Chapter 5, Problem 95A

Interpretation Introduction

Interpretation:

Wavelength of light with a frequency of $5.77\times {10}^{14}Hz$ needs to be determined.

Concept introduction:

Wavelength of light is inversely proportional to frequency and directly proportional to velocity of light.

Answer to Problem 95A

Wavelength $\lambda =5.1\times {10}^{-7}m$

Explanation of Solution

Given: Frequency of light $5.77\times {10}^{14}Hz$

Wavelength relates to frequency as follows:

$\lambda =v/f$

In which $f$ is the frequency, $v$ is the speed of light and $\lambda$ is the wavelength.

$v=3\times {10}^{8}m/s$

And

$f=5.77{.10}^{14}Hz=5.77\times {10}^{14}{s}^{-1}$

Calculation:

$\lambda =v/f$

$\lambda =\frac{3\times {10}^{8}m/s}{5.77\times {10}^{14}{s}^{-1}}$

Or,

$\lambda =5.1\times {10}^{-7}m$

Conclusion

Thus, wavelength $\lambda =5.1\times {10}^{-7}m$.