A proton (p), a deuteron (d), and an alpha particle (alpha) each have the same de Broglie wavelength. What is the correct order of their kinetic energies?

Eₚ < E_alpha < E_d
E_d < Eₚ < E_alpha
Eₚ < E_d < E_alpha
E_alpha < E_d < Eₚ

Correct answer: E_alpha < E_d < Eₚ

Solution

Since lambda = h/sqrt(2*m*KE), for the same lambda: KE = h²/(2*m*lambda²). KE is inversely proportional to m. Masses: proton ~ 1u, deuteron ~ 2u, alpha ~ 4u. So KEₚ > KE_d > KE_alpha, i.e. E_alpha < E_d < Eₚ.

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