Chapter 5, Problem 104A

Interpretation Introduction

Interpretation:

The number of photons of infrared radiation having frequency of $4.88\times {10}^{13}\text{Hz}$ and required to provide energy of $\text{1}\text{.00}\text{J}$ needs to be determined.

Concept introduction:

In the electromagnetic radiation spectrum, the infrared region has the range of wavelength from 700 nm to 1 mm. This range lies between visible light and radio waves.

Answer to Problem 104A

The number of photons of infrared radiation is $3.10\times {10}^{19}$.

Explanation of Solution

Photons can be calculated by using the equation given below where $v$ represents the frequency of the photon i.e. $4.88\times {10}^{13}{\text{s}}^{-1}$ and h represents the Plank’s constant i.e. $6.626\times {10}^{-34}\text{J}\text{.s}$. First, calculate the energy of the photon as follows:

$\begin{array}{c}{\text{E}}_{\text{photon}}=\text{h}v\\ =\left(6.626\times {10}^{-36}\text{J}{\text{.s}}^{-1}\right)\times \left(4.88\times {10}^{13}{\text{s}}^{-1}\right)\\ =3.23\times {10}^{-20}\text{J}\end{array}$

Hence, the energy of the photon is $3.23\times {10}^{-20}\text{J}$.

Once the energy of the photon is calculated, divide the energy of $\text{1}\text{.00}\text{J}$ by the energy of the photon i.e. $3.23\times {10}^{-20}\text{J}$.

$\begin{array}{c}\text{n}=\frac{\text{E}}{{\text{E}}_{\text{photon}}}\left(\text{n}=\text{number}\text{of}\text{photons}\right)\\ =\frac{1.00\text{J}}{3.23\times {10}^{-20}\text{J}}\\ =3.10\times {10}^{19}\text{photons}\end{array}$

Hence, the number of photons of infrared radiation is $3.10\times {10}^{19}$.

Conclusion

The number of photons of infrared radiation is $3.10\times {10}^{19}$.