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Question
The half-life of 67Ga is 78 h. How long will it take to decay 12% of the sample of Ga?
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Solution
Given: t1/2 = 78 h, N0 = 100, N = 100 - 12 = 88
To find: t
Formulae:
- `lambda = 0.693/"t"_(1//2)`
- `lambda = 2.303/"t" log_10 ("N"_0/"N")`
Calculation:
- `lambda = 0.693/"t"_(1//2) = 0.693/78 = 8.885 xx 10^-3"h"^-1`
- `lambda = 2.303/"t" log_10 ("N"_0/"N")`
∴ `8.885 xx 10^-3 = 2.303/"t" log_10 (100/88)`
`8.885 xx 10^-3 = 2.303/"t" log_10 1.1364`
t = `2.303/(8.885 xx 10^-3) xx 0.0555`
= 14.39 h
Time taken for decay of 12% of sample of Ga is 14.39 h.
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