Chapter 31, Problem 50P

To determine

The wavelength of photons.

Answer to Problem 50P

The wavelength is $\mathrm{\lambda }=7.041\text{ m}$ and it lies in radio wave region of the spectrum.

Explanation of Solution

Given info:

Magnetic field, $\mathrm{B}=1.000\text{ T}$

Formula used:

The wavelength can be given as:

  $\mathrm{\lambda }=\frac{\mathrm{c}}{\mathrm{f}}$

Calculation:

The frequency for the given magnetic field will be:

  $\mathrm{f}=42.58\text{ MHz}=42.58\times {10}^6\text{Hz}$

Also, the speed of light is $\mathrm{c}=3\times {10}^8\text{m/s}$

So, the wavelength can be calculated as follows:

  $\begin{array}{l}\mathrm{\lambda }=\frac{3\times {10}^8\text{m/s}}{42.58\times {10}^6\text{Hz}}\\ \mathrm{\lambda }=7.041\text{ m}\end{array}$

Hence, the wavelength lies in the radio wave region of the spectrum.

Conclusion:

Thus, the wavelength is $\mathrm{\lambda }=7.041\text{ m}$ and it lies in radio wave region of the spectrum.