Chapter 28.1, Problem 3PP

To determine

To Calculate: Energy difference between fourth and second energy level in the hydrogen atom.

Answer to Problem 3PP

  $2.55\text{eV}$

Explanation of Solution

Given data:

For second energy level, $n_2=2$

For fourth energy level, $n_4=4$

Formula used:

Energy of hydrogen atom in energy level n can be:

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

Calculation:

For second energy level, $n_2=2$

  $E\left(2\right)=\frac{1}{2^2}\times \left(-13.6\right)=-3.4\text{eV}$

For fourth energy level, $n_4=4$

  $E\left(4\right)=\frac{1}{4^2}\times \left(-13.6\right)=-0.85\text{eV}$

Energy difference:

  $E_4-E_2=-0.85\text{eV}-\left(-3.4\text{eV}\right)=2.55\text{eV}$

Conclusion:

Energy difference between fourth and second energy level in the hydrogen atom is $2.55\text{eV}$ .