Chapter 41, Problem 1CQ

To determine

The highest energy state among the three hydrogen atom states $6p$, $5d$ and $4f$.

Answer to Problem 1CQ

Solution: The highest energy state is $4f$.

Explanation of Solution

Given Info: The states of hydrogen atom are $6p$, $5d$

and $4f$.

Formula for the energy of the atom in $n^{\text{th}}$ state is, $E_{\text{n}}=-\frac{13.6\text{eV}}{n^2}$

• $E_{\text{n}}$ is the energy of the atom in $n^{\text{th}}$ state.

• $n$ is the level of energy states.

Substitute $6$ for $n$ to find $E_{\text{n}}$.

$\begin{array}{c}{E}_6=-\frac{13.6\text{eV}}{6^2}\\ =-0.38\text{eV}\end{array}$

Substitute $5$ for $n$ to find $E_{\text{n}}$.

$\begin{array}{c}{E}_5=-\frac{13.6\text{eV}}{5^2}\\ =-0.544\text{eV}\end{array}$

Substitute $4$ for $n$ to find $E_{\text{n}}$.

$\begin{array}{c}{E}_4=-\frac{13.6\text{eV}}{4^2}\\ =-0.85\text{eV}\end{array}$

Conclusion: Therefore, the highest energy state is $6p$.