Physics Nuclear Physics MDCAT 2018
PMDC Verified Question 57 of 98
Calculate the half-life of bismuth-214 which has a decay constant of \( 4.3 \times 10^{-5} \text{ s}^{-1} \)?
A
\( 2.9 \times 10^{-4} \text{ s} \)
B
\( 3.9 \times 10^{3} \text{ s} \)
C
\( 1.6 \times 10^{4} \text{ s} \)
D
\( 2.9 \times 10^{5} \text{ s} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: \( 1.6 \times 10^{4} \text{ s} \)


Concept:

The mathematical relationship between the decay constant (\(\lambda\)) and the half-life (\(T_{1/2}\)) is strictly defined.

Formula:

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

Solution:

  • Given: \(\lambda = 4.3 \times 10^{-5} \text{ s}^{-1}\).


  • Plug into the formula: $$ T_{1/2} = \frac{0.693}{4.3 \times 10^{-5}} $$


  • Bring the exponent up: $$ T_{1/2} = \left( \frac{0.693}{4.3} \right) \times 10^{5} $$


  • Estimate the division: \( 0.693 / 4.3 \approx 0.161 \).


  • Adjust scientific notation: \( 0.161 \times 10^{5} = 1.61 \times 10^{4} \text{ s} \).


Why other options are incorrect:

Option A is the result of multiplying the constants instead of dividing. Options B and D are math errors in handling the \(10^{-5}\) denominator.

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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