Question

Write the formula for de Broglie wavelength. An electron is moving with speed of $0.5\times {10}^{3}m/s$. Find the de Broglie wavelength associated with it.

Answer 1

Mass of electron$=m_e=9.11\times {10}^{-31}Kg$

speed of electron$=V_e=0.5\times {10}^{3}m/s$

Planck constant$=h=6.626\times {10}^{-34}{m}^{2}Kg/s$

De Broglie wavelength associated with electron $=\lambda$

Momentum of the electron is given by,

Momentum of the electron$=P=m_e{V}_e=\frac{h}{\lambda }$

putting the values we get,

$P=9.11\times {10}^{-31}\times 0.5\times {10}^3=\frac{6.626\times {10}^{-34}}{\lambda }$

$\therefore \lambda =\frac{6.626\times {10}^{-34}}{9.11\times {10}^{-31}\times 0.5\times {10}^3}$

$\therefore \lambda =1.46\times {10}^{-6}m=$ De Broglie wavelength