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Dual Nature of Radiation and Matter question

2016 · Q135
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Dual Nature of Radiation and Matter question

2016 · Q135

NEETPhysicsDual Nature of Radiation and MatterMCQ+4 / −1
An electron of mass m and a photon have same energy E. The ratio of de-Broglie wavelengths associated with them is
  1. A
    c(2mE)12c{\left( {2mE} \right)^{{1 \over 2}}}c(2mE)21​
  2. B
    1c(2mE)12{1 \over c}{\left( {{{2m} \over E}} \right)^{{1 \over 2}}}c1​(E2m​)21​
  3. C
    1c(E2m)12{1 \over c}{\left( {{E \over {2m}}} \right)^{{1 \over 2}}}c1​(2mE​)21​
  4. D
    (E2m)12{\left( {{E \over {2m}}} \right)^{{1 \over 2}}}(2mE​)21​
View written solutionFree

Correct answer: C

For electron De-Broglie wavelength,

λ\lambda λe = h2mE{h \over {\sqrt {2mE} }}2mE​h​

For photon of energy, E = hν\nu ν = hcλp{{hc} \over {{\lambda _p}}}λp​hc​

⇒\Rightarrow⇒ λ\lambda λp = hcE{{hc} \over E}Ehc​

∴\therefore∴ λeλp{{{\lambda _e}} \over {{\lambda _p}}}λp​λe​​ = h2mE×Ehc{h \over {\sqrt {2mE} }} \times {E \over {hc}}2mE​h​×hcE​ = 1c(E2m)12{1 \over c}{\left( {{E \over {2m}}} \right)^{{1 \over 2}}}c1​(2mE​)21​

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