Single Choice

Hydrogen atom in ground state is excited by a monochromatic radiation of $$\lambda= 975 \overset {o}{A}$$. Number of spectral lines in the resulting spectrum emitted will be

A$$3$$
B$$2$$
C$$6$$
Correct Answer
D$$10$$

Solution

Energy of the photon, $$E=\dfrac {hc}{\lambda}=\dfrac {1240}{97.5}=12.75eV$$
This energy is equal to energy gap between $$n = 1 (-13.6)$$ and $$n = 4(-0.85)$$.
So by this energy, the electron will excite from $$n = 1$$ to $$n= 4$$.
When the electron will fall back, numbers of spectral lines emmitted $$=\dfrac {n(n-1)}{2}=\dfrac {(4)(4-1)}{2}=6$$

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