Chapter 5.3, Problem 17SP

Interpretation Introduction

Interpretation: The energy of the quantum of radiant needs to be calculated using a given frequency.

Concept Introduction: Quantum is defined as the smallest amount of energy absorbed or emitted as electromagnetic radiation. It is directly proportional to the frequency of the radiation.

The relation between the energy of quantum and frequency of radiation is as follows:

  $E=hv$

Here, h is Planck’s constant $6.626\times {10}^{-34}\text{ Js}$

Answer to Problem 17SP

  $3.313\times {10}^{-22}\text{ J}$

Explanation of Solution

The given frequency of radiation is $5\times {10}^{11}{\text{ s}}^{-1}$ . Energy of quantum can be calculated using the following formula:

  $E=hv$

Substitute the values,

  $\begin{array}{c}E=\left(6.626\times {10}^{-34}\text{ Js}\right)\left(5\times {10}^{11}{\text{s}}^{-1}\right)\\ =33.13\times {10}^{-34+11}\text{ J}\\ =33.13\times {10}^{-23}\text{ J}\\ =3.313\times {10}^{-22}\text{ J}\end{array}$

Therefore, the energy of the quantum of radiant required is $3.313\times {10}^{-22}\text{ J}$ .

Conclusion

The energy of a quantum of radiant required is $3.313\times {10}^{-22}\text{ J}$ .