Physics Nuclear Physics MDCAT 2015
PMDC Verified Question 71 of 98
A certain radioactive nuclide of mass number 'x' decay by \(\beta\)-emission and \(\alpha\)-emission to a second nuclide of mass number 't', which of the following correctly relates 'x' and 't'?
A
x = t - 4
B
x + 3 = t
C
x = t + 4
D
x - 1 = t
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: x = t + 4


Concept:

We must track the changes purely to the mass number during sequential decay.

Solution:

  • Initial mass number = \(x\).


  • Beta Emission: A neutron turns into a proton. Mass number does not change. So, \(\Delta A_{\beta} = 0\).


  • Alpha Emission: The nucleus ejects a helium nucleus (2p + 2n). Mass number decreases by 4. So, \(\Delta A_{\alpha} = -4\).


  • The final mass number \(t\) is the initial mass \(x\) minus 4:
    $$ t = x - 4 $$


  • Rearranging the equation to solve for \(x\):
    $$ x = t + 4 $$


Why other options are incorrect:

Option A sets \(t = x + 4\), implying the nucleus gained mass, which is impossible in decay. Options B and D introduce incorrect constants.

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.

Previous Question All Nuclear Physics MCQs Next Question

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.

Enter Arena Sprint iOS App Android App