Dual Nature of Matter

JEE Main level, single correct, medium

42 of 200

Question 42 of 200

The de Broglie wavelengths for an electron and a photon are λe{\lambda }_{e} and λp{\lambda }_{p} respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two?

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Answer: (A) λp∝λe2{\lambda }_{p}\propto {\lambda }_{e}^{2}

De-Broglie wavelength for electron is given by, λe=h2mk{\lambda }_{e}=\dfrac{h}{\sqrt{2mk}}
For photon k=hcλp⇒λp=hckk=\dfrac{hc}{{\lambda }_{p}}\Rightarrow {\lambda }_{p}=\dfrac{hc}{k}. Therefore,
λe=hλp2mhc{\lambda }_{e}=\dfrac{h\sqrt{{\lambda }_{p}}}{\sqrt{2mhc}}
λp∝λe2{\lambda }_{p}\propto {{\lambda }_{e}}^{2}

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