Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET 202622 AprilEvening Shift
Exam
MHT CET
Year
2026
Date
22 April
Shift
Evening Shift
Subject
Physics
Chapter
Dual Nature of Matter

MHT CET 2026 · 22 April · Evening Shift · Physics · Dual Nature of Matter

The de-Broglie wavelength of the free electron is ' λ ' and has a...

The de-Broglie wavelength of the free electron is 'λ\lambda' and has a kinetic energy EkE_k. If the kinetic energy of the free electron is made double, the new de-Broglie wavelength is 'λ1\lambda_1'. If λ1=x λ\lambda_1 = x\,\lambda, then the value of xx is

Options

  1. A12\dfrac{1}{2}
  2. B12\dfrac{1}{\sqrt{2}}
  3. C22
  4. D2\sqrt{2}

Correct answer

B. 12\dfrac{1}{\sqrt{2}}

Step-by-step solution

The de-Broglie wavelength λ\lambda of an electron with kinetic energy EkE_k is given by

λ=h2mEk\lambda = \dfrac{h}{\sqrt{2mE_k}}

When the kinetic energy is doubled, the new kinetic energy is Ek′=2EkE_k' = 2E_k. The new de-Broglie wavelength λ1\lambda_1 becomes

λ1=h2m(2Ek)=12h2mEk\lambda_1 = \dfrac{h}{\sqrt{2m(2E_k)}} = \dfrac{1}{\sqrt{2}} \dfrac{h}{\sqrt{2mE_k}}

λ1=12λ\lambda_1 = \dfrac{1}{\sqrt{2}} \lambda

Given λ1=xλ\lambda_1 = x \lambda, comparing the two expressions gives

x=12x = \dfrac{1}{\sqrt{2}}

Answer: 12\dfrac{1}{\sqrt{2}}
Practice Dual Nature of Matter on Quantrex Academy →

More from Dual Nature of Matter

An electron and positron are accelerated from rest to the same kinetic energy. The ratio… MHT CET Medical 2026An electron of mass m and charge e initially at rest gets accelerated by a constant… MHT CET Medical 2026The wavelength λ_e of an electron and λ_P of a photon of same energy E are related as MHT CET Medical 2026A light of wavelength λ(λ < λ_0) falls on a metal surface. The momentum of the fastest… MHT CET Medical 2026The de Broglie wavelength of an electron with kinetic energy K_1 is λ_1 . If the kinetic… MHT CET Medical 2026A student plots two different graphs using the same photoelectric experiment data. 1.… MHT CET Medical 2026In a photoelectric cell, for the incident radiation of wavelength λ , the fastest… MHT CET Medical 2026A particle is dropped from a height ' y '. The de-Broglie wavelength of the particle as a… MHT CET Medical 2026 Full Dual Nature of Matter list All MHT CET Medical PYQs