Class NEET 2026 ALL Q #1899
COMPETENCY BASED
APPLY
4 Marks 2026 NTA-RE-NEET-2026 MCQ SINGLE
A photon and an electron, each of 20 eV energy, move in free space. The ratio of linear momentum of electron $p_e$ to that of photon $p_{Ph}$ is:
(Take speed of light $c=3 \times 10^8$ ms$^{-1}$, charge of electron $e = -1.6 \times 10^{-19}$ C and mass of electron $m_e = 9 \times 10^{-31}$ kg)
(A) 275
(B) $\frac{2}{450}$
(C) $\frac{1}{250}$
(D) 225
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Correct Answer: D

AI Tutor Explanation

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Detailed Solution

Step 1: Momentum of a Photon

The energy of a photon is given by $E = p_{Ph}c$. Therefore, the momentum of the photon is: $$p_{Ph} = \frac{E}{c}$$

Step 2: Momentum of an Electron

For a non-relativistic electron, the kinetic energy is $E = \frac{p_e^2}{2m_e}$. Rearranging for momentum: $$p_e = \sqrt{2m_eE}$$

Step 3: Calculating the Ratio

The ratio $\frac{p_e}{p_{Ph}}$ is: $$\frac{p_e}{p_{Ph}} = \frac{\sqrt{2m_eE}}{E/c} = \frac{c\sqrt{2m_eE}}{E} = c\sqrt{\frac{2m_e}{E}}$$

Step 4: Substitution and Calculation

Convert energy $E = 20 \text{ eV}$ to Joules: $E = 20 \times 1.6 \times 10^{-19} \text{ J} = 3.2 \times 10^{-18} \text{ J}$. Substitute the values: $$\frac{p_e}{p_{Ph}} = 3 \times 10^8 \times \sqrt{\frac{2 \times 9 \times 10^{-31}}{3.2 \times 10^{-18}}}$$ $$\frac{p_e}{p_{Ph}} = 3 \times 10^8 \times \sqrt{\frac{18 \times 10^{-31}}{3.2 \times 10^{-18}}} = 3 \times 10^8 \times \sqrt{5.625 \times 10^{-13}}$$ $$\frac{p_e}{p_{Ph}} \approx 3 \times 10^8 \times 0.75 \times 10^{-6} \approx 225$$

Final Answer: 225

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student must identify and apply two distinct physical models (photon energy-momentum relation and non-relativistic kinetic energy-momentum relation) to solve a comparative ratio problem.
Knowledge Dimension: PROCEDURAL
Justification: The question requires a sequence of mathematical steps involving unit conversion and algebraic manipulation of physical formulas.
Syllabus Audit: In the context of NEET, this is classified as COMPETENCY. It tests the student's ability to differentiate between wave-particle duality concepts and perform precise numerical calculations under time constraints.

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