Question.
Calculate the wavelength of an electron moving with a velocity of $2.05 \times 10^{7} \mathrm{~ms}^{-1}$.
Calculate the wavelength of an electron moving with a velocity of $2.05 \times 10^{7} \mathrm{~ms}^{-1}$.
Solution:
According to de Broglie’s equation
$\lambda=\frac{\mathrm{h}}{m v}$
Where, $\lambda=$ wavelength of moving
particle $m=$ mass of particle $v=$
velocity of particle $\mathrm{h}=$ Planck's
constant
Substituting the values in the expression of $\lambda$ :
$\lambda=\frac{6.626 \times 10^{-34} \mathrm{Js}}{\left(9.10939 \times 10^{-31} \mathrm{~kg}\right)\left(2.05 \times 10^{7} \mathrm{~ms}^{-1}\right)}$
$\lambda=3.548 \times 10^{-11} \mathrm{~m}$
Hence, the wavelength of the electron moving with a velocity of $2.05 \times 10^{7} \mathrm{~ms}^{-1}$ is $3.548$ $\times 10^{-11} \mathrm{~m}$.
According to de Broglie’s equation
$\lambda=\frac{\mathrm{h}}{m v}$
Where, $\lambda=$ wavelength of moving
particle $m=$ mass of particle $v=$
velocity of particle $\mathrm{h}=$ Planck's
constant
Substituting the values in the expression of $\lambda$ :
$\lambda=\frac{6.626 \times 10^{-34} \mathrm{Js}}{\left(9.10939 \times 10^{-31} \mathrm{~kg}\right)\left(2.05 \times 10^{7} \mathrm{~ms}^{-1}\right)}$
$\lambda=3.548 \times 10^{-11} \mathrm{~m}$
Hence, the wavelength of the electron moving with a velocity of $2.05 \times 10^{7} \mathrm{~ms}^{-1}$ is $3.548$ $\times 10^{-11} \mathrm{~m}$.