Physics Nuclear Physics MDCAT 2011
PMDC Verified Question 90 of 98
Half-life of a radioactive element is:
A
Inversely proportional to square of decay constant
B
Directly proportional to decay constant
C
Directly proportional to square of decay constant
D
Inversely proportional to decay constant
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: Inversely proportional to decay constant


Concept:

The half-life (\(T_{1/2}\)) is the time required for exactly half of the radioactive nuclei in a sample to undergo decay.

Formula:

$$ T_{1/2} = \frac{\ln(2)}{\lambda} \approx \frac{0.693}{\lambda} $$

Solution:

  • The formula shows that \(T_{1/2}\) is equal to a constant divided by \(\lambda\).


  • Therefore, half-life is mathematically inversely proportional to the decay constant \(\lambda\).


  • A larger decay constant means a higher probability of decay per second, which results in a much shorter half-life.


Why other options are incorrect:

Option A and C incorrectly involve squares. Option B suggests that a highly active element (large \(\lambda\)) would decay slowly (large \(T_{1/2}\)), which contradicts physics.

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