Question

Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy $12.1eV$. According to Bohr's theory, the spectral lines emitted by hydrogen will be

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

Answer 1

The correct option is B three

When an electron is excited from an energy level $n_i$ to an energy level $n_f$ then the energy gap $\Delta E$ is given by
$\Delta E=13.6Z^2(\frac{1}{n_i^2}-\frac{1}{n_f^2})$
Energy provided is $12.1eV$ and $Z=1$ for hydrogen. Also $n_i=1$ for ground state electrons.
Hence
$12.1=13.6(1-\frac{1}{n_f^2})$
which gives $n_f=3$
Now no. of emissions lines is given by
$\frac{n(n-1)}{2}$
Here $n=3$. Hence no. of spectral lines emitted
= $\frac{3\times 2}{2}=3$