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Q.

An $α -$ particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their De-Broglie wavelength :

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a

$λ_{α} > λ_{p} > λ_{e}$

b

$λ_{α} < λ_{p} < λ_{e}$

c

$λ_{α} = λ_{p} = λ_{e}$

d

$λ_{α} > λ_{p} < λ_{e}$

answer is B.

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Detailed Solution

$λ = \frac{h}{p} = \frac{h}{\sqrt{2 m k}}$

$λ \propto \frac{1}{\sqrt{m}} \Rightarrow λ_{e} > λ_{p} > λ_{α}$

As $m_{α} > m_{p} > m_{e}$

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