A proton and an electron have the same de Broglie wavelength. If $\mathrm{K}_\mathrm{p}$ and $\mathrm{K}_\mathrm{e}$ be the kinetic energies of proton and electron respectively. Then choose the correct relation :

(D) $\mathrm{K}_\mathrm{p}<\mathrm{K}_\mathrm{e}$

(B) $\mathrm{K}_\mathrm{p}=\mathrm{K}_\mathrm{e}$

JEE Main · 2024 · 08 Apr 2024 · Shift 2 · Modern Physics

A proton and an electron have the same de Broglie wavelength. If

K_{p}

and

K_{e}

be the kinetic energies of proton and electron respectively. Then choose the correct relation :

(A) $K_{p} > K_{e}$
(B) $K_{p} = K_{e}$
(C) $K_{p} = K_{e}^{2}$
(D) $K_{p} < K_{e}$ ✓ Correct

Answer: (D)

Solution

Equal de Broglie wavelength

\Rightarrow

equal momentum

p

(since

λ = h / p

K E = \frac{p ^{2}}{2 m}

For the same

p

K E \propto 1/ m

. Since

m_{p} > m_{e}

K_{p} < K_{e}

JEE Main · 2024 · 08 Apr 2024 · 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 →