Question

What is the wavelength of ultraviolet light whose frequency is $\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{15}}\mathbf{}\mathit{H}\mathit{z}$?

Short answer

The wavelength of the ultraviolet light is $60\text{nm}$.

Step-by-step solution

Identification of given data

The frequency ultraviolet light $f=5\times {10}^{15}\text{Hz}$

Determine the formulas to calculate the wavelength of the ultraviolet light.

The expression to calculate the wavelength is given as follows.

$\mathit{\lambda }\mathbf{=}\frac{\mathbf{v}}{\mathbf{f}}$ …(i)

Here,$\mathit{\nu }$ is the speed of the light.

Determining the wavelength of the ultraviolet light.

Calculate the wavelength of the ultraviolet light.

Substitute$5\times {10}^{15}\text{Hz}$ for f and$3\times {10}^{8}m/s$ for $\nu$into equation (i).

$$\begin{gathered} \lambda =\frac{3\times {10}^{8}m/s}{5\times {10}^{15} \text{Hz}} \\ =\frac{3\times {10}^{-7}}{5} \text{m} \\ =0.6\times {10}^{-7} \text{m} \\ =60\text{nm} \end{gathered}$$

Hence the wavelength of the ultraviolet light is $60\text{nm}$.