Question
Asked Oct 30, 2019
9. A sample of tritium-3 decayed to 94.5% of its original amount after a year
(a) What is the half-life of tritium-3?
(b) How long would it take the sample to decay to 20% of its original amount?
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9. A sample of tritium-3 decayed to 94.5% of its original amount after a year (a) What is the half-life of tritium-3? (b) How long would it take the sample to decay to 20% of its original amount?

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check_circleExpert Solution
Step 1

Consider N (t) is the amount of tritium-3 relative to the original amount, then general form is,

N(t) Ce
It is known that N (0) = 1, so
1= N(0)1-Ce0)
1 Ce C 1
Also is known that N (1)= 0.945, so
0.945 N(1)0.945 = Ce*
0.945 CeIn(0.945) = În (Ce)
In (0.945) k
C 1
.N(t) e(0943)
= 0.945
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N(t) Ce It is known that N (0) = 1, so 1= N(0)1-Ce0) 1 Ce C 1 Also is known that N (1)= 0.945, so 0.945 N(1)0.945 = Ce* 0.945 CeIn(0.945) = În (Ce) In (0.945) k C 1 .N(t) e(0943) = 0.945

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Step 2

(a) The half life time of tritium-3 can be obtained by eq...

.N(1) 0.5
0.9456 0.5
In(0.945)-In (0.5)
t In (0.945) In (0.5)
In(0.5)
to
In (0.945)
to12.25
Thus, the half-life of tritium is approximately 12.25 years
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.N(1) 0.5 0.9456 0.5 In(0.945)-In (0.5) t In (0.945) In (0.5) In(0.5) to In (0.945) to12.25 Thus, the half-life of tritium is approximately 12.25 years

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