The energy of electron in ground state of hydrogen atom is \(\boxed{-2.1799\times{{10}^{-18}}{\text{ J}}}\) , and the energy electron in excited state when n is equal to 2 is \(\boxed{-5.4498\times{{10}^{-19}}{\text{ J}}}\) .
Further explanation:
The ground state of an electron in an atom refers to its lowest energy state. The energy of the ground state is also known as zero-point energy. An excited state in an atom is a state that has higher energy than the ground state.
In case of a hydrogen atom,
The formula to calculate energy of an electron in a hydrogen atom is,
\({E_n}=\frac{{\left({-2.1799\times{{10}^{-18}}{\text{ J}}}\right)}}{{{n^2}}}\)
Here, n is a principal quantum number or energy level of an electron.
For an electron in the ground state, the value of n is 1. Thus the energy of an electron in ground state is,
\(\begin{gathered}{E_n}=\frac{{\left({-2.1799\times{{10}^{-18}}{\text{ J}}}\right)}}{{{n^2}}}\hfill\\{E_1}=\frac{{\left({-2.1799\times{{10}^{-18}}{\text{ J}}}\right)}}{{{{\left(1\right)}^2}}}\hfill\\{{\mathbf{E}}_{\mathbf{1}}}{\mathbf{=-2}}{\mathbf{.1799\times1}}{{\mathbf{0}}^{{\mathbf{-18}}}}{\mathbf{ J}}\hfill\\\end{gathered}\)
Therefore, the energy of an electron in energy level of n is equal to 2 can be calculated as follows:
First, substitute 2 for the value of n.
\(\begin{gathered}{E_n}=\frac{{\left({-2.1799\times{{10}^{-18}}{\text{ J}}}\right)}}{{{n^2}}}\\{E_2}=\frac{{\left({-2.1799\times{{10}^{-18}}{\text{ J}}}\right)}}{{{{\left(2\right)}^2}}}\\\end{gathered}\)
Then, calculate the energy as follows:
\(\begin{aligned}{E_2}=-0.54498\times{10^{-18}}{\text{ J}}\\\simeq{\mathbf{-5}}{\mathbf{.4498\times1}}{{\mathbf{0}}^{{\mathbf{-19}}}}{\mathbf{ J}}\\\end{aligned}\)
Learn more:
1. Ranking of elements according to their first ionization energy.:https://brainly.com/question/1550767
2. Chemical equation representing the first ionization energy for lithium.:https://brainly.com/question/5880605
Answer details:
Grade: Senior school
Subject: Chemistry
Chapter: Hydrogen atom
Keywords: Hydrogen atom, ground state, excited state, energy of an electron, energy in ground state, energy of electron in excited state, n=2, n=1, energy level, -5.4498x10^-19.
