Question

The de Broglie wavelengths for an electron and a photon are λe and λp, respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two?

• A. $λ_p ∝ λ^{2}_e$
• B. $λ_p ∝ λ_e$
• C. $λ_p ∝ \sqrtλ_e$
• D. $λ_p ∝ \sqrt{\frac{1}{λ_e}}$

Answer 1

Answer: (A)

$λ_p ∝ λ^{2}_e$

Answer 2

The correct answer is (A) : $λ_p ∝ λ^{2}_e$
$λ_p = \frac{h}{p} = \frac{hc}{E} .... (i)$
$λ_e = \frac{h}{\sqrt{2mE}} .... (ii)$
From (i) and (ii)
$λ_p ∝ λ^{2}_e$