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Question #43688

Difficulty: 8/10 | 🟢 Free

The Question

An elevator of height $h$ is accelerating upwards with a constant acceleration $a$ in a region of uniform downward gravitational field $g$ . A massive nucleus, initially at rest on the floor of the elevator, undergoes a nuclear transition. It releases an internal energy $Q$ by emitting a single gamma-ray photon vertically upwards. Assume the mass of the nucleus is sufficiently large such that its recoil kinetic energy is negligible. The photon is subsequently absorbed by a perfectly absorbing detector fixed to the ceiling of the elevator. What is the magnitude of the impulse imparted to the detector by the photon, as measured in the reference frame of the elevator? (Let $c$ be the speed of light in vacuum, and assume $(g+a)h \ll c^2$ ).

Options

A.
$\frac{Q}{c} \left( 1 - \frac{(g+a)h}{c^2} \right)$
B.
$\frac{Q}{c} \left( 1 + \frac{(g+a)h}{c^2} \right)$
C.
$\frac{Q}{c} \left( 1 - \frac{gh}{c^2} \right)$
D.
$\frac{Q}{c}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Q-value Calculation|Impulse-Momentum Theorem|Apparent Weight in Accelerating Elevators

Why This Question Is Tricky

Common Mistakes

This question tests the intersection of modern physics and non-inertial mechanics.

The primary trap is assuming that a photon, being 'massless', does not interact with gravitational or pseudo-forces, leading students to incorrectly choose Q/c (Option D).

Even if students account for gravity (Option C), they often fail to apply the Principle of Equivalence, forgetting that the elevator's upward acceleration creates a pseudo-force that acts on the photon's mass-energy equivalent ( $E/c^2$ ).

This forces the student to redefine the effective Q-value energy distribution in an accelerating frame, recognizing that the fictitious force does negative work on the propagating energy.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Nuclei - Class 12
Concept	Q-value Calculation
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free