Hydrogen atom in ground state is excited by a monochromatic radiation of `lambda = 975 Å`. Number of spectral lines in the resulting spectrum emitted will be

Options

A. `3`
B. `2`
C. `6`
D. `10`

Answer

C

Explanation

Here, `lambda=975Å=975xx10^(-10)m`
`E=(hc)/lambda=(6.63xx10^(-34)xx3xx10^(8))/(975xx10^(-10)) "joule"`
`=(6.63xx3xx10^(-16))/(975xx1.6xx10^(-19))eV=12.75 eV`
`:. E_(n)=-13.6+12.75=-8.5 eV=-13.6/(n^(2))`
Which given n=4, i.e, hydrogen atom will be excited to n=4.
Number of spectral lines `=(n(n+1))/2=(4(4-1))/2=6`