Question

Ionization potential of a hydrogen atom is \[13.6{\text{eV}}\]. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy \[12.1{\text{ eV}}\] . According to Bohr's theory, the spectral lines emitted by hydrogen will be:
A.One
B.Two
C.Three
D.Four

Answer 1

Hint: To answer this question, recall the concept of Bohr atomic theory. He modified the atomic structure model and explained that the electrons move in fixed orbitals and not anywhere in between and he also explained that each orbit has a fixed energy level.
The formula used:
 \[{{\text{E}}_{\text{n}}} = \dfrac{{ - 13.6}}{{{{\text{n}}^{\text{2}}}}}\], where \[{\text{n}}\]is the shell of the electron and \[{{\text{E}}_{\text{n}}}\] is the excited energy level

Complete step by step answer:
According to Bohr's theory, you should know that the electrons in an atom move from a lower energy level to a higher energy level. This phenomenon occurs by the gain of energy where an electron moves from a higher energy level to lower energy level by losing energy.
The given values in the questions are ionization energy (IE) \[13.6eV\]and
Excited photon energy is \[12.1{\text{ eV}}\].
Therefore, the energy of the atom at the excited state: \[13.6 - 12.1\; = 1.5{\text{eV}}\]
\[ \Rightarrow {{\text{E}}_{\text{n}}} = 1.5{\text{eV}}\].
The formula of exciting energy is given by: \[{{\text{E}}_{\text{n}}} = \dfrac{{ - 13.6}}{{{{\text{n}}^{\text{2}}}}}\].
Substituting the values in the equation:
\[ \Rightarrow 1.5 = \dfrac{{ - 13.6}}{{{n^2}}}\]
\[ \Rightarrow {n^2} = 9\]
\[ \Rightarrow n = 3\]
Thus, the excited electron is in the 3rd orbit. When the excited electron comes back to the ground state it will jump from 3rd orbit to 2nd orbit, 2nd to 1st orbit and 3rd to 1st orbit and ​thus, 3 spectral lines are emitted.

The correct answer is option C.

Note:
Limitations of Bohr’s Model of an Atom
1.Bohr’s model was not able to explain the Zeeman Effect. It is defined as the splitting of the spectral lines in presence of the magnetic field.
2.It was not able to explain the Stark effect which is the splitting of spectral lines in presence of an electric field.
3.It violates the Heisenberg Uncertainty Principle.
4.It could not explain the spectra obtained from larger atoms.