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Q.

If $E_{1}$ , $E_{2}$ and $E_{3}$ represents respectively the kinetic energies of an electron, an $α$ -particle and a proton each having same de-Broglie wavelength, then

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a

$E_{2} > E_{3} > E_{1}$

b

$E_{1} = E_{2} = E_{3}$

c

$E_{1} > E_{2} > E_{3}$

d

$E_{1} > E_{3} > E_{2}$

answer is A.

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Detailed Solution

$λ = \frac{h}{\sqrt{2 E m}}$
where, $λ =$ constant
$∴ E m =$ constant
or $E \propto \frac{1}{m}$

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If E1, E2 and E3 represents respectively the kinetic energies of an electron, an α-particle and a proton each having same de-Broglie wavelength, then