Chapter 7, Problem 7.27P

Interpretation Introduction

Interpretation:

The energy difference for the transition of an electron from $n=5$ to $n=2$ for 1 mole of $\text{H}$ atoms is to be determined.

Concept introduction:

Bohr’s atomic model had the following postulates:

1) The electrons in atoms revolve around the nucleus in certain circular orbits. The orbits are the energy levels. The orbits closer to the nucleus are of lesser energy than the ones further from the nucleus.

2) The energy of an electron changes sharply upon transition from one energy level to another.

3) The angular momentum of an electron moving around the nucleus is quantised. Thus the angular momentum of an electron is a whole number multiple of $\text{h/}2\pi$.

The equation to find the difference in the energy between the two levels in hydrogen-like atoms is,

$\Delta E=-2.18\times {10}^{-18}\text{ J}\left(\frac{1}{n_{\text{final}}^2}-\frac{1}{n_{\text{initial}}^2}\right)$        (1)

Here,

$\Delta E$ is the difference in the energy between two levels.

$n_{\text{final}}$ is the lower energy level.

$n_{\text{initial}}$ is the higher energy level.