Chapter 5.3, Problem 24LC

Interpretation Introduction

Interpretation: The frequency of radiation emitted by a hydrogen lamp in the visible region of the spectrum needs to be determined using the given wavelength.

Concept Introduction: The relation between wavelength and frequency of radiation is as follows:

  $v=\frac{c}{\lambda }$

Here, $v$ is the frequency of radiation, $\lambda$ is the wavelength of radiation, and c is the speed of light. The value of the speed of light is constant that is $3\times {10}^8\text{ m/s}$ .

Answer to Problem 24LC

  $4.6\times {10}^{14}\text{ Hz}$

Explanation of Solution

From the given wavelength of radiation, the frequency can be calculated as follows:

  $v=\frac{c}{\lambda }$

Here, the value of the speed of light is constant that is $3\times {10}^8\text{ m/s}$ and the wavelength of radiation is given $6.56\times {10}^{-5}\text{ cm}$ .

Substitute the values in the above formula,

  $\begin{array}{c}v=\frac{3\times {10}^8\text{ m/s}}{6.56\times {10}^{-5}\text{ cm}\left(\frac{{10}^{-2}\text{ m}}{1\text{ cm}}\right)}\\ =0.46\times {10}^{8+5+2}{\text{ s}}^{-1}\\ =0.46\times {10}^{15}{\text{ s}}^{-1}\\ =4.6\times {10}^{14}{\text{ s}}^{-1}\end{array}$

Here,

  $1\text{ Hz}=1{\text{ s}}^{-1}$

Thus,

  $\begin{array}{c}v=4.6\times {10}^{14}{\text{ s}}^{-1}\left(\frac{1\text{ Hz}}{1{\text{ s}}^{-1}}\right)\\ =4.6\times {10}^{14}\text{ Hz}\end{array}$

Conclusion

The frequency of radiation emitted by a hydrogen lamp in the visible region of the spectrum is $4.6\times {10}^{14}\text{ Hz}$ .