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

Options:

1. 5R/36, 3R/16, 21R/100
2. 3R/4, 3R/16, 7R/144
3. 7R/144, 3R/16, 16R/255
4. 5R/36, 3R/16, 21R/24

Solution:

For Balmer series:

n₁ = 2

Wave number:

ν̅ = R(1/2² − 1/n²)

For n = 3:

ν̅ = R(1/4 − 1/9)

= 5R/36

For n = 4:

ν̅ = R(1/4 − 1/16)

= 3R/16

For n = 5:

ν̅ = R(1/4 − 1/25)

= 21R/100

These three values appear in Option 1.

Answer:

Option 1