First slide

Matter waves (DC Broglie waves)

Question

A particle of mass 1 mg has the same wavelength as an electron moving with a velocity of 3 x $10^{6}$ ms^-1. The velocity of the particle is

Moderate

A

$2.7 x 10^{- 18} {ms}^{- 1}$
B

$9 x 10^{- 2} {ms}^{- 1}$
C

$3 x 10^{- 31} {ms}^{- 1}$
D

$2.7 x 10^{- 21} {ms}^{- 1}$

Solution

Wavelength of a particle is given by
$\begin{array}{l} λ = \frac{h}{p} \\ Where h is Planck' s constant . \\ Wavelength of an electron is given by λ_{e} = \frac{h}{p_{e}} \\ But λ = λ_{e} \\ So, p = p_{e} \\ o r mv = m_{e} v_{e} or v = \frac{m_{e} v_{e}}{m} \\ Putting the under given data \\ m_{e} = 9 .1 \times 10^{- 31} kg, \\ v_{e} = 3 \times 10^{6} m / s, \\ m = 1 mg = 1 \times 10^{- 6} kg \\ v = \frac{9 .1 \times 10^{- 31} \times 3 \times 10^{6}}{1 \times 10^{- 6}} = 2 .7 \times 10^{- 18} {ms}^{- 1} \end{array}$

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