Physics Nuclear Physics NUMS 2022
PMDC Verified Question 46 of 98
A 32g radioactive element decays and remains 2g after 60 days. What is the half-life of radioactive element:
A
2 days
B
6 days
C
10 days
D
15 days
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: 15 days


Concept:

The amount of a radioactive sample halves over each consecutive half-life.

Solution:

  • We track the decay from the initial 32g down to 2g by repeatedly dividing by 2:


  • 32g \(\rightarrow\) 16g (1st half-life)


  • 16g \(\rightarrow\) 8g (2nd half-life)


  • 8g \(\rightarrow\) 4g (3rd half-life)


  • 4g \(\rightarrow\) 2g (4th half-life)


  • It takes exactly 4 half-lives to reach 2g.


  • The total time is 60 days. Thus, \( T_{1/2} = \frac{60}{4} = 15\text{ days} \).


Why other options are incorrect:

Option C assumes 6 half-lives. Option B assumes 10 half-lives. Option A is a severe math error.

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