Chapter 16.2, Problem 16PP

To determine

To Calculate: The frequency of light having wavelength $513\text{nm}$ .

Answer to Problem 16PP

The frequency light having wavelength $513\text{nm}$ is $\boxed{f=5.85\times {10}^{14}\text{Hz}}$ .

Explanation of Solution

Given:

The wavelength of the light is $\lambda =513\text{nm}$ .

Formula used:

The expression for frequency of oxygen’s spectral line is

  $f=\frac{c}{\lambda }$  ...... (1)

Here, $c$ and $\lambda$ are speed of light and wavelength.

Calculation:

Convert the wavelength of oxygen’s spectral line from nm to m

  $\begin{array}{l}\lambda =513\text{nm}\\ \lambda \text{=513}\text{nm}\times \left(\frac{{10}^{-9}\text{m}}{\text{nm}}\right)\\ \lambda =513\times {10}^{-9}\text{m}\end{array}$

Speed of light is $c=3\times {10}^8\text{m}\cdot {\text{s}}^{\text{-1}}$ .

Substitute $3\times {10}^8{\text{ms}}^{\text{-1}}$ for $c$ and $513\times {10}^9\text{m}$ for $\lambda$ in equation (1)

  $\begin{array}{l}f=\frac{3\times {10}^8\text{m}\cdot {\text{s}}^{\text{-1}}}{513\times {10}^{-9}\text{m}}\\ f=5.85\times {10}^{14}{\text{s}}^{\text{-1}}\\ \boxed{f=5.85\times {10}^{14}\text{Hz}}\end{array}$

Conclusion:

Hence, the frequency light having wavelength $513\text{nm}$ is $\boxed{f=5.85\times {10}^{14}\text{Hz}}$ .