Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of $\lambda_{\mathrm{o}}$. If the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be:

(D) $\frac{\lambda_{0}}{\sqrt{2}}$

JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Modern Physics

Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of

λ_{o}

. If the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be:

(A) $3 λ_{0}$
(B) $9 λ_{0}$
(C) $\frac{λ _{0}}{2}$
(D) $\frac{λ _{0}}{2}$ ✓ Correct

Answer: (D)

Solution

An electron accelerated through a potential

V

has de Broglie wavelength

λ = \frac{h}{2 m e V}

, so

λ \propto \frac{1}{V}

. Raising the voltage from

20 kV

40 kV

scales the wavelength by

\frac{20}{40} = \frac{1}{2}

. The new wavelength is

\frac{λ _{0}}{2}

JEE Main · 2023 · 25 Jan 2023 · Shift 1 · 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 →