An α-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavelength:

Solution

Physics sir · 3 steps

Same kinetic energy means λ depends only on mass: the heavier the particle, the shorter its wave.

1. Momentum from energy. Kinetic energy is K = p²/2m, so the momentum is p = √2mK. Put this into λ = h/p.

   λ = h/√2mK ⇒ λ ∝ 1/√m (same K)

2. Compare the masses. The α-particle is about 4 times as heavy as the proton, and the proton is about 1836 times as heavy as the electron. So m_α > mₚ > mₑ.
3. So. Since λ falls as mass rises, the order flips: λ_α < λₚ < λₑ, which is option (d).

The idea to keep. Write λ = h/√2mK. At equal kinetic energy, the lightest particle has the longest de Broglie wavelength. Charge does not enter unless the particles are accelerated through a voltage.

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