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

Options

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

Answer

C

Explanation

Energy of incident photon,
`E=hf=(hC)/(lambda)`
`:.E=(6.625xx10^(-34)xx3xx10^(8))/(975xx10^(-10)xx1.6xx10^(-19))eV`
`0.012746xx10^(3)`
`=12.75eV`
Now `E=-(13.6)/(n^(2))-(-(13.6)/(1^(2)))`
`12.75=-(13.6)/(n^(2))+13.6`
`:.(13.6)/(n^(2))=13.6-12.75`
`:.(13.6)/(n^(2))=0.85eV`
`:.n^(2)=(13.6)/(0.85)=16`
`:. n=4`
`:.` No, of spectral lines,
`=(n(n-1))/(2)`
`=(4(4-1))/(2)`
`=6`