Physics Nuclear Physics ETEA 2019
PMDC Verified Question 54 of 98
There are initially 400 atoms in a radioactive sample. What would be the number of atoms after 3 half-lives?
A
400
B
200
C
50
D
25
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: 50


Concept:

The number of remaining radioactive atoms halves with the passage of every complete half-life period.

Formula:

$$ N = N_0 \left(\frac{1}{2}\right)^n $$

Solution:

  • Initial atoms \(N_0 = 400\).


  • Number of half-lives \(n = 3\).


  • Calculate using sequential division:


  • 1 half-life: 400 \(\rightarrow\) 200


  • 2 half-lives: 200 \(\rightarrow\) 100


  • 3 half-lives: 100 \(\rightarrow\) 50


Why other options are incorrect:

200 is after 1 half-life. 25 is after 4 half-lives. 400 means no decay occurred.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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