Proton (P) and electron (e) will have same de-Broglie wavelength when the ratio of their momentum is (assume, mₚ=1849 mₑ ):

Solution

Physics sir · 3 steps

Here λ = h/p has no mass in it, so equal wavelengths mean equal momenta, full stop.

1. de Broglie relation. Any particle with momentum p has wavelength λ = h/p. Here h is Planck's constant, the same for every particle.

   λₚ = λₑ ⇒ h/pₚ = h/pₑ ⇒ pₚ = pₑ

2. Mass does not enter. The mass ratio mₚ = 1849 mₑ is a distractor. It decides how fast each particle must move for that momentum: the electron must go 1849 times faster. It does not change the momentum ratio.
3. So. pₚ : pₑ = 1 : 1, which is option (a).

The idea to keep. Since λ = h/p, equal de Broglie wavelengths always mean equal momenta, whatever the masses. Mass matters only when the question gives you energy or a voltage instead.

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