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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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Question

The half-life of 67Ga is 78 h. How long will it take to decay 12% of the sample of Ga?

Numerical
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Solution

Given: t1/2 = 78 h, N0 = 100, N = 100 - 12 = 88

To find: t

Formulae: 

  1. `lambda = 0.693/"t"_(1//2)`
  2. `lambda = 2.303/"t" log_10 ("N"_0/"N")`

Calculation:

  1. `lambda = 0.693/"t"_(1//2) = 0.693/78 = 8.885 xx 10^-3"h"^-1`
  2. `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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Chapter 13: Nuclear Chemistry and Radioactivity - Exercises [Page 203]

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Balbharati Chemistry [English] Standard 11 Maharashtra State Board
Chapter 13 Nuclear Chemistry and Radioactivity
Exercises | Q 4. (C) | Page 203

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