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for the years, in the form of tree rings or river-bottom sediments. In some cases
we can use these natural time markers to determine the time which has passed
Sỉnce some earÌy event.
When we cannot count the years for the measurement of long times, we
must look for other ways to measure. One of the most successful is the use of
radioactive material as a “clock.” In this case we do not have a periodic occurrence,
as for the day or the pendulum, but a new kind of “regularity.” We fñnd that the
radioactivity of a particular sample of material decreases by the same ƒraction
for successive equal increases in its age. If we plot a graph of the radioactivity
observed as a function of time (say in days), we obtain a curve like that shown
in Eig. 5-3. We observe that if the radioactivity decreases to one-half in 7' days
(called the “half-life”), then it decreases to one-quarter in another 7” days, and so
on. In an arbitrary time interval £ there are #/7' “halfFlives,” and the fraction
left after this time # is (3)!⁄.
T we knew that a piece of material, say a piece of wood, had contained an
amount A of radioactive material when it was formed, and we found out by a
đirect measurement that it now contains the amount Ö, we could compute the
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TIMES
YEARS SECONDS LIFE OF
77777???
1018 Age of universe
109 Aqe of earth U238
106 Earliest men
1012 Aqe of pyramids
Ra226
Age of U.S.
109 Life of a man HŠ
One day
103 Light goes from sun to earth Neutron
1 One heart beat
103 Period of a sound wave
1086 Period of radiowave Muon
7*-meson
109 Light travels one foot
1012 Period of molecular rotation
10-15 Period of atomic vibration
70-meson
1018 Light crosses an atom
Period of nuclear vibration
10-2 Light crosses a nucleus Strange
particle
77777???
--- Trang 107 ---
RADIOACTIVITY
1/2+—-—— `
1/4 ——— 1 _——_—>
0 T 2T 3T TIME
Fig. 5-3. The decrease with time of radioactivity. The activity de-
creases by one-half in each “half-life,” 7.
age of the object, ý, by solving the equation
(1) = BA.
There are, fortunately, cases in which we can know the amount of radioactivity
that was in an object when it was formed. We know, for example, that the carbon
dioxide in the aiïr contains a certain small fraction of the radioactive carbon
isotope C1 (replenished continuously by the action of eosmie rays). I we measure
the #oføÏ carbon content of an object, we know that a certain fraction of that
amount was originally the radioactive C!“; we know, therefore, the starting
amount 4 to use in the formula above. Carbon-14 has a half-life of 5000 years.
By careful measurements we can measure the amount left after 20 half-lives or
so and can therefore “date” organic objects which grew as long as 100,000 years
W©e would like to know, and we think we do know, the life of stïll older things.
Much of our knowledge is based on the measurements oŸ other radioactive isobopes
which have diferent half-lives. lf we make measurements with an isotope with a
longer half-life, then we are able to measure longer times. Uranium, for example,
has an isotope whose half-life is about 109 years, so that if some material was
formed with uranium in it 10 years ago, only half the uranium would remain
today. When the uranium disintegrates, it changes into lead. Consider a piece of
rock which was formed a long time ago in some chemical process. Lead, being of
a chemical nature diferent from uranium, would appear in one part of the rock
and uranium would appear in another part of the rock. The uranium and lead
would be separate. If we look at that piece of rock today, where there should only
--- Trang 108 ---
be uranium we will now find a certain fraction of uranium and a certain fraction
of lead. By comparing these ractions, we can tell what percent of the uranium
disappeared and changed into lead. By this method, the age of certain rocks has
been determined to be several billion years. An extension of this method, not
using particular rocks but looking at the uranium and lead in the oceans and
using averages over the earth, has been used to determine (within the past few
years) that the age of the earth itself is approximately 4.5 billion years.
Tt is encouraging that the age of the earth is found to be the same as the age
of the meteorites which land on the earth, as determined by the uranium method.
lt appears that the earth was formed out of rocks Ñoating in space, and that the
meteorites are, quite likely, some of that material left over. At some time more
than fñve billion years ago, the universe started. It is now believed that at least
our part of the universe had its beginning about ten or twelve billion years ago.
W©e do not know what happened before then. In fact, we may well ask again:
Does the question make any sense? Does an earlier tỉme have any meaning?
5-5 Units and standards of tỉme
W©e have implied that it is convenient if we start with some standard unit of
time, say a day or a second, and refer all other times to some multiple or fraction
of this unit. What shall we take as our basic standard of time? Shall we take the
human pulse? If we compare pulses, we fnd that they seem to vary a lot. Ôn
comparing ©wo clocks, one fnds they do not vary so much. You might then say,
well, let us take a clock. But whose clock? 'Phere 1s a story of a 5wiss boy who
wanted all of the clocks in his town to ring noon at the same time. So he went
around trying to convince everyone oŸ the value of this. Everyone thought it was
a marvelous idea so long as all of the other clocks rang noon when his didl lt is
rather difficult to decide whose clock we should take as a standard. Fortunately,
we all share one clock—the earth. Eor a long time the rotational period of the