Chapter 27, Problem 57P

To determine

Draw the energy-level diagram for ${\text{He}}^{\text{+}}$ ion

Answer to Problem 57P

Solution:

The energy-level diagram for ${\text{He}}^{\text{+}}$ ion has been drawn.

Explanation of Solution

The ${\text{He}}^{\text{+}}$ ion is more likely a hydrogen atom with 1 electron, except that it has 2 protons in its nucleus. The value of energy for the state is given by the square of the product of positive and negative charges so the formula for each energy state become

$E_n=-\frac{Z^2(13.6\text{eV})}{n^2}=-\frac{2^2\left(13.6\text{eV}\right)}{n^2}=-\frac{(54.4\text{eV)}}{n^2}$