Chapter 28.1, Problem 4PP

To determine

To Calculate: Radius of the second, third and fourth energy levels of the hydrogen atom.

Explanation of Solution

Given data:

Radius of innermost orbit, $r_1=5.3\times {10}^{-11}\text{m = 0}\text{.053 nm}$

For second energy level, $n_2=2$

For third energy level, $n_3=3$

For fourth energy level, $n_4=4$

Formula used:

Orbital radius of energy level n in the hydrogen atom can be obtained by:

  $r_n=n^2\left(0.053\text{nm}\right)$

Calculation:

For second energy level, $n_2=2$

  $\begin{array}{l}{r}_n=n^2\left(0.053\text{nm}\right)\\ r_2=2^2\left(0.053\text{nm}\right)\\ r_2=0.212\text{nm}\end{array}$

For third energy level, $n_3=3$

  $\begin{array}{l}{r}_n=n^2\left(0.053\text{nm}\right)\\ r_3=3^2\left(0.053\text{nm}\right)\\ r_3=0.477\text{nm}\end{array}$

For fourth energy level, $n_4=4$

  $\begin{array}{l}{r}_n=n^2\left(0.053\text{nm}\right)\\ r_4=4^2\left(0.053\text{nm}\right)\\ r_4=0.848\text{nm}\end{array}$