The de Broglie wavelength of an electron having kinetic energy E is λ. If the kinetic energy of electron becomes E/4, then its de-Broglie wavelength will be :

Solution

Physics sir · 3 steps

Write the wavelength in terms of kinetic energy; then a quarter of the energy means double the wavelength.

1. Momentum from energy. For an electron of mass m, kinetic energy E = p²/2m, so its momentum is p = √2mE.

   λ = h/p = h/√2mE ⇒ λ ∝ 1/√E

2. Take the ratio. The mass and h do not change, so λ'/λ = √(E/(E/4)) = √4 = 2.
3. So. The new wavelength is λ' = 2λ, which is option (b).

The idea to keep. For a particle of fixed mass, λ = h/√2mE, so λ ∝ 1/√E. Less energy means a longer wavelength, and only by the square root of the change.

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