Question

Number of spectral lines in Balmer series when an electron returns from \[{7^{th}}\] to \[{1^{st}}\] orbit of hydrogen atom is:
a.) 5
b.) 6
c.) 21
d.) 15

Answer 1

Hint: To solve this question we must recall the concepts of the Hydrogen spectrum. We should remember that the number of spectral lines of a particular series were the all possible transitions from a higher energy level to the energy level corresponding to that particular series.

Complete step by step solution:
The wavelengths of emitted light depend on the energy difference between the two levels.
In a pure sample of hydrogen gas, the emission spectrum looks like distinct lines of discrete wavelengths that are absolutely specific to the element hydrogen. Some of these lines lie in the visible range of the electromagnetic spectrum, while others lie in the ultraviolet or infrared range.
The series of visible lines in the hydrogen atom spectrum is called the Balmer series. This series of spectral emission lines occur when the electron transitions from a high-energy level to the lower energy level of n=2.

To calculate the total number of spectral lines in the transition, we use the formula:
\[N = ({n_2} - {n_1})\]
Where,
\[{n_1}\]= lowest energy level
\[{n_2}\]=highest energy level
In this case for Balmer series,
\[{n_2} = 2\]
Substituting this equation in accordance with the question, we get,
\[N = (7 - 2) = 5\]
Hence, the correct answer is Option (A) 5 lines.

Additional information:
The Balmer series is particularly useful in the field of astronomy as the Balmer lines appear in many stellar objects due to the abundance of hydrogen in the universe, and therefore are commonly seen and relatively strong compared to lines from other elements.

Note: Let us now learn a little about the other lines in the hydrogen spectrum. The Lyman series involves jumps to or from the ground state, the Paschen series to n=3, the Brackett series to n=4, and the Pfund series to n=5. While the Lyman series is in the ultraviolet, Paschen, Brackett, Pfund, and Humphreys series are in the infrared region.