First slide

Matter waves (DC Broglie waves)

Question

A particle of mass M at rest decays into two particles of masses r?11 and m₂ having non-zero velocities. The ratio of the de Broglie wavelengths of the particles, $λ_{1}, λ_{2}$ is

Easy

A

$m_{1} / m_{2}$
B

$m_{2} / m_{1}$
C

1.0
D

$\sqrt{m_{2}} / \sqrt{m_{1}}$

Solution

$According to de Broglie λ = h / mv \frac{λ_{1}}{λ_{2}} = \frac{h / (m_{1} v_{1})}{h / (m_{2} v_{2})} = \frac{m_{2} v_{2}}{m_{1} v_{1}} Applying the law of conservation of momentum m_{1} v_{1} = m_{2} v_{2} From eqs . (1) atrd (2), we Be \frac{λ_{1}}{λ_{2}} = \frac{m_{1} v_{1}}{m_{1} v_{1}} = 1$

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