Chapter 28, Problem 36A

To determine

To write: A physics problem with real-life objects for which the following equation would be a part of the solution:

  $E=13.6\text{ eV}\left(\frac{1}{1^2}-\frac{1}{3^2}\right)$

Explanation of Solution

Introduction:

Energy of a hydrogen atom is given by,

  $E_n=-13.6\text{ eV }\times \frac{1}{n^2}$

Where $n$ is the principal quantum number.

A real problem for the given solution can be written as follows:

A hydrogen atom is at $E_3$ energy level. How much energy would be released if the atom dropped down to $E_1$ energy level.

Conclusion:

According to above written problem, $E_f=E_1$ and $E_i=E_3$ . On calculating the energy of the hydrogen atom at both the levels and then using the formula of energy transitions of an atom, the given solution is obtained.

  $\begin{array}{l}E=E_f-E_i\\ \text{ =}{E}_1-E_3\\ \text{ =}\frac{-13.6}{1^2}-\frac{-13.6}{3^2}\\ =13.6\text{ eV}\left(\frac{1}{1^2}-\frac{1}{3^2}\right)\end{array}$