First slide

Matter waves (DC Broglie waves)

Question

de Broglie wavelength of neutron having kinetic energy of 5 MeV is $λ$ . Then what will be the de Broglie wavelength of $α -$ particle having kinetic energy of 20 MeV?

Easy

A

$\frac{λ}{4}$
B

$\frac{λ}{2}$
C

$λ$
D

$2 λ$

Solution

$\frac{p^{2}}{2 m} = E \Rightarrow p = \sqrt{2 m E} \Rightarrow λ = \frac{h}{p} = \frac{h}{\sqrt{2 m E}}$
$∴ \frac{λ_{α}}{λ_{n}} = \sqrt{\frac{m_{n}}{m_{α}}} . \sqrt{\frac{E_{n}}{E_{α}}}$
$\Rightarrow \frac{λ_{α}}{λ} = \sqrt{\frac{m}{4 m}} . \sqrt{\frac{5}{20}} = \frac{1}{4} \Rightarrow λ_{α} = \frac{λ}{4}$

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