First slide

Matter waves (DC Broglie waves)

Question

An electron with speed V and a photon with speed C have the same de Broglie wave length. If the energy and momentum of electron are $E_{e} and P_{e}$ and that of photon are $E_{p} and P_{p}$ respectively, Then correct statement is _____

Moderate

A

$\frac{E_{e}}{E_{p}} = \frac{2 c}{V}$
B

$\frac{E_{e}}{E_{p}} = \frac{V}{2 c}$
C

$\frac{P_{e}}{P_{p}} = \frac{2 c}{V}$
D

$\frac{P_{e}}{P_{p}} = \frac{V}{2 c}$

Solution

$\begin{array}{l} \frac{E_{e}}{E_{p}} = \frac{\frac{1}{2} {mV}^{2}}{hν} = \frac{1}{2} V \times \frac{mV}{h} \times \frac{h}{hν} = \frac{V}{2} \times \frac{1}{λ_{e}} \times \frac{1}{(\frac{c}{λ_{p}})} \\ Since λ_{e} = λ_{p} \\ \frac{E_{e}}{E_{p}} = \frac{V}{2 c} \\ Also, Since λ_{e} = λ_{p} \\ We can write \\ \frac{h}{P_{e}} = \frac{h}{P_{p}} \\ \Rightarrow P_{e} = P_{p} \end{array}$

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