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De Broglie's Hypothesis

If Ee, Eα, Ep...

Question

If $E_{e}, E_{α}, E_{p}$ represents the kinetic energies of an electron, alpha particle and a proton respectively, each moving with same de-Broglie wavelength then:

A

E_{e} = E_{α} = E_{p}

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B

E_{e} > E_{α} > E_{p}

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C

E_{α} > E_{p} > E_{e}

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D

E_{e} > E_{p} > E_{α}

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Solution

The correct option is D $E_{e} > E_{p} > E_{α}$
$λ = \frac{h}{\sqrt{2 m E}}$
For constant wavelength, kinetic energy is also inversely proportional to the mass.
$m_{α} > m_{p} > m_{e}$
Hence, order of kinetic energy is
$E_{e} > E_{p} > E_{α}$

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