Physics Nuclear Physics MDCAT 2010
PMDC Verified Question 93 of 98
In the half-life of an element, the equation for the number of decaying atoms is given by:
A
\(\Delta N = N \Delta t\)
B
\(\Delta N \propto -N \Delta t\)
C
\(\Delta N = K N \Delta t\)
D
\(\Delta N = -\lambda N \Delta t\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: \(\Delta N = -\lambda N \Delta t\)


Concept:

The fundamental law of radioactive decay states that the rate of decay of a radioactive sample is directly proportional to the number of radioactive nuclei present at that time.

Formula:

$$ \frac{\Delta N}{\Delta t} = -\lambda N $$

Solution:

  • \(\Delta N\) is the change in the number of undecayed nuclei.


  • \(N\) is the current number of nuclei, and \(\Delta t\) is the time interval.


  • \(\lambda\) is the decay constant.


  • The negative sign indicates that the number of parent nuclei \(N\) is decreasing over time. Rearranging yields: \(\Delta N = -\lambda N \Delta t\).


Why other options are incorrect:

Option A is missing the decay constant and the negative sign. Option B is a proportionality, not an equation. Option C uses an undefined constant \(K\) and misses the critical negative sign.

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.

Want to solve full-length papers under timed exam conditions?

Practice with zero-scroll lockdown sprints, dynamic latency zone timers, live peer selection telemetry, and the automated Amber mistake recovery loop.