Question

The amount of energy emitted when an electron jumps from $n=4\text{to}n=2$ in an H-atom is:

• A. $4.08\times {10}^{-19}\text{J}$
• B. $0.408\times {10}^{-19}\text{J}$
• C. $2.02\times {10}^{-19}\text{J}$
• D. $40.8\times {10}^{-19}\text{J}$

Answer 1

The correct option is A $4.08\times {10}^{-19}\text{J}$

Energy emitted when an electron makes a transition from a higher energy level to a lower energy level is given by :
$E_{\text{emitted}}=13.6\text{eV}\times (\frac{1}{n_1^2}-\frac{1}{n_2^2})$
Where, $n_2$ is the higher energy level and $n_1$ is the lower energy level.
$\Rightarrow E=13.6\text{eV}\times (\frac{1}{4}-\frac{1}{16})=2.55\text{eV}$
$\Rightarrow E=2.55\times 1.602\times {10}^{-19}\text{J}$
$\Rightarrow E=4.08\times {10}^{-19}\text{J}$.