The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series. (R = Rydberg constant)

The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series

Q. The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series.

(R = Rydberg constant)

(A) 5R/36 , 3R/16 , 21R/100

(B) 7R/144 , 3R/16 , 16R/255

(D) 5R/36 , 8R/9 , 15R/16

Correct Answer: (A)

Explanation

For the Balmer series of hydrogen atom, the electron transitions take place from higher energy levels (n = 3, 4, 5, …) to the level n = 2.

The wave number of a spectral line is given by the Rydberg formula:

Wave number = R ( 1 / 2² − 1 / n² )

For n = 3:

Wave number = R ( 1/4 − 1/9 ) = 5R/36

For n = 4:

Wave number = R ( 1/4 − 1/16 ) = 3R/16

For n = 5:

Wave number = R ( 1/4 − 1/25 ) = 21R/100

All the above wave numbers correspond to transitions ending at n = 2.

Hence, these spectral lines belong to the Balmer series.

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