Chapter 26.2, Problem 15PP

To determine

The wavelength of a green light having frequency $5.7\times {10}^{14}\text{Hz}$ .

Answer to Problem 15PP

The wavelength of a green light is $\boxed{\lambda =5.26\times {10}^{-7}\text{m}}$ .

Explanation of Solution

Given:

Frequency of an electromagnetic wave is $f=5.7\times {10}^{14}\text{Hz}$ .

Formula used:

The wavelength of electromagnetic waves is expressed as

  $\lambda =\frac{c}{f}$  ...... (1)

Here, $c$ and $f$ are speed of light in vacuum and frequency of an EM wave.

Calculation:

Substitute $3.0\times {10}^8{\text{ms}}^{\text{-1}}$ for $c$ and $5.7\times {10}^{14}\text{Hz}$ for $f$ in equation (1)

  $\begin{array}{l}\lambda =\frac{3.0\times {10}^8{\text{ms}}^{\text{-1}}}{8.2\times {10}^{14}\text{Hz}}\\ \lambda =\frac{3.0\times {10}^8{\text{ms}}^{\text{-1}}}{5.70\times {10}^{14}\text{Hz}}\\ \boxed{\lambda =5.26\times {10}^{-7}\text{m}}\end{array}$

Conclusion:

Hence, the wavelength of a green light is $\boxed{\lambda =5.26\times {10}^{-7}\text{m}}$ .