Question

The de-Broglie wavelength of an electron (mass $1\times {10}^{-30}kg$, charge$=1.6\times {10}^{-19}C$) with kinetic energy of $200eV$ is: (Planck's constant $6.6\times {10}^{-34}J$):

• 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 $8.25\times {10}^{-11}m$

The de-Broglie wavelength $\lambda =\frac{h}{\sqrt{2mk}}$
Given $h=6.6\times {10}^{-34}Js$
$m=1\times {10}^{-30}kg$
$K=200eV=200\times 1.6\times {10}^{-19}J$
Substituting all these values
$\lambda =\frac{6.6\times {10}^{-34}}{\sqrt{2\times 1\times {10}^{-30}\times 200\times 1.6\times {10}^{-19}}}$
$=0.825\times {10}^{-10}=8.25\times {10}^{-11}m$