First slide

Wave nature of matter

Question

If the momentum of an electron is changed by $∆ p$ , then the de-Broglie wavelength associated with it changes by 0.50%. The initial momentum of the electron will be

Moderate

A

$\frac{Δ p}{200}$
B

$\frac{Δ p}{199}$
C

$199 Δ p$
D

$400 Δ p$

Solution

$\begin{array}{l} I n i t i a l l y : λ = \frac{h}{p} \\ F i n a l l y : λ - \frac{0.5}{100} λ = \frac{h}{p + Δ p} \\ \Rightarrow \frac{199 λ}{200} = \frac{h}{p + Δ p} \\ \Rightarrow \frac{199}{200} \frac{h}{p} = \frac{h}{p + Δ p} \\ \Rightarrow p = 199 Δ p \end{array}$

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