Question

In the hydrogen atom if the reference level of potential energy is assumed to be zero at the ground state level. Choose the incorrect statement.
$\left( {\text{A}} \right)$ The total energy of the shell increases with increases in the value of $n$.
$\left( {\text{B}} \right)$ The total energy of the shell decreases with increases in the value of $n$.
$\left( {\text{C}} \right)$ The difference in total energy of any two shells remains the same.
$\left( {\text{D}} \right)$ The total energy at the ground state becomes $13.6eV$.

Answer 1

According to Bohr, an electron can revolve only in certain orbits of definite radii. These orbits are called stable orbits or stationary orbits. In stationary orbits, the electrons do not radiate energy despite their acceleration towards the center of the orbit.

Complete step by step answer:
The hydrogen atom has only one electron and this normally occupies the lowest level and has the energy of $- 13.6eV$. When the electron is at this level, the atom is said to be in the ground state. At room temperature, nearly all the atoms of hydrogen are in the ground state.
If a hydrogen atom absorbs energy, the electron gets promoted into one of the higher energy levels. The atoms are now said to be excited. Thus, when the electron occupies other than the lowest energy level, the atom is said to be excited.
Once in an excited state, the atom is unstable. After a short interval, the electron falls back into the lowest state so that the atom is again in the ground state. The energy that was originally imparted is emitted as electromagnetic waves.
The total energy of an electron in a stationary orbit is negative which means that electrons are bound to the nucleus and it is not free to leave the atoms.
Total energy, ${E_n} = - \dfrac{{13.6}}{{{n^2}}}eV$
Where, $n = 1,{\text{ }}2,{\text{ }}3,{\text{ }} \ldots \ldots .$
The total energy of the electron increases, (it becomes less negative) as the electron goes to higher orbits. When n goes to infinity, then energy is equal to zero. And the electron becomes free.
By observing all these statements we can say the total energy of the shell decreases with increases in the value of n is an incorrect option. The remaining option is correct.
Because from the total energy equation, we can say that energy is inversely proportional to ${n^2}$

Thus, The incorrect option is B.

Note: The minimum energy required to free the electron from the ground state of an atom is called ionization energy.
The minimum energy required to excite an atom in the ground state to one of the higher stationary states is called excitation energy.