First slide

Matter waves (DC Broglie waves)

Question

A proton accelerated through a potential difference of 100V, has de – Brogile wavelength $λ_{0}$ . The de – Brogile wavelength of an $α$ - particle, accelerated through 800 V is

Moderate

A

$\frac{λ_{0}}{\sqrt{2}}$
B

$\frac{λ_{0}}{2}$
C

$\frac{λ_{0}}{4}$
D

$\frac{λ_{0}}{8}$

Solution

$\frac{p^{2}}{2 m} = qV$
$p = \sqrt{2 mqV}$
$λ = \frac{h}{\sqrt{2 mqV}}$
$\frac{λ_{1}}{λ_{2}} = \sqrt{\frac{m_{2} q_{2} V_{2}}{m_{1} q_{1} V_{1}}} = \sqrt{\frac{4 m 2 q 800}{mq 100}}$
$\frac{λ_{0}}{λ_{2}} = \sqrt{64}$
$λ_{2} = \frac{λ_{o}}{8}$

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