Question

The de Broglie wavelength of an electron (mass = $1\times {10}^{-30}$ kg, charge = $1.6\times {10}^{-1}C$) with a kinetic energy of 200 eV is (Planck's constant = $6.6\times {10}^{-34}Js$)

• A. $9.60\times {10}^{-11}m$
• B. $8.25\times {10}^{-11}m$
• C. $6.25\times {10}^{-11}m$
• D. $5.00\times {10}^{-11}m$

Answer 1

The correct option is B $8.25\times {10}^{-11}m$

Given : $m=1\times {10}^{-30}$ kg $e=1.6\times {10}^{-19}C$ $h=6.6\times {10}^{-34}Js$

Kinetic energy $K=200eV$

de Broglie wavelength $\lambda =\frac{h}{\sqrt{2mK}}=\frac{h}{\sqrt{2m\left(200\right)e}}$

$\therefore$ $\lambda =\frac{6.6\times {10}^{-34}}{\sqrt{2\left({10}^{-30}\right)\left(200\right)(1.6\times {10}^{-19})}}$

OR $\lambda =\frac{6.6\times {10}^{-34}}{8\times {10}^{-24}}$ $⟹$ $\lambda =8.25\times {10}^{-11}m$