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A 3/4 of the original amount of radioisotope decays in 60 minutes. What is its half-life?

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Question

A 3/4 of the original amount of radioisotope decays in 60 minutes. What is its half-life?

Numerical
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Solution

Given: N0 = 100,

For N, `100 xx 3/4 = 75` ∴ 100 - 75 = 25, t = 60 min

To find: t1/2

Formulae: 

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

Calculation:

  1. `lambda = 2.303/"t" log_10 ("N"_0/"N")`
    `= 2.303/60 log_10 (100/25)`
    `= 2.303/60 log_10 4`
    = 0.0231 min-1
  2. `"t"_(1//2) = 0.693/lambda = 0.693/0.0231` = 30 min

Half-life of the radioisotope is 30 min.

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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. (H) | Page 203

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