Question

Number of spectral line in hydrogen atom is
A. $6$
B. $8$
C. $15$
D. None of the above

Answer 1

Hint:Recall the concept of spectrum of the hydrogen atom. From this emission spectrum, determine when we get the spectral lines for a hydrogen atom. We get the spectral lines when the electron in the hydrogen atom is excited and jumps from the higher energy levels to the lower energy levels. Hence, check the number of spectral lines we can get from the spectrum of the hydrogen atom.

Complete step by step answer:
We know that when the electron in the hydrogen atom gets extra energy, it excites from lower energy level to the higher energy level depending on the energy given to the electron.Since this excited electron is unstable, it cannot stay in the same higher energy level for a long time. It can stay in that higher energy level only for a nanosecond.

After this nanosecond, the excited electron returns back to its original energy level by emitting its excess energy. While returning to the original energy level, there are spectral lines formed in the spectrum of the hydrogen atom depending on the energy levels from which the electron is jumping and the energy level to which the electron is jumping.

The number of spectral lines in the spectrum of the hydrogen atom depends on the number of the energy level from which the electron is jumping and the manner in which it is descending in the lower energy levels. If the higher energy level is infinite then the number of spectral lines will also be infinite. Therefore, the number of spectral lines for hydrogen atoms are infinite.

Hence, the correct option is D.

Note: The students can check the number of spectral lines from the formula for number of spectral lines for hydrogen atom which is $$N={\displaystyle \frac{n\left(n-1\right)}{2}}$$. If the value of this energy level is infinite then the number of spectral lines obtained for hydrogen atom will also be infinite as the division of infinity by any number is also infinity.