Atoms and Nuclei

The formula for wavelength is:
‌

1

λ

=R(‌

1

n12

−‌

1

n22

)
First Line of Lyman Series:
For Lyman series, n1=1. The first line means n2=2.
‌

1

λL

=R(‌

1

12

−‌

1

22

)=R(1−‌

1

4

)=R(‌

3

4

)=‌

3R

4

So, λL=‌

4

3R

Second Line of Balmer Series:
For Balmer series, n1=2. The second line means n2=4.
‌

1

λB

=R(‌

1

22

−‌

1

42

)=R(‌

1

4

−‌

1

16

)=R(‌

3

16

)=‌

3R

16

So, λB=‌

16

3R

Find the Ratio:
Now, find ‌

λL

λB

:
‌

λL

λB

=‌

‌ 4 3R

16 3R

=‌

4

16

=‌

1

4

This means λL:λB=1:4