Ionization potential of hydrogen atom is `13.6 V`. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy `12.1 eV`. The spectral lines emitted by hydrogen atoms according to Bohr's theory will be

Options

A. one
B. two
C. three
D. four

Answer

C

Explanation

Ionisation potential of hydrogen atom is `13.6eV`. Energy rquired for exciting the hydrogen atom in the ground state to orbit n is given by
`E=E_n-E_1`
i.e, ` 12.1=-(13.6)/(n^2)-((-13.6)/(1^2))=-(13.6)/(n^2)+13.6`
or, `-1.5=(-13.6)/(n^2)` or, `n^2=(13.6)/(1.5)=9` or, ` n=3`
Number of spectral lines emitted `=(n(-1))/(2)=(3xx2)/(2)=3`.