First slide

Matter waves (DC Broglie waves)

Question

The speed of an electron having wavelength of $10^{- 10}$ m is

Moderate

A

4.24 x $10^{6}$ m/s
B

5.25 x $10^{6}$ m/s
C

7.25 x $10^{6}$ m/s
D

6.25 x $10^{6}$ m/s

Solution

The de-Broglie wavelength is given by $λ = \frac{h}{p}$
where h is Planck's constant and p is momentum. Also p = mu
where m is mass, u is velocity $u = \frac{h}{mλ}$
Putting the numerical values, we have
$\begin{array}{l} h = 6 .6 \times 10^{- 34} Js, m = 9 .1 \times 10^{- 31} kg, λ = 10^{- 10} m \\ \Rightarrow u = \frac{6 .6 \times 10^{- 34}}{9 .1 \times 10^{- 31} \times 10^{- 10}} = 7 .25 \times 10^{6} m / s \end{array}$

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