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JEE Main 202120 JulyEvening Shift
Exam
JEE Main
Year
2021
Date
20 July
Shift
Evening Shift
Subject
Physics
Chapter
Dual Nature of Matter

JEE Main 2021 · 20 July · Evening Shift · Physics · Dual Nature of Matter

An electron having de-Broglie wavelength λ is incident on a target...

An electron having de-Broglie wavelength λ\lambda is incident on a target in a XX-ray tube. Cut-off wavelength of emitted XX-ray is:

Options

  1. A00
  2. B2m2c2λ2h2\dfrac{2{m}^{2}{c}^{2}{\lambda}^{2}}{{h}^{2}}
  3. C2mcλ2h\dfrac{2mc{\lambda}^{2}}{h}
  4. Dhcmc\dfrac{hc}{mc}

Correct answer

C. 2mcλ2h\dfrac{2mc{\lambda}^{2}}{h}

Step-by-step solution

λ=hmv\lambda = \dfrac{h}{mv}

Kinetic energy, P22m=h22mλ2=hcλc\dfrac{{P}^{2}}{2m} = \dfrac{{h}^{2}}{2m{\lambda}^{2}} = \dfrac{hc}{{\lambda}_{c}}

λc=2mλ2ch{\lambda}_{c} = \dfrac{2m{\lambda}^{2}c}{h}

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