A monochromatic light is incident on a hydrogen . . .

Question : A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is x×10¹⁵Hz. The value of x is __________. [Given h=4.25×10^-15 eVs]

Doubt by Ankit

Solution : 
We know, 
Maximum number of spectral line are given by the formula 

[n(n-1)]/2

where n is the orbit from which the electron is falling back i.e. n₂.

ATQ
[n(n-1)]/2 = 6
n(n-1) = 12
n²-n=12

n²-n-12=0
n²-4n+3n-12=0
n(n-4)+3(n-4)=0
(n-4)(n+3)=0
n-4=0 OR n+3=0
n=4 OR n=-3
but n can't be negative. 

so n=-3 is rejected. 

Hence, n=4 i.e. n₂=4 and n1=1

E=E₄-E₁
hν=0.85-(-13.6)
hν=12.75
ν=12.75/4.25×10^-15
v=3×10¹⁵ Hz

on comparing with 
v=x×10¹⁵ Hz

Hence, we get x=3.