Chapter 5, Problem 51A

Interpretation Introduction

Interpretation:

Energy of an ultraviolet photon that has a wavelength $1.18\times {10}^{-8}m$ needs to be determined.

Concept introduction:

The relation between energy, Planck’s constant and wavelength is as follows:

$E=hv$

Here, h is Planck’s constant and v is frequency.

Answer to Problem 51A

$1.68\times {10}^{-16}J$

Explanation of Solution

Given:

Wavelength of photon = $1.18\times {10}^{-8}m$

As per, wave equation of motion:

$C=\lambda \times v$

Where $c$ is a constant whose value is $3\times {10}^{8}m/s,$ and v represents frequency

Calculation:

Now putting value of $\lambda =1.18\times {10}^{-9}$ m and $c=3\times {10}^{8}m{s}^{-1}$ ,

$\begin{array}{l}3\times {10}^{8}m/s=1.18\times {10}^{-9}m\times v\\ v=\frac{3\times {10}^{8}m/s}{1.18\times {10}^{-9}m}\\ =2.54\times {10}^{17}{\text{ s}}^{-1}\end{array}$

Now, as per Planck Einstein equation

$E_{photon}= hv$

Where $E$ is energy of photon,

$h$ refers to Planck’s constant

And

$v$ refers to frequency.

Now putting value of $h=6.626\times {10}^{-34}Js$ and $v=2.54\times 10s^{-1},$

$\begin{array}{l}{E}_{photon}= hv\\ E_{photon}=\left(6.626\times {10}^{-34}\text{ Js}\right)\left(2.54\times {10}^{17}{\text{ s}}^{-1}\right)\\ E_{photon}=16.8\times {10}^{-17}J\\ =1.68\times {10}^{-16}J\end{array}$.

Conclusion

Thus, energy of photon is $1.68\times {10}^{-16}J$.