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Q.

An electron, a proton and an alpha particle have kinetic energies of 16E, 4E and E respectively. What is the quantitative order of their de Broglie wavelengths?

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a

$λ_{e} > λ_{α} > λ_{p}$

b

$λ_{e} > λ_{p} = λ_{α}$

c

$λ_{p} = λ_{α} = λ_{e}$

d

$λ_{p} > λ_{e} > λ_{α}$

answer is A.

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Detailed Solution

As we know,

de Broglie wavelength is

$λ \propto \frac{1}{\sqrt{m \cdot (K E)}} \Rightarrow λ_{e} > λ_{P} = λ_{α}$

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An electron, a proton and an alpha particle have kinetic energies of 16E, 4E and E respectively. What is the quantitative order of their de Broglie wavelengths?