Question

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

• A. 3
• B. 2
• C. 6
• D. 10

Answer 1

The correct option is C

6

Energy of the photon, E = hc/λ

E = (6.63 x 10^-34 x 3 x 10⁸)/(975 x 10^-10)J

E = (6.63 x 10^-34 x 3 x 10⁸)/(975 x 10^-10 x 1.6 x 10^-19) eV

We get,

E = 12.75 eV

After absorbing a photon of energy 12.75 eV, the electron will reach to the third excited state of energy -0.85 eV, since energy difference corresponding to n = 1 and n= 4 is 12.75 eV Therefore,

Number of spectral lines emitted = n(n-1)/2 = 4(4-1)/2 = 6

Hence, number of spectral lines emitted in the resulting spectrum is 6

So, the correct option is (C)