NEET Physics Atomic Physics NEET PYQ-Atomic Physics

Ionization potential of hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. According to Bohr's theory, the spectral lines emitted by hydrogen will be:     [AIPMT (S) 2006]

A) two

B) three

C) four

D) one

Correct Answer: B

Solution :

Ionization energy corresponding to ionization potential \[=-13.6\text{ }eV\]

Photon energy incident \[=12.1\text{ }eV\]

So, the energy of electron in excited state

\[=-13.6\,+12.1=-1.5\,eV\]

i.e., \[{{E}_{n}}=-\frac{13.6}{{{n}^{2}}}eV\]

\[-1.5\,=\frac{-13.6}{{{n}^{2}}}\]

\[\Rightarrow \] \[{{n}^{2}}=\frac{-13.6}{-1.5}\approx 9\]

\[\therefore \] \[n=3\]

i.e., energy of electron in excited state corresponds to third orbit.

The possible spectral lines are when electron jumps from orbit 3rd or 2nd; 3rd to 1st and 2nd to 1st. Thus 3 spectral lines are emitted.