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An electron, an α-particle and a proton have the same kinetic energy. Which of these has the longest de Broglie wavelength?

Asked in GUJCET 2023 · Same or changed energy

Answer: (2) Electron

Step-by-step solution

Given: the same kinetic energy K for all three particles.

Idea: λ = h/(√2mK), so at fixed K, λ ∝ 1/(√m): the lightest particle has the longest wavelength.

Masses: mₑ mₚ < m_α ≈ 4mₚ.

The electron is about 1836 times lighter than the proton, so λₑ ≈ 43 λₚ.

So the electron has the longest de Broglie wavelength.

Why the other options are wrong

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