JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Modern Physics

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An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is (

c =

speed of light in vacuum)

(A) $c (2 m E)^{1/2}$
(B) $\frac{1}{c} (\frac{E}{2 m})^{1/2}$ ✓ Correct
(C) $\frac{1}{c} (\frac{2 E}{m})^{1/2}$
(D) $(\frac{E}{2 m})^{1/2}$

Answer: (B)

Solution

For the electron of kinetic energy

E

the de Broglie wavelength is

λ_{e} = \frac{h}{2 m E}

, while a photon of the same energy has

λ_{p h} = \frac{h c}{E}

. Taking the ratio,

\frac{λ _{e}}{λ _{p h}} = \frac{h / 2 m E}{h c / E} = \frac{E}{c 2 m E} = \frac{1}{c} \frac{E}{2 m}

JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Single correct option

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