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NEET 2016
Exam
NEET
Year
2016
Subject
Physics
Chapter
Dual Nature of Matter

NEET 2016 · Physics · Dual Nature of Matter

Electrons of mass, m with de-Broglie wavelength, λ fall on the...

Electrons of mass, mm with de-Broglie wavelength, λ\lambda fall on the target in an X-ray tube. The cutoff wavelength, (λ0)\left({\lambda}_{0}\right) of the emitted X-ray is

Options

  1. Aλ0=2mcλ2h{\lambda}_{0} = \dfrac{2mc{\lambda}^{2}}{h}
  2. Bλ0=2hmc{\lambda}_{0} = \dfrac{2h}{mc}
  3. Cλ0=2m2c2λ3h2{\lambda}_{0} = \dfrac{2{m}^{2}{c}^{2}{\lambda}^{3}}{{h}^{2}}
  4. Dλ0=λ{\lambda}_{0} = \lambda

Correct answer

A. λ0=2mcλ2h{\lambda}_{0} = \dfrac{2mc{\lambda}^{2}}{h}

Step-by-step solution

Momentum, P=hλ⇒E=P22m⇒h22mλ2=hcλ0P = \dfrac{h}{\lambda} ⇒ E = \dfrac{{P}^{2}}{2m} ⇒ \dfrac{{h}^{2}}{2m{\lambda}^{2}} = \dfrac{hc}{{\lambda}_{0}}

⇒λ0=hch22mλ2⇒ {\lambda}_{0} = \dfrac{hc}{{h}^{2}}2m{\lambda}^{2}

=2mcλ2h= \dfrac{2mc{\lambda}^{2}}{h}.

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