First slide

Matter waves (DC Broglie waves)

Question

If a stationary positron and electron combine, the wavelength of resulting radiation will be
$[m_{0} = s t a t i o n a r y m a s s o f e l e c t r o n]$

Moderate

A

$\frac{2 h}{m_{0} C^{2}}$
B

$\frac{h}{m_{0} C^{2}}$
C

$\frac{2 h}{m_{0} C}$
D

$\frac{h}{m_{0} C}$

Solution

(4)
From conservation of linear momentum, two identical photons travel in opposite directions with equal magnitude of momentum and energy $\frac{h c}{λ} .$
From Conservation of Energy
$\frac{h c}{λ} + \frac{h c}{λ} = m_{0} C^{2} + m o C^{2} \Rightarrow λ = \frac{h}{m_{o} C}$

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