Physics Nuclear Physics UHS 2022
PMDC Verified Question 30 of 98
The half-life of Strontium (Sr) is 8.70 hours. Its decay constant is:
A
0.000022 s
B
45000 /s
C
0.000022 /s
D
0.000032 /s
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: 0.000022 /s


Concept:

The decay constant (\(\lambda\)) is inversely proportional to the half-life. Time must be strictly converted into SI units (seconds) to obtain a standard decay constant.

Formula:

$$ \lambda = \frac{0.693}{T_{1/2}} $$

Solution:

  • Given: \(T_{1/2} = 8.70\text{ hours}\).


  • Convert hours to seconds: $$ T_{1/2} = 8.70 \times 3600\text{ s} = 31320\text{ s} $$


  • Apply the formula: $$ \lambda = \frac{0.693}{31320} $$


  • Estimate: \(0.693 / 30000 \approx 2.3 \times 10^{-5}\).


  • Exact calculation: \( \approx 0.0000221\text{ s}^{-1} \).


Why other options are incorrect:

Option A has the wrong unit (seconds instead of per second). Option B is a massive math error (multiplying instead of dividing). Option D uses incorrect numbers.

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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