Question

Hydrogen atom emits blue light when an electron in it jumps from $n=4$ energy level to $n=2$ energy level. Which colour of light would the atom emit when an electron in it jumps from $n=5$ level to the $n=2$ level?

• A. Red
• B. Yellow
• C. green
• D. violet

Answer 1

The correct option is D violet

Energy emitted during the transition of an electron, in hydrogen atom, is given by,
$E_n-E_p=E_1(\frac{1}{p^2}-\frac{1}{n^2})$

In transition, from orbit $5\to 2$,

$E_{5\to 2}=E_1(\frac{1}{2^2}-\frac{1}{5^2})=\frac{21E_1}{100}$

In transition, from orbit $4\to 2$,

$E_{4\to 2}=E_1(\frac{1}{2^2}-\frac{1}{4^2})=\frac{3E_1}{4}$

As more energy is liberated in transition from orbit $5\to 2$, as compared to the transition from orbit $4\to 2$, and, more energy liberated means more frequency of the emitted light.
Now, violet has more frequency, less wavelength and more energy as compared Red.

Hence, $\left(D\right)$ is the correct answer.

Alternate solution:

Based on the intuition about energy emitted during transition of an electron, we can conclude that, more energy will be emitted during the $5\to 2$ transition.
i.e. $E_{5\to 2}>E_{4\to 2}$
So, more energy should be emitted due to the $5\to 2$ transition. And, violet has more energy than red.

Hence, $\left(D\right)$ is the correct answer.

$$\begin{array}{c}\text{Why this question?}\\ \text{This question is based on the emission spectra of hyfrogen atom}\end{array}$$