Question

Calculate the wavelength of an electron if it is travelling at a speed of $1.6\times {10}^8{\text{ms}}^{-1}$.

Mass of an electron $=9.1\times {10}^{-31}\text{kg}$

• A. $4.5\times {10}^{-11}\text{m}$
• B. $4.5\times {10}^{-12}\text{m}$
• C. $4.5\times {10}^{-10}\text{m}$
• D. $4.5\times {10}^{-13}\text{m}$

Answer 1

The correct option is B $4.5\times {10}^{-12}\text{m}$

Given:

$v=1.6\times {10}^8{\text{ms}}^{-1}$

The wavelength associated with an electron is given by,

$\lambda =\frac{h}{p}=\frac{h}{mv}$

$\Rightarrow \lambda =\frac{6.6\times {10}^{-34}}{9.1\times {10}^{-31}\times 1.6\times {10}^8}$

$\Rightarrow \lambda =4.5\times {10}^{-12}\text{m}$

Hence, option $\left(A\right)$ is the correct answer.