Question

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

• A. $3$
• B. $2$
• C. $6$
• D. $10$

Answer 1

Answer: (C)

$6$

Energy of the photon, $E=\frac{hc}{\lambda }=\frac{1240}{97.5}=12.75eV$
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 $=\frac{n(n-1)}{2}=\frac{\left(4\right)(4-1)}{2}=6$