Atoms and Nuclei Part 2

The frequency of the emitted radiation by a particular hydrogen like ion when it makes transition from n1=ninitial to n2=nfinal is given by
f=RZ2C(

1

n2

−

1

n1

)
where, c = velocity of light
and R = Rydberg’s constant.
For H-atom, Z = 1
So, for transition from n = 3 to n = 1
f1=RC(1−

1

32

) ...(i)
Similarly for transition from n = 2 to n = 1,
f2=RC(1−

1

22

) ...(ii)
Dividing Eq. (i) by Eq. (ii), we get

f1

f2

=

Rc(1− 1 9 )

Rc(1− 1 4 )

=

8 9

34

=

32

27

Here, f1=2.92×1015‌Hz
⇒

2.92×1015

f2

=

32

27

⇒f2=

2.92×1015×27

32

=2.46×1015‌Hz