A moving proton and electron have the same de-Broglie wavelength. If K and P denote the K.E. and momentum respectively. Then choose the correct option :

Solution

Physics sir · 3 steps

Same wavelength means same momentum; then the lighter particle carries more kinetic energy.

1. Same momentum. de Broglie wavelength is λ = h/p. If the proton and the electron have the same λ, they must have the same momentum: pₚ = pₑ.
2. Link K to p. Kinetic energy written in terms of momentum is K = p²/2m. With p fixed, K depends only on the mass, and a bigger mass gives a smaller K.

   Kₚ/Kₑ = mₑ/mₚ ≈ 1/1836

3. So. The proton is about 1836 times heavier, so Kₚ < Kₑ while pₚ = pₑ. That is option (a).

The idea to keep. Equal de Broglie wavelength always means equal momentum. To compare energies, use K = p²/2m: at the same momentum, the heavier particle has less kinetic energy.

Answer from the NTA final answer key. Solution by PrepWiser.