First slide

Matter waves (DC Broglie waves)

Question

A proton and an $α$ –particle are accelerated from rest to the same energy. The de Broglie wavelengths $λ_{p}$ and $λ_{α}$ are in the ratio,

Moderate

A

4 : 1
B

2 : 1
C

1 : 1
D

$\sqrt{2} : 1$

Solution

$As λ = \frac{h}{p} = \frac{h}{\sqrt{2 mKE}}$
$∴ λ \propto \frac{1}{\sqrt{m}} (Kinetic energies are same) \frac{λ_{p}}{λ_{α}} = \sqrt{\frac{m_{α}}{m_{p}}} \frac{λ_{p}}{λ_{α}} = \sqrt{\frac{4 m_{p}}{m_{p}}} ∴ \frac{λ_{p}}{λ_{α}} = \frac{2}{1}$

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