JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Modern Physics

WhatsApp Email

An electron moving with speed v and a photon moving with speed c, have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is :

(A) $\frac{v}{2 c}$ ✓ Correct
(B) $\frac{2 c}{v}$
(C) $\frac{v}{3 c}$
(D) $\frac{3 c}{v}$

Answer: (A)

Solution

Equal de Broglie wavelengths mean equal momenta,

p = \frac{h}{λ}

, for the electron and the photon. The electron is non-relativistic, so with

p = m v

its kinetic energy is

K_{e} = \frac{p ^{2}}{2 m} = \frac{p v}{2}

A photon of the same momentum carries energy

K_{p h} = p c

. Dividing,

\frac{K _{e}}{K _{p h}} = \frac{p v /2}{p c} = \frac{v}{2 c}

The ratio of the kinetic energies is

\frac{v}{2 c}

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Modern Physics →

More JEE Main questions on Modern Physics

7.9 MeV α-particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) ______ m.
[ $\frac{1}{4 π ϵ _{0}} = 9 \times 1 0^{9}$ Nm²/C² and electron charge $= 1.6 \times 1 0^{- 19}$ C]
JEE Main 2026View solution →
The minimum frequency of photon required to break a particle of mass 15.348 amu into $4 α$ particles is ______ kHz.
[mass of He nucleus = 4.002 amu, $1$ amu $= 1.66 \times 1 0^{- 27}$ kg, $h = 6.6 \times 1 0^{- 34}$ J.s and $c = 3 \times 1 0^{8}$ m/s]
JEE Main 2026View solution →
The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly $____$ nm.
JEE Main 2026View solution →
Light is incident on a metallic plate having work function $110 \times 1 0^{- 20} J$ . If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ______ $rad / s$ . ( …
JEE Main 2026View solution →
The energy of an electron in an orbit of the Bohr's atom is $- 0.04 E_{0} eV$ where $E_{0}$ is the ground state energy. If L is the angular momentum of the electron in this orbit and h is the Planck's constant, then …
JEE Main 2026View solution →
A particle having electric charge $3 \times 1 0^{- 19} C$ and mass $6 \times 1 0^{- 27} kg$ is accelerated by applying an electric potential of 1.21 V . Wavelength of the matter wave associated with the particle is $α \times 1 0^{- 12} m$ . The va …
JEE Main 2026View solution →