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# Calculate the Broglie wavelength of an electron moving with 1% of the speed of light ?

$\begin{array}{1 1} (a)\;2.43 \times 10^{-10}\;m \\(b)\;3.43 \times 10^{-10}\;m \\ (c)\;2.43 \times 10^{-11}\;m \\ (d)\;2.43 \times 10^{-12}\;m \end{array}$

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A)
Solution :
According to be Brogile equation $\lambda= \large\frac{h}{mv}$
Mass of electron $=9.1 \times 10^{-31}\;kg$
Planck's constant $=6.626 \times 10^{-34}\;kgm^2s^{-1}$
Velocity of electron =1 % of speed of light
$\qquad= 3.0 \times 10^8 \times 0.01=3 \times 10^{6}\;ms^{-1}$
wave length of electron $(\lambda)= \large\frac{h}{m}$
$\qquad= \large\frac{(6.626 \times 10^{-34}\;kg m^2s^{-1})}{(9.1 \times 10^{-31}\;kg) \times (3 \times 10^6 ms^{-1})}$
$\qquad= 2.43 \times 10^{-10}\;m$