Question

Given the mass of an electron is $9.1\times {10}^{-31}$Kg and K.E. is $3.0\times {10}^{-25}$ J, calculate its wavelength.

Answer 1

Step 1: Given

• Mass of an electron (m) = $9.1\times {10}^{-31}$kg
• Kinetic energy (KE) = $3.0\times {10}^{–25}$J
• Planck’s constant = h = $6.6\times {10}^{-34}$Js

Step 2: Finding the velocity

The formula to find the kinetic energy is, $KE=\frac{1}{2}m{v}^2$, where $\mathrm{m}$ is the mass and $\mathrm{v}$ is the velocity.

Find velocity by rearranging this formula and substituting the values.

That is

$$\begin{gathered} v=\sqrt{\frac{2KE}{m}} \\ v=\sqrt{\frac{2\times 3.0\times {10}^{–25}}{9.1\times {10}^{-31}}} \\ v=\sqrt{6.586x{10}^4}m{s}^{-1} \\ v=811.579m{s}^{-1} \end{gathered}$$

Step 3: Finding the wavelength ($\lambda$)

The formula to find the wavelength is $\lambda =\frac{h}{mv}$

Substitute the values,

$$\begin{gathered} \lambda =\frac{6.6\times {10}^{-34}}{9.1\times {10}^{-31}x811.579} \\ \lambda =8.99x{10}^{-7}m \end{gathered}$$

Hence, the wavelength of the electron is $8.99x{10}^{-7}m.$