Question

Calculate de-Broglie wavelength of an electron having kinetic energy of $1\text{GeV}$. Given mass of electron $m=9.1\times {10}^{-31}\text{kg},h=6.6\times {10}^{-34}\text{Js}$ and $e=1.6\times {10}^{-19}\text{C}$

• A. $78\times {10}^{-14}\text{m}$
• B. $7.8\times {10}^{-14}\text{m}$
• C. $3.8\times {10}^{-14}\text{m}$
• D. $38\times {10}^{-14}\text{m}$

Answer 1

The correct option is C $3.8\times {10}^{-14}\text{m}$

Given,

$K.E=1\text{GeV}={10}^9\text{eV}=1.6\times {10}^{-10}\text{J}$

The de-Broglie wavelength is given by,

$\lambda =\frac{h}{\sqrt{2mKE}}=\frac{6.6\times {10}^{-34}}{\sqrt{2\times 9.1\times {10}^{-31}\times 1.6\times {10}^{-10}}}$

$=\frac{6.6\times {10}^{-34}}{1.70\times {10}^{-20}}=3.8\times {10}^{-14}\text{m}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.