Question

Consider a hydrogen atom in the ground state. What is the energy of its electron?

Answer 1

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.:brainly.com/question/1550767

2. Chemical equation representing the first ionization energy for lithium.: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.

Answer 2

The energy of an electron in a hydrogen atom is:
E= (-2.179 x 10 ^-18 J)(1/n^2)

where n is the principle energy level of the electron.

E= (-2.179 x 10 ^-18 J)(1/4)
E= -2.179 x 10 ^-18 J
E = -5.4 x 10 ^-19 J