A He-atom is de-excited from and energy level "n" to ground state to emit two consecutive photons of wavelength `1085Å`. Then n will be-

Options

A. 3
B. 4
C. 5
D. 6

Answer

C

Explanation

`E=-13.6 z^(2)//n^(2) =-(13.6xx4)/(n^(2)) =-(54.4)/(n^(2)) eV`
in coming to ground state
`DeltaE=E_(0) -E_(i)`
`=((-54.5)/(n^(2))) -((-54.4)/(1))`
`=54.4 (1-(1)/n^(2)) eV`
But `DeltaE =E_(pb) =(hc)/(lambda_(1)) +(hc)/(lambda_(2))`
`=12400 ((1)/(1085) +(1)/(304)) eV`
From (1) & (2)
`54.4(1-(1)/(n^(2))) =52.08`
`rArr 1-(-1)/(n^(2)) =0.96 rArr n=5`