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

NEET 2016 · Physics · Dual Nature of Matter

An electron of mass m and a photon have same energy E. The ratio of...

An electron of mass m and a photon have same energy E.E. The ratio of de-Broglie wavelengths associated with them is:
(cc being velocity of light)

Options

  1. A\dfrac{1}{c}{\left(\dfrac{E}{2m}\right)}^{\dfrac{1}{2}}
  2. B{\left(\dfrac{E}{2m}\right)}^{\dfrac{1}{2}}
  3. Cc{\left(2mE\right)}^{\dfrac{1}{2}}
  4. D\dfrac{1}{c}{\left(\dfrac{2m}{E}\right)}^{\dfrac{1}{2}}

Correct answer

A. \dfrac{1}{c}{\left(\dfrac{E}{2m}\right)}^{\dfrac{1}{2}}

Step-by-step solution

De-Broglie wavelength is given by

λe=hp=h2m.E{\lambda}_{e} = \dfrac{h}{p} = \dfrac{h}{\sqrt{2m . E}} for electron

De-Broglie wavelength of photon is given by

λp=hp=hEc=hcE{\lambda}_{p} = \dfrac{h}{p} = \dfrac{h}{\dfrac{E}{c}} = \dfrac{hc}{E}

λeλp=12mE.Ec=1cE2m\dfrac{{\lambda}_{e}}{{\lambda}_{p}} = \dfrac{1}{\sqrt{2mE}} . \dfrac{E}{c} = \dfrac{1}{c}\sqrt{\dfrac{E}{2m}}
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