Question

De Broglie proposed the wave nature of electrons suggesting matter waves.
Find the momentum, speed and De-Broglie wavelength of an electron with Kinetic energy of $120eV$.

Answer 1

Here , $E=120eV=120\times 1.6\times {10}^{-19}J$ , $m_e=9.1\times {10}^{-31}kg$ , $h=6,6\times {10}^{-34}Js$

Now , if $v$ be the speed of electron , then

$E=1/2m_e{v}^2$

or $v=\sqrt{2E/m_e}$

or $v=\sqrt{2\times 120\times 1.6\times {10}^{-19}/9.1\times {10}^{-31}}$

or $v=6.49\times {10}^{6}m/s$

Now , momentum of electron,

$p=m_{e}v=9.1\times {10}^{-31}\times 6.49\times {10}^6=5.9\times {10}^{-24}kgm/s$

de-Broglie wavelength of the electron,

$\lambda =h/p=6.6\times {10}^{-34}/5.9\times {10}^{-24}=1.1\times {10}^{-10}m$