Question

What is the energy of a hydrogen atom in the first excited state if the potential energy is taken to be zero at ground state?

Answer 1

Hint: Let us know that atoms are made up of an atomic nucleus and electrons that are constantly moving about it. Discrete energy levels with the highest possibility of holding electrons have been discovered by scientists. These energy levels are made up of electrons with a specific quantity of energy. The ground state is the lowest attainable energy level for electrons in a system, whereas the excited state is any state of the system with a higher energy than the ground state.

Complete answer:
We know that the total energy of hydrogen atom in ground state is \[ - 13.6{\text{eV}}\]
And, the total energy in the first excited state is \[ - 3.4{\text{eV}}\]
And the potential energy in ground state is \[{\text{27}}{\text{.2eV}}\]
According to the question, the potential energy at ground state is taken to be zero.
This means that the whole energy spectrum will now be shifted by a value of \[{\text{27}}{\text{.2eV}}\].
In this condition, the energy of a hydrogen atom in the first excited state will be given by,
\[ - 3.4{\text{eV + 27}}{\text{.2eV}} = 23.8{\text{e}}V\]

Note:
We need to know that atoms can exist in a variety of energy states. The energy states are discrete, meaning that they only exist at certain values. As a result, an atom can only migrate to a new energy level if it absorbs or emits the exact amount of energy needed to bridge the gap between two energy levels. An electron is normally in its ground state, which has the lowest energy. It may jump from the ground state to a higher energy level, known as an excited state, after absorbing energy.