224,
"split": "test",
"question": "Calculate the volume in mL of $0.25 \\mathrm{M} \\mathrm{NaI}$ that would be needed to precipitate all the $\\mathrm{g}^{2+}$ ion from $45 \\mathrm{~mL}$ of a $0.10 \\mathrm{M} \\mathrm{Hg}\\left(\\mathrm{NO}_{3}\\right)_{2}$ solution according to the following reacti... |
math-ai/minervamath | [
{
"role": "user",
"content": "A slab of plate glass containing dissolved helium (He) is placed in a vacuum furnace at a temperature of $400^{\\circ} \\mathrm{C}$ to remove the helium from the glass. Before vacuum treatment, the concentration of helium is constant throughout the glass. After 10 minutes in va... | math | {
"style": "rule",
"ground_truth": "258"
} | {
"index": 225,
"split": "test",
"question": "A slab of plate glass containing dissolved helium (He) is placed in a vacuum furnace at a temperature of $400^{\\circ} \\mathrm{C}$ to remove the helium from the glass. Before vacuum treatment, the concentration of helium is constant throughout the glass. After 10 min... |
math-ai/minervamath | [
{
"role": "user",
"content": "Subproblem 0: What is the working temperature for silica glass in Celsius?\n\n\nSolution: \\boxed{1950}.\n\nFinal answer: The final answer is 1950. I hope it is correct.\n\nSubproblem 1: What is the softening temperature for silica glass in Celsius?\n\nLet's think step by step ... | math | {
"style": "rule",
"ground_truth": "1700"
} | {
"index": 226,
"split": "test",
"question": "Subproblem 0: What is the working temperature for silica glass in Celsius?\n\n\nSolution: \\boxed{1950}.\n\nFinal answer: The final answer is 1950. I hope it is correct.\n\nSubproblem 1: What is the softening temperature for silica glass in Celsius?"
} |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: Two lasers generate radiation of (1) $9.5 \\mu {m}$ and (2) $0.1 \\mu {m}$ respectively.\n\nSubproblem 0: Determine the photon energy (in eV, to two decimal places) of the laser generating radiation of $9.5 \\mu {m}$.\n\n\nSolution: \\[\n\\begin{aligned}\n{E} &={h} v=... | math | {
"style": "rule",
"ground_truth": "12.4"
} | {
"index": 227,
"split": "test",
"question": "Preamble: Two lasers generate radiation of (1) $9.5 \\mu {m}$ and (2) $0.1 \\mu {m}$ respectively.\n\nSubproblem 0: Determine the photon energy (in eV, to two decimal places) of the laser generating radiation of $9.5 \\mu {m}$.\n\n\nSolution: \\[\n\\begin{aligned}\n{E... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: $\\mathrm{Bi}_{2} \\mathrm{~S}_{3}$ dissolves in water according to the following reaction:\n\\[\n\\mathrm{Bi}_{2} \\mathrm{~S}_{3}(\\mathrm{~s}) \\Leftrightarrow 2 \\mathrm{Bi}^{3+}(\\mathrm{aq})+3 \\mathrm{~s}^{2-}(\\mathrm{aq})\n\\]\nfor which the solubility produc... | math | {
"style": "rule",
"ground_truth": "5.3e-9"
} | {
"index": 228,
"split": "test",
"question": "Preamble: $\\mathrm{Bi}_{2} \\mathrm{~S}_{3}$ dissolves in water according to the following reaction:\n\\[\n\\mathrm{Bi}_{2} \\mathrm{~S}_{3}(\\mathrm{~s}) \\Leftrightarrow 2 \\mathrm{Bi}^{3+}(\\mathrm{aq})+3 \\mathrm{~s}^{2-}(\\mathrm{aq})\n\\]\nfor which the solubil... |
math-ai/minervamath | [
{
"role": "user",
"content": "Whiskey, suspected to be of the \"moonshine\" variety, is analyzed for its age by determining its amount of naturally occurring tritium (T) which is a radioactive hydrogen isotope $\\left({ }^{3} \\mathrm{H}\\right)$ with a half-life of $12.5$ years. In this \"shine\" the activ... | math | {
"style": "rule",
"ground_truth": "50.7"
} | {
"index": 229,
"split": "test",
"question": "Whiskey, suspected to be of the \"moonshine\" variety, is analyzed for its age by determining its amount of naturally occurring tritium (T) which is a radioactive hydrogen isotope $\\left({ }^{3} \\mathrm{H}\\right)$ with a half-life of $12.5$ years. In this \"shine\"... |
math-ai/minervamath | [
{
"role": "user",
"content": "Subproblem 0: What is the working temperature for silica glass in Celsius?\n\n\nSolution: \\boxed{1950}.\n\nFinal answer: The final answer is 1950. I hope it is correct.\n\nSubproblem 1: What is the softening temperature for silica glass in Celsius?\n\n\nSolution: \\boxed{1700}... | math | {
"style": "rule",
"ground_truth": "800"
} | {
"index": 230,
"split": "test",
"question": "Subproblem 0: What is the working temperature for silica glass in Celsius?\n\n\nSolution: \\boxed{1950}.\n\nFinal answer: The final answer is 1950. I hope it is correct.\n\nSubproblem 1: What is the softening temperature for silica glass in Celsius?\n\n\nSolution: \\b... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: A first-order chemical reaction is found to have an activation energy $\\left(E_{A}\\right)$ of 250 $\\mathrm{kJ} /$ mole and a pre-exponential (A) of $1.7 \\times 10^{14} \\mathrm{~s}^{-1}$.\n\nSubproblem 0: Determine the rate constant at $\\mathrm{T}=750^{\\circ} \\... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 231,
"split": "test",
"question": "Preamble: A first-order chemical reaction is found to have an activation energy $\\left(E_{A}\\right)$ of 250 $\\mathrm{kJ} /$ mole and a pre-exponential (A) of $1.7 \\times 10^{14} \\mathrm{~s}^{-1}$.\n\nSubproblem 0: Determine the rate constant at $\\mathrm{T}=750^{... |
math-ai/minervamath | [
{
"role": "user",
"content": "Determine the energy gap (in eV) between the electronic states $n=7$ and $n=8$ in hydrogen. Please format your answer as $n \\times 10^x$ where $n$ is to 1 decimal place.\n\nLet's think step by step and output the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6.5e-2"
} | {
"index": 232,
"split": "test",
"question": "Determine the energy gap (in eV) between the electronic states $n=7$ and $n=8$ in hydrogen. Please format your answer as $n \\times 10^x$ where $n$ is to 1 decimal place."
} |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: The decay rate of ${ }^{14} \\mathrm{C}$ in living tissue is $15.3$ disintegrations per minute per gram of carbon. Experimentally, the decay rate can be measured to $\\pm 0.1$ disintegrations per minute per gram of carbon. The half-life of ${ }^{14} \\mathrm{C}$ is 57... | math | {
"style": "rule",
"ground_truth": "41585"
} | {
"index": 233,
"split": "test",
"question": "Preamble: The decay rate of ${ }^{14} \\mathrm{C}$ in living tissue is $15.3$ disintegrations per minute per gram of carbon. Experimentally, the decay rate can be measured to $\\pm 0.1$ disintegrations per minute per gram of carbon. The half-life of ${ }^{14} \\mathrm... |
math-ai/minervamath | [
{
"role": "user",
"content": "Estimate the ionic radius of ${Cs}^{+}$ in Angstroms to 2 decimal places. The lattice energy of $\\mathrm{CsCl}$ is $633 \\mathrm{~kJ} / \\mathrm{mol}$. For $\\mathrm{CsCl}$ the Madelung constant, $\\mathrm{M}$, is $1.763$, and the Born exponent, $\\mathrm{n}$, is 10.7. The ion... | math | {
"style": "rule",
"ground_truth": "1.69"
} | {
"index": 234,
"split": "test",
"question": "Estimate the ionic radius of ${Cs}^{+}$ in Angstroms to 2 decimal places. The lattice energy of $\\mathrm{CsCl}$ is $633 \\mathrm{~kJ} / \\mathrm{mol}$. For $\\mathrm{CsCl}$ the Madelung constant, $\\mathrm{M}$, is $1.763$, and the Born exponent, $\\mathrm{n}$, is 10.... |
math-ai/minervamath | [
{
"role": "user",
"content": "Given the ionic radii, $\\mathrm{Cs}^{+}=1.67 \\AA, \\mathrm{Cl}^{-}=1.81 \\AA$, and the Madelung constant $\\mathrm{M}(\\mathrm{CsCl})=1.763$, determine to the best of your ability the molar Crystal energy ( $\\Delta \\mathrm{E}_{\\text {cryst }}$ ) for $\\mathrm{CsCl}$. Pleas... | math | {
"style": "rule",
"ground_truth": "7.02e5"
} | {
"index": 235,
"split": "test",
"question": "Given the ionic radii, $\\mathrm{Cs}^{+}=1.67 \\AA, \\mathrm{Cl}^{-}=1.81 \\AA$, and the Madelung constant $\\mathrm{M}(\\mathrm{CsCl})=1.763$, determine to the best of your ability the molar Crystal energy ( $\\Delta \\mathrm{E}_{\\text {cryst }}$ ) for $\\mathrm{CsC... |
math-ai/minervamath | [
{
"role": "user",
"content": "Determine the amount (in grams) of boron (B) that, substitutionally incorporated into $1 \\mathrm{~kg}$ of germanium (Ge), will establish a charge carrier density of $3.091 \\mathrm{x}$ $10^{17} / \\mathrm{cm}^{3}$. Please format your answer as $n \\times 10^x$ where $n$ is to ... | math | {
"style": "rule",
"ground_truth": "1.04e-3"
} | {
"index": 236,
"split": "test",
"question": "Determine the amount (in grams) of boron (B) that, substitutionally incorporated into $1 \\mathrm{~kg}$ of germanium (Ge), will establish a charge carrier density of $3.091 \\mathrm{x}$ $10^{17} / \\mathrm{cm}^{3}$. Please format your answer as $n \\times 10^x$ where ... |
math-ai/minervamath | [
{
"role": "user",
"content": "Subproblem 0: Is an energy level of $-1.362 \\times 10^{-19} {~J}$ an allowed electron energy state in atomic hydrogen?\n\n\nSolution: $E_{e l} =-\\frac{1}{n^{2}} {~K}$ \\\\\n$-1.362 \\times 10^{-19} {~J}=-\\frac{1}{{n}^{2}} \\times 2.18 \\times 10^{-18} {~J}$\\\\\n${n} &=\\sqr... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"index": 237,
"split": "test",
"question": "Subproblem 0: Is an energy level of $-1.362 \\times 10^{-19} {~J}$ an allowed electron energy state in atomic hydrogen?\n\n\nSolution: $E_{e l} =-\\frac{1}{n^{2}} {~K}$ \\\\\n$-1.362 \\times 10^{-19} {~J}=-\\frac{1}{{n}^{2}} \\times 2.18 \\times 10^{-18} {~J}$\\\\\n${... |
math-ai/minervamath | [
{
"role": "user",
"content": "Determine the highest linear density of atoms (atoms/m) encountered in vanadium (V). Please format your answer as $n \\times 10^x$ where $n$ is to 2 decimal places.\n\nLet's think step by step and output the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3.75e9"
} | {
"index": 238,
"split": "test",
"question": "Determine the highest linear density of atoms (atoms/m) encountered in vanadium (V). Please format your answer as $n \\times 10^x$ where $n$ is to 2 decimal places."
} |
math-ai/minervamath | [
{
"role": "user",
"content": "Strontium fluoride, $\\mathrm{SrF}_{2}$, has a $\\mathrm{K}_{\\mathrm{sp}}$ value in water of $2.45 \\times 10^{-9}$ at room temperature.\nCalculate the solubility of $\\mathrm{SrF}_{2}$ in water. Express your answer in units of molarity. Please format your answer as $n \\times... | math | {
"style": "rule",
"ground_truth": "8.49e-4"
} | {
"index": 239,
"split": "test",
"question": "Strontium fluoride, $\\mathrm{SrF}_{2}$, has a $\\mathrm{K}_{\\mathrm{sp}}$ value in water of $2.45 \\times 10^{-9}$ at room temperature.\nCalculate the solubility of $\\mathrm{SrF}_{2}$ in water. Express your answer in units of molarity. Please format your answer as ... |
math-ai/minervamath | [
{
"role": "user",
"content": "You wish to dope a single crystal of silicon (Si) with boron (B). The specification reads $5 \\times 10^{16}$ boron atoms/ $\\mathrm{cm}^{3}$ at a depth of $25 \\mu \\mathrm{m}$ from the surface of the silicon. What must be the effective concentration of boron in units of atoms... | math | {
"style": "rule",
"ground_truth": "0.7773"
} | {
"index": 240,
"split": "test",
"question": "You wish to dope a single crystal of silicon (Si) with boron (B). The specification reads $5 \\times 10^{16}$ boron atoms/ $\\mathrm{cm}^{3}$ at a depth of $25 \\mu \\mathrm{m}$ from the surface of the silicon. What must be the effective concentration of boron in unit... |
math-ai/minervamath | [
{
"role": "user",
"content": "An electron beam strikes a crystal of cadmium sulfide (CdS). Electrons scattered by the crystal move at a velocity of $4.4 \\times 10^{5} \\mathrm{~m} / \\mathrm{s}$. Calculate the energy of the incident beam. Express your result in eV, and as an integer. CdS is a semiconductor... | math | {
"style": "rule",
"ground_truth": "3"
} | {
"index": 241,
"split": "test",
"question": "An electron beam strikes a crystal of cadmium sulfide (CdS). Electrons scattered by the crystal move at a velocity of $4.4 \\times 10^{5} \\mathrm{~m} / \\mathrm{s}$. Calculate the energy of the incident beam. Express your result in eV, and as an integer. CdS is a sem... |
math-ai/minervamath | [
{
"role": "user",
"content": "Subproblem 0: Determine the inter-ionic equilibrium distance in meters between the sodium and chlorine ions in a sodium chloride molecule knowing that the bond energy is $3.84 \\mathrm{eV}$ and that the repulsive exponent is 8. Please format your answer as $n \\times 10^x$ wher... | math | {
"style": "rule",
"ground_truth": "12.5"
} | {
"index": 242,
"split": "test",
"question": "Subproblem 0: Determine the inter-ionic equilibrium distance in meters between the sodium and chlorine ions in a sodium chloride molecule knowing that the bond energy is $3.84 \\mathrm{eV}$ and that the repulsive exponent is 8. Please format your answer as $n \\times ... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: A consumer's preferences are representable by the following utility function:\n\\[\n u(x, y)=x^{\\frac{1}{2}}+y\n\\]\n\nObtain the marginal rate of substitution of the consumer at an arbitrary point $(X,Y)$, where $X>0$ and $Y>0$.\n\nLet's think step by step and outp... | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{2} X^{-\\frac{1}{2}}"
} | {
"index": 243,
"split": "test",
"question": "Preamble: A consumer's preferences are representable by the following utility function:\n\\[\n u(x, y)=x^{\\frac{1}{2}}+y\n\\]\n\nObtain the marginal rate of substitution of the consumer at an arbitrary point $(X,Y)$, where $X>0$ and $Y>0$."
} |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: Xiaoyu spends all her income on statistical software $(S)$ and clothes (C). Her preferences can be represented by the utility function: $U(S, C)=4 \\ln (S)+6 \\ln (C)$.\n\nCompute the marginal rate of substitution of software for clothes.\n\nLet's think step by step a... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3} \\frac{C}{S}"
} | {
"index": 244,
"split": "test",
"question": "Preamble: Xiaoyu spends all her income on statistical software $(S)$ and clothes (C). Her preferences can be represented by the utility function: $U(S, C)=4 \\ln (S)+6 \\ln (C)$.\n\nCompute the marginal rate of substitution of software for clothes."
} |
math-ai/minervamath | [
{
"role": "user",
"content": "What algebraic condition describes a firm that is at an output level that maximizes its profits, given its capital in the short-term? Use standard acronyms in your condition.\n\nLet's think step by step and output the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "MR=SRMC"
} | {
"index": 245,
"split": "test",
"question": "What algebraic condition describes a firm that is at an output level that maximizes its profits, given its capital in the short-term? Use standard acronyms in your condition."
} |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: Moldavia is a small country that currently trades freely in the world barley market. Demand and supply for barley in Moldavia is governed by the following schedules:\nDemand: $Q^{D}=4-P$\nSupply: $Q^{S}=P$\nThe world price of barley is $\\$ 1 /$ bushel.\n\nSubproblem ... | math | {
"style": "rule",
"ground_truth": "3"
} | {
"index": 246,
"split": "test",
"question": "Preamble: Moldavia is a small country that currently trades freely in the world barley market. Demand and supply for barley in Moldavia is governed by the following schedules:\nDemand: $Q^{D}=4-P$\nSupply: $Q^{S}=P$\nThe world price of barley is $\\$ 1 /$ bushel.\n\nS... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: Consider the market for apple juice. In this market, the supply curve is given by $Q_{S}=$ $10 P_{J}-5 P_{A}$ and the demand curve is given by $Q_{D}=100-15 P_{J}+10 P_{T}$, where $J$ denotes apple juice, $A$ denotes apples, and $T$ denotes tea.\n\nSubproblem 0: Assum... | math | {
"style": "rule",
"ground_truth": "57"
} | {
"index": 247,
"split": "test",
"question": "Preamble: Consider the market for apple juice. In this market, the supply curve is given by $Q_{S}=$ $10 P_{J}-5 P_{A}$ and the demand curve is given by $Q_{D}=100-15 P_{J}+10 P_{T}$, where $J$ denotes apple juice, $A$ denotes apples, and $T$ denotes tea.\n\nSubproble... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: Suppose, in the short run, the output of widgets is supplied by 100 identical competitive firms, each having a cost function:\n\\[\nc_{s}(y)=\\frac{1}{3} y^{3}+2\n\\]\nThe demand for widgets is given by:\n\\[\ny^{d}(p)=6400 / p^{\\frac{1}{2}}\n\\]\n\nSubproblem 0: Obt... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"index": 248,
"split": "test",
"question": "Preamble: Suppose, in the short run, the output of widgets is supplied by 100 identical competitive firms, each having a cost function:\n\\[\nc_{s}(y)=\\frac{1}{3} y^{3}+2\n\\]\nThe demand for widgets is given by:\n\\[\ny^{d}(p)=6400 / p^{\\frac{1}{2}}\n\\]\n\nSubprob... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: Sebastian owns a coffee factory in Argentina. His production function is:\n\\[\nF(K, L)=(K-1)^{\\frac{1}{4}} L^{\\frac{1}{4}}\n\\]\nConsider the cost of capital to be $r$ and the wage to be $w$. Both inputs are variable, and Sebastian faces no fixed costs.\n\nWhat is ... | math | {
"style": "rule",
"ground_truth": "\\frac{K-1}{L}"
} | {
"index": 249,
"split": "test",
"question": "Preamble: Sebastian owns a coffee factory in Argentina. His production function is:\n\\[\nF(K, L)=(K-1)^{\\frac{1}{4}} L^{\\frac{1}{4}}\n\\]\nConsider the cost of capital to be $r$ and the wage to be $w$. Both inputs are variable, and Sebastian faces no fixed costs.\n... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: There are two algebraic conditions describing a firm that is at a capital level that minimizes its costs in the long-term.\n\nWrite the condition which involves the SRAC, or short-run average cost?\n\nLet's think step by step and output the final answer within \\boxed... | math | {
"style": "rule",
"ground_truth": "SRAC=LRAC"
} | {
"index": 250,
"split": "test",
"question": "Preamble: There are two algebraic conditions describing a firm that is at a capital level that minimizes its costs in the long-term.\n\nWrite the condition which involves the SRAC, or short-run average cost?"
} |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: There are two algebraic conditions describing a firm that is at a capital level that minimizes its costs in the long-term.\n\nSubproblem 0: Write the condition which involves the SRAC, or short-run average cost?\n\n\nSolution: \\boxed{SRAC=LRAC}, short-run average cos... | math | {
"style": "rule",
"ground_truth": "SRMC=LRMC"
} | {
"index": 251,
"split": "test",
"question": "Preamble: There are two algebraic conditions describing a firm that is at a capital level that minimizes its costs in the long-term.\n\nSubproblem 0: Write the condition which involves the SRAC, or short-run average cost?\n\n\nSolution: \\boxed{SRAC=LRAC}, short-run a... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: Suppose, in the short run, the output of widgets is supplied by 100 identical competitive firms, each having a cost function:\n\\[\nc_{s}(y)=\\frac{1}{3} y^{3}+2\n\\]\nThe demand for widgets is given by:\n\\[\ny^{d}(p)=6400 / p^{\\frac{1}{2}}\n\\]\n\nObtain the short ... | math | {
"style": "rule",
"ground_truth": "100 p^{\\frac{1}{2}}"
} | {
"index": 252,
"split": "test",
"question": "Preamble: Suppose, in the short run, the output of widgets is supplied by 100 identical competitive firms, each having a cost function:\n\\[\nc_{s}(y)=\\frac{1}{3} y^{3}+2\n\\]\nThe demand for widgets is given by:\n\\[\ny^{d}(p)=6400 / p^{\\frac{1}{2}}\n\\]\n\nObtain ... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: Moldavia is a small country that currently trades freely in the world barley market. Demand and supply for barley in Moldavia is governed by the following schedules:\nDemand: $Q^{D}=4-P$\nSupply: $Q^{S}=P$\nThe world price of barley is $\\$ 1 /$ bushel.\n\nCalculate t... | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 253,
"split": "test",
"question": "Preamble: Moldavia is a small country that currently trades freely in the world barley market. Demand and supply for barley in Moldavia is governed by the following schedules:\nDemand: $Q^{D}=4-P$\nSupply: $Q^{S}=P$\nThe world price of barley is $\\$ 1 /$ bushel.\n\nC... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: Suppose, in the short run, the output of widgets is supplied by 100 identical competitive firms, each having a cost function:\n\\[\nc_{s}(y)=\\frac{1}{3} y^{3}+2\n\\]\nThe demand for widgets is given by:\n\\[\ny^{d}(p)=6400 / p^{\\frac{1}{2}}\n\\]\n\nSubproblem 0: Obt... | math | {
"style": "rule",
"ground_truth": "64"
} | {
"index": 254,
"split": "test",
"question": "Preamble: Suppose, in the short run, the output of widgets is supplied by 100 identical competitive firms, each having a cost function:\n\\[\nc_{s}(y)=\\frac{1}{3} y^{3}+2\n\\]\nThe demand for widgets is given by:\n\\[\ny^{d}(p)=6400 / p^{\\frac{1}{2}}\n\\]\n\nSubprob... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: A consumer's preferences are representable by the following utility function:\n\\[\n u(x, y)=x^{\\frac{1}{2}}+y\n\\]\n\nSubproblem 0: Obtain the marginal rate of substitution of the consumer at an arbitrary point $(X,Y)$, where $X>0$ and $Y>0$.\n\n\nSolution: \\[ M R... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4p^2}"
} | {
"index": 255,
"split": "test",
"question": "Preamble: A consumer's preferences are representable by the following utility function:\n\\[\n u(x, y)=x^{\\frac{1}{2}}+y\n\\]\n\nSubproblem 0: Obtain the marginal rate of substitution of the consumer at an arbitrary point $(X,Y)$, where $X>0$ and $Y>0$.\n\n\nSolutio... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: Consider the market for apple juice. In this market, the supply curve is given by $Q_{S}=$ $10 P_{J}-5 P_{A}$ and the demand curve is given by $Q_{D}=100-15 P_{J}+10 P_{T}$, where $J$ denotes apple juice, $A$ denotes apples, and $T$ denotes tea.\n\nAssume that $P_{A}$... | math | {
"style": "rule",
"ground_truth": "6.2"
} | {
"index": 256,
"split": "test",
"question": "Preamble: Consider the market for apple juice. In this market, the supply curve is given by $Q_{S}=$ $10 P_{J}-5 P_{A}$ and the demand curve is given by $Q_{D}=100-15 P_{J}+10 P_{T}$, where $J$ denotes apple juice, $A$ denotes apples, and $T$ denotes tea.\n\nAssume th... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: In Cambridge, shoppers can buy apples from two sources: a local orchard, and a store that ships apples from out of state. The orchard can produce up to 50 apples per day at a constant marginal cost of 25 cents per apple. The store can supply any remaining apples deman... | math | {
"style": "rule",
"ground_truth": "75"
} | {
"index": 257,
"split": "test",
"question": "Preamble: In Cambridge, shoppers can buy apples from two sources: a local orchard, and a store that ships apples from out of state. The orchard can produce up to 50 apples per day at a constant marginal cost of 25 cents per apple. The store can supply any remaining ap... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: You manage a factory that produces cans of peanut butter. The current market price is $\\$ 10 /$ can, and you know the following about your costs (MC stands for marginal cost, and ATC stands for average total cost):\n\\[\n\\begin{array}{l}\nMC(5)=10 \\\\\nATC(5)=6 \\\... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"index": 258,
"split": "test",
"question": "Preamble: You manage a factory that produces cans of peanut butter. The current market price is $\\$ 10 /$ can, and you know the following about your costs (MC stands for marginal cost, and ATC stands for average total cost):\n\\[\n\\begin{array}{l}\nMC(5)=10 \\\\\nAT... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: Suppose there are exactly two consumers (Albie and Bubbie) who demand strawberries. Suppose that Albie's demand for strawberries is given by\n\\[\nq_{a}(p)=p^{\\alpha} f_{a}\\left(I_{a}\\right)\n\\]\nand Bubbie's demand is given by\n\\[\nq_{b}(p)=p^{\\beta} f_{b}\\lef... | math | {
"style": "rule",
"ground_truth": "\\alpha"
} | {
"index": 259,
"split": "test",
"question": "Preamble: Suppose there are exactly two consumers (Albie and Bubbie) who demand strawberries. Suppose that Albie's demand for strawberries is given by\n\\[\nq_{a}(p)=p^{\\alpha} f_{a}\\left(I_{a}\\right)\n\\]\nand Bubbie's demand is given by\n\\[\nq_{b}(p)=p^{\\beta} ... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: You have been asked to analyze the market for steel. From public sources, you are able to find that last year's price for steel was $\\$ 20$ per ton. At this price, 100 million tons were sold on the world market. From trade association data you are able to obtain esti... | math | {
"style": "rule",
"ground_truth": "X_{d}=125-1.25 P"
} | {
"index": 260,
"split": "test",
"question": "Preamble: You have been asked to analyze the market for steel. From public sources, you are able to find that last year's price for steel was $\\$ 20$ per ton. At this price, 100 million tons were sold on the world market. From trade association data you are able to o... |
math-ai/minervamath | [
{
"role": "user",
"content": "Harmonic Oscillator Subjected to Perturbation by an Electric Field: An electron is connected by a harmonic spring to a fixed point at $x=0$. It is subject to a field-free potential energy\n\\[\nV(x)=\\frac{1}{2} k x^{2} .\n\\]\nThe energy levels and eigenstates are those of a h... | math | {
"style": "rule",
"ground_truth": "\\hbar \\omega(v+1 / 2)-\\frac{E_{0}^{2} e^{2}}{2 m \\omega^{2}}"
} | {
"index": 261,
"split": "test",
"question": "Harmonic Oscillator Subjected to Perturbation by an Electric Field: An electron is connected by a harmonic spring to a fixed point at $x=0$. It is subject to a field-free potential energy\n\\[\nV(x)=\\frac{1}{2} k x^{2} .\n\\]\nThe energy levels and eigenstates are th... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: The following concern the independent particle model. You may find the following set of Coulomb and exchange integrals useful (energies in $\\mathrm{eV}$):\n$\\mathrm{J}_{1 s 1 s}=17.0 Z$ \n$\\mathrm{~J}_{1 s 2 s}=4.8 Z$ \n$\\mathrm{~K}_{1 s 2 s}=0.9 Z$ \n$\\mathrm{~J... | math | {
"style": "rule",
"ground_truth": "7.6 Z"
} | {
"index": 262,
"split": "test",
"question": "Preamble: The following concern the independent particle model. You may find the following set of Coulomb and exchange integrals useful (energies in $\\mathrm{eV}$):\n$\\mathrm{J}_{1 s 1 s}=17.0 Z$ \n$\\mathrm{~J}_{1 s 2 s}=4.8 Z$ \n$\\mathrm{~K}_{1 s 2 s}=0.9 Z$ \n$\... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: A pulsed Nd:YAG laser is found in many physical chemistry laboratories.\n\nFor a $2.00 \\mathrm{~mJ}$ pulse of laser light, how many photons are there at $1.06 \\mu \\mathrm{m}$ (the Nd:YAG fundamental) in the pulse? PAnswer to three significant figures.\n\nLet's thi... | math | {
"style": "rule",
"ground_truth": "1.07e16"
} | {
"index": 263,
"split": "test",
"question": "Preamble: A pulsed Nd:YAG laser is found in many physical chemistry laboratories.\n\nFor a $2.00 \\mathrm{~mJ}$ pulse of laser light, how many photons are there at $1.06 \\mu \\mathrm{m}$ (the Nd:YAG fundamental) in the pulse? PAnswer to three significant figures."
} |
math-ai/minervamath | [
{
"role": "user",
"content": "Given that the work function of chromium is $4.40 \\mathrm{eV}$, calculate the kinetic energy of electrons in Joules emitted from a clean chromium surface that is irradiated with ultraviolet radiation of wavelength $200 \\mathrm{~nm}$.\n\nLet's think step by step and output the... | math | {
"style": "rule",
"ground_truth": "2.88e-19"
} | {
"index": 264,
"split": "test",
"question": "Given that the work function of chromium is $4.40 \\mathrm{eV}$, calculate the kinetic energy of electrons in Joules emitted from a clean chromium surface that is irradiated with ultraviolet radiation of wavelength $200 \\mathrm{~nm}$."
} |
math-ai/minervamath | [
{
"role": "user",
"content": "Compute the momentum of one $500 \\mathrm{~nm}$ photon using $p_{\\text {photon }}=E_{\\text {photon }} / c$ where $c$ is the speed of light, $c=3 \\times 10^{8} \\mathrm{~m} / \\mathrm{s}$, and $\\nu=c / \\lambda$. Express your answer in kilogram meters per second, rounding y... | math | {
"style": "rule",
"ground_truth": "1.325e-27"
} | {
"index": 265,
"split": "test",
"question": "Compute the momentum of one $500 \\mathrm{~nm}$ photon using $p_{\\text {photon }}=E_{\\text {photon }} / c$ where $c$ is the speed of light, $c=3 \\times 10^{8} \\mathrm{~m} / \\mathrm{s}$, and $\\nu=c / \\lambda$. Express your answer in kilogram meters per second, ... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: This problem deals with the H\\\"uckel MO theory of $\\pi$-conjugated systems.\nTo answer each question, you will need to construct the Hückel MOs for each of the molecules pictured, divide them into sets of occupied and unoccupied orbitals, and determine the relevant... | math | {
"style": "rule",
"ground_truth": "11.9"
} | {
"index": 266,
"split": "test",
"question": "Preamble: This problem deals with the H\\\"uckel MO theory of $\\pi$-conjugated systems.\nTo answer each question, you will need to construct the Hückel MOs for each of the molecules pictured, divide them into sets of occupied and unoccupied orbitals, and determine th... |
math-ai/minervamath | [
{
"role": "user",
"content": "A baseball has diameter $=7.4 \\mathrm{~cm}$. and a mass of $145 \\mathrm{~g}$. Suppose the baseball is moving at $v=1 \\mathrm{~nm} /$ second. What is its de Broglie wavelength\n\\[\n\\lambda=\\frac{h}{p}=\\frac{h}{m \\nu}\n\\]\n? Give answer in meters.\n\nLet's think step by... | math | {
"style": "rule",
"ground_truth": "4.6e-24"
} | {
"index": 267,
"split": "test",
"question": "A baseball has diameter $=7.4 \\mathrm{~cm}$. and a mass of $145 \\mathrm{~g}$. Suppose the baseball is moving at $v=1 \\mathrm{~nm} /$ second. What is its de Broglie wavelength\n\\[\n\\lambda=\\frac{h}{p}=\\frac{h}{m \\nu}\n\\]\n? Give answer in meters."
} |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: Consider the Particle in an Infinite Box ``superposition state'' wavefunction,\n\\[\n\\psi_{1,2}=(1 / 3)^{1 / 2} \\psi_{1}+(2 / 3)^{1 / 2} \\psi_{2}\n\\]\nwhere $E_{1}$ is the eigen-energy of $\\psi_{1}$ and $E_{2}$ is the eigen-energy of $\\psi_{2}$.\n\nSubproblem 0:... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3} E_{1}+\\frac{2}{3} E_{2}"
} | {
"index": 268,
"split": "test",
"question": "Preamble: Consider the Particle in an Infinite Box ``superposition state'' wavefunction,\n\\[\n\\psi_{1,2}=(1 / 3)^{1 / 2} \\psi_{1}+(2 / 3)^{1 / 2} \\psi_{2}\n\\]\nwhere $E_{1}$ is the eigen-energy of $\\psi_{1}$ and $E_{2}$ is the eigen-energy of $\\psi_{2}$.\n\nSub... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: Consider the Particle in an Infinite Box ``superposition state'' wavefunction,\n\\[\n\\psi_{1,2}=(1 / 3)^{1 / 2} \\psi_{1}+(2 / 3)^{1 / 2} \\psi_{2}\n\\]\nwhere $E_{1}$ is the eigen-energy of $\\psi_{1}$ and $E_{2}$ is the eigen-energy of $\\psi_{2}$.\n\nSuppose you d... | math | {
"style": "rule",
"ground_truth": "E_{1},E_{2}"
} | {
"index": 269,
"split": "test",
"question": "Preamble: Consider the Particle in an Infinite Box ``superposition state'' wavefunction,\n\\[\n\\psi_{1,2}=(1 / 3)^{1 / 2} \\psi_{1}+(2 / 3)^{1 / 2} \\psi_{2}\n\\]\nwhere $E_{1}$ is the eigen-energy of $\\psi_{1}$ and $E_{2}$ is the eigen-energy of $\\psi_{2}$.\n\nSup... |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: Evaluate the following integrals for $\\psi_{J M}$ eigenfunctions of $\\mathbf{J}^{2}$ and $\\mathbf{J}_{z}$. \n\n$\\int \\psi_{22}^{*}\\left(\\widehat{\\mathbf{J}}^{+}\\right)^{4} \\psi_{2,-2} d \\tau$\n\nLet's think step by step and output the final answer within \\... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 270,
"split": "test",
"question": "Preamble: Evaluate the following integrals for $\\psi_{J M}$ eigenfunctions of $\\mathbf{J}^{2}$ and $\\mathbf{J}_{z}$. \n\n$\\int \\psi_{22}^{*}\\left(\\widehat{\\mathbf{J}}^{+}\\right)^{4} \\psi_{2,-2} d \\tau$"
} |
math-ai/minervamath | [
{
"role": "user",
"content": "Preamble: Consider the 3-level $\\mathbf{H}$ matrix\n\\[\n\\mathbf{H}=\\hbar \\omega\\left(\\begin{array}{ccc}\n10 & 1 & 0 \\\\\n1 & 0 & 2 \\\\\n0 & 2 & -10\n\\end{array}\\right)\n\\]\nLabel the eigen-energies and eigen-functions according to the dominant basis state character.... | math | {
"style": "rule",
"ground_truth": "10.1"
} | {
"index": 271,
"split": "test",
"question": "Preamble: Consider the 3-level $\\mathbf{H}$ matrix\n\\[\n\\mathbf{H}=\\hbar \\omega\\left(\\begin{array}{ccc}\n10 & 1 & 0 \\\\\n1 & 0 & 2 \\\\\n0 & 2 & -10\n\\end{array}\\right)\n\\]\nLabel the eigen-energies and eigen-functions according to the dominant basis state ... |
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