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0.5 g sample of 201Tl decays to 0.0788 g in 8 days. What is its half-life? - Chemistry

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Question

0.5 g sample of 201Tl decays to 0.0788 g in 8 days. What is its half-life?

Numerical
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Solution

Given: N0 = 0.5 g, N = 0.0788 g, t = 8 days

To find: t1/2

Formulae: 

  1. `lambda = 2.303/"t" log_10 ("N"_0/"N")`
  2. t1/2 = `0.693/lambda`

Calculation:

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

`= 2.303/8 log_10 (0.5/0.0788)`

`= 2.303/8 log_10 (6.3452)`

`= 2.303/8 xx 0.8024`

λ = 0.231 d-1

2. `"t"_(1//2) = 0.693/lambda`

`"t"_(1//2) = 0.693/0.231`

`"t"_(1//2)` = 3d

The half-life of 201Tl is 3d.

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Radioactive Decays
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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. (D) | Page 203

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