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

Explanation

Energy of the photion, `E=(hc)/(lambda)`
`E=(6.63xx10^(-34)xx3xx10^(8))/(975xx10^(-10))J`
`=(6.63xx975xx10^(-10)xx1.6xx10^(-19))eV=12.75eV`
After absorbing a photon of energy 12.75 eV, the electron will reach to third excited state of energy `-0.85eV`, since enrgy difference corresponding to n = 1 and n = 4 is 12.75 eV.
`therefore" Number of spectrual lines emitted"`
difference corresponding to n = 1 and n = 4 is 12.75 eV.
`therefore" Number of spectrual lines emitted"`
`=((n)(n-1))/(2)=((4)(4-1))/(2)=6`