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NEET 2021
Exam
NEET
Year
2021
Subject
Physics
Chapter
Dual Nature of Matter

NEET 2021 · Physics · Dual Nature of Matter

An electromagnetic wave of wavelength λ is incident on a...

An electromagnetic wave of wavelength λ\lambda is incident on a photosensitive surface of negligible work function. If mm mass is of photoelectron emitted from the surface has de-Broglie wavelength λd{\lambda}_{d}, then :

Options

  1. Aλ=(2mhc)λd2\lambda = \left(\dfrac{2m}{hc}\right){\lambda}_{d}^{2}
  2. B{\lambda}_{d} = (2mch)λ2\left(\dfrac{2mc}{h}\right){\lambda}^{2}
  3. Cλ=(2mch)λd2\lambda = \left(\dfrac{2mc}{h}\right){\lambda}_{d}^{2}
  4. Dλ=(2hmc)λd2\lambda = \left(\dfrac{2h}{mc}\right){{\lambda}_{d}}^{2}

Correct answer

C. λ=(2mch)λd2\lambda = \left(\dfrac{2mc}{h}\right){\lambda}_{d}^{2}

Step-by-step solution

From Einstein's equation,

{E}_{incident} = ϕ + k{E}_\max

hf=0+12mv2hf = 0 + \dfrac{1}{2}m{v}^{2}

hcλ=p22m⇒p=2mhcλ\dfrac{hc}{\lambda} = \dfrac{{p}^{2}}{2m} ⇒ p = \sqrt{\dfrac{2mhc}{\lambda}}

λd=hp=h2mhcλ=\lambdah2mc{\lambda}_{d} = \dfrac{h}{p} = \dfrac{h}{\sqrt{\dfrac{2mhc}{\lambda}}} = \sqrt{\dfrac{\lambdah}{2mc}}

⇒λ=(2mch)λd2⇒ \lambda = \left(\dfrac{2mc}{h}\right){\lambda}_{d}^{2}

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