(A) The force on the electron is $F = eE$. The acceleration is $a = \frac{eE}{m}$.Since the electron starts from rest,its velocity at time $t$ is $v =

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(A) The force on the electron is $F = eE$. The acceleration is $a = \frac{eE}{m}$.Since the electron starts from rest,its velocity at time $t$ is $v = at = \frac{eEt}{m}$.The momentum of the electron is $p = mv = m(\frac{eEt}{m}) = eEt$.The de-Broglie wavelength is given by $\lambda = \frac{h}{p} = \frac{h}{eEt}$.To find the rate of change of wavelength,we differentiate $\lambda$ with respect to time $t$:$\frac{d\lambda}{dt} = \frac{d}{dt}(\frac{h}{eEt}) = \frac{h}{eE} \frac{d}{dt}(t^{-1}) = \frac{h}{eE} (-t^{-2}) = -\frac{h}{eEt^2}$.

Class 12 Physics Dual Nature of Radiation and Matter Matter Waves and de Broglie Wavelength

Medium

An electron of mass $m$ and charge $e$ initially at rest gets accelerated by a constant electric field $E$. The rate of change of de-Broglie wavelength of the electron at time $t$ is (Ignore relativistic effect) ($h=$ Planck's constant).

MHT CET 2025 All MHT CET

A
$-\frac{h}{eEt^2}$
B
$-\frac{eEt}{h}$
C
$\frac{-mh}{eEt^2}$
D
$-\frac{h}{eE}$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Physics Questions

Chapter

Dual Nature of Radiation and Matter

Subtopic

Matter Waves and de Broglie Wavelength

Previous Year

MHT CET 2025 Paper All MHT CET years →

$A$ light of wavelength $\lambda$ is incident on a photosensitive surface of negligible work function. The photoelectrons emitted from the surface have de-Broglie wavelength $\lambda_1$. Then the ratio $\lambda : \lambda_1^2$ is ($h =$ Planck's constant,$c =$ velocity of light,$m =$ mass of electron).

MediumMHT CET 2025

View Solution

Calculate the $(a)$ momentum,and $(b)$ de Broglie wavelength of the electrons accelerated through a potential difference of $56 \; V$.

Medium

View Solution

What is the de Broglie wavelength of
$(a)$ a bullet of mass $0.040 \; kg$ travelling at the speed of $1.0 \; km/s$
$(b)$ a ball of mass $0.060 \; kg$ moving at a speed of $1.0 \; m/s$,and
$(c)$ a dust particle of mass $1.0 \times 10^{-9} \; kg$ drifting with a speed of $2.2 \; m/s$?

Medium

View Solution

The ratio of de Broglie wavelength of molecules of hydrogen and helium in two gas jars kept separately at temperatures of $27\,^oC$ and $127\,^oC$ respectively is

Difficult

View Solution

The graph which shows the variation of $\left(\frac{1}{\lambda^2}\right)$ and its kinetic energy,$E$ is (where $\lambda$ is de Broglie wavelength of a free particle):

MediumNEET 2024

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

An electron of mass $m$ and charge $e$ initially at rest gets accelerated by a constant electric field $E$. The rate of change of de-Broglie wavelength of the electron at time $t$ is (Ignore relativistic effect) ($h=$ Planck's constant).

Similar Questions

Calculate the $(a)$ momentum,and $(b)$ de Broglie wavelength of the electrons accelerated through a potential difference of $56 \; V$.

What is the de Broglie wavelength of$(a)$ a bullet of mass $0.040 \; kg$ travelling at the speed of $1.0 \; km/s$$(b)$ a ball of mass $0.060 \; kg$ moving at a speed of $1.0 \; m/s$,and$(c)$ a dust particle of mass $1.0 \times 10^{-9} \; kg$ drifting with a speed of $2.2 \; m/s$?

The ratio of de Broglie wavelength of molecules of hydrogen and helium in two gas jars kept separately at temperatures of $27\,^oC$ and $127\,^oC$ respectively is

The graph which shows the variation of $\left(\frac{1}{\lambda^2}\right)$ and its kinetic energy,$E$ is (where $\lambda$ is de Broglie wavelength of a free particle):

Vedclass Test Series

Exam Paper Generator

Online Exam Module

What is the de Broglie wavelength of
$(a)$ a bullet of mass $0.040 \; kg$ travelling at the speed of $1.0 \; km/s$
$(b)$ a ball of mass $0.060 \; kg$ moving at a speed of $1.0 \; m/s$,and
$(c)$ a dust particle of mass $1.0 \times 10^{-9} \; kg$ drifting with a speed of $2.2 \; m/s$?