Dual behaviour of matter proposed by de Broglie led to the discovery of electron microscope often used for the highly magnified images of biological molecules and other type of material
Question:
Dual behaviour of matter proposed by de Broglie led to the discovery of electron microscope often used for the highly magnified images of biological molecules and other type of material. If the velocity of the electron in this microscope is $1.6 \times 10^{6} \mathrm{~ms}^{-1}$, calculate de Broglie wavelength associated with this electron.
Solution:
From de Broglie's equation,
$\lambda=\frac{\mathrm{h}}{m v}$
$\lambda=\frac{6.626 \times 10^{-34} \mathrm{Js}}{\left(9.10939 \times 10^{-31} \mathrm{~kg}\right)\left(1.6 \times 10^{6} \mathrm{~ms}^{-1}\right)}$
$=4.55 \times 10^{-10} \mathrm{~m}$
$\lambda=455 \mathrm{pm}$
$\therefore$ de Broglie's wavelength associated with the electron is $455 \mathrm{pm}$.