Physics Nuclear Physics MDCAT 2010
PMDC Verified Question 94 of 98
Decay constant '\(\lambda\)' is given as:
A
\( -\frac{\Delta N / N}{\Delta t} \)
B
\( -\frac{N}{\Delta t} \)
C
\( -\frac{\Delta N}{\Delta t} \)
D
\( \frac{\Delta N / N}{\Delta t} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: \( -\frac{\Delta N / N}{\Delta t} \)


Concept:

The decay constant \(\lambda\) represents the probability of decay per unit time for a given nucleus. It is derived directly from the radioactive decay law.

Solution:

  • Start with the radioactive decay law: $$ \frac{\Delta N}{\Delta t} = -\lambda N $$


  • Rearrange the equation to solve for \(\lambda\): $$ \lambda = -\frac{\Delta N}{N \Delta t} = -\frac{\Delta N / N}{\Delta t} $$


  • The term \(\Delta N / N\) represents the fractional change in the number of nuclei.


Why other options are incorrect:

Option B calculates a frequency, not the decay constant. Option C defines activity (rate of decay), not the decay constant itself. Option D misses the necessary negative sign.

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