H-atoms in ground state (13.6eV) are excited by monochromatic radiations of photon of energy 12.1eV. Find the number of spectral lines emitted in H atom.

Question

$(a)\;1\qquad(b)\;2\qquad(c)\;3\qquad(d)\;4$

Answer 1

$E_n=-13.6+12.1=1.5eV$

$\therefore n^2=\large\frac{E_1}{E_n}$

$\Rightarrow \large\frac{13.6}{1.5}$$=9$

$\Rightarrow n=3$

Thus transition occurs from $3^{rd}$ to $1^{st}$ orbit.

$\therefore$ spectral lines emitted $=\sum \Delta n$

$\Rightarrow \sum(3-1)$

$\Rightarrow \sum(2)$

$\Rightarrow 1+2=3$

Hence (c) is the correct answer.