JEE Main · 2022 · 28 Jun 2022 · Shift 1 · Modern Physics

The de Broglie wavelengths for an electron and a photon are

λ_{e}

and

λ_{p}

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) $λ_{p} \propto λ_{e}^{2}$ ✓ Correct
(B) $λ_{p} \propto λ_{e}$
(C) $λ_{p} \propto λ_{e}$
(D) $λ_{p} \propto \frac{1}{λ _{e}}$

Answer: (A)

Solution

For an electron:

λ_{e} = \frac{h}{2 m K}

. For a photon with kinetic energy

K

K = \frac{h c}{λ _{p}}

, so

λ_{p} = \frac{h c}{K}

. From the electron equation:

K = \frac{h ^{2}}{2 m λ _{e}^{2}}

. Substituting into the photon equation:

λ_{p} = \frac{h c \cdot 2 m λ _{e}^{2}}{h ^{2}} = \frac{2 m c λ _{e}^{2}}{h}

. Therefore,

λ_{p} \propto λ_{e}^{2}

. The answer is (A).

JEE Main · 2022 · 28 Jun 2022 · Shift 1 · Single correct option

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