Chapter 44, Problem 1OQ

To determine

The frequency of the photons absorbed related to the magnetic field.

Answer to Problem 1OQ

Option (b). The frequency is directly proportional to the magnetic field.

Explanation of Solution

Write the expression for magnetic potential energy.

    $U=-\overrightarrow{\mu }\cdot \overrightarrow{B}$                                                                                                       (I)

Here, $U$ is the magnetic potential energy, $\overrightarrow{\mu }$ is the magnetic moment, and $\overrightarrow{B}$ is the magnetic field.

Write the expression for potential energy.

    $U=hf$                                                                                                            (II)

Here, $h$ is Planck’s constant and $f$ is the frequency.

Equate (I) and (II).

    $hf=-\overrightarrow{\mu }\cdot \overrightarrow{B}$                                                                                                    (III)

Conclusion:

From equation (III) it is clear that increase in the frequency linearly increases the magnetic field.

Therefore option (b) is correct.

The frequency is not proportional to the square of the magnetic field. Therefore option (a) is incorrect.

The frequency depends on magnetic field. Therefore option (c) is incorrect.

The frequency directly proportional to the magnetic field. Therefore option (d) is incorrect.

The frequency linearly increases the magnetic field. Therefore option (e) is incorrect.