Question

How do you calculate the energy of an electron?

Answer 1

Step 1: Bohr's model for calculating the energy of hydrogen-like atoms:

We can calculate the energy of an electron for hydrogen or hydrogen-like atoms by using the Bohr model of the atom.

An expression relating to the energy of an electron in the hydrogen atom according to the Bohr model is given by;

$\mathrm{E}=-\frac{13.6}{{\mathrm{n}}^2}\mathrm{eV}$

Where n is represented as the principal quantum number.

Step 2: Calculation of the energy of an electron:

For an electron existing in the ground state of a hydrogen atom the value of the principal quantum number,$\mathrm{n}=1:$

Hence, the energy of an electron in the ground state can be calculated by using the above formula,

$\begin{array}{l}\mathrm{E}=-\frac{13.6}{1^2}\\ =-13.6\mathrm{eV}\end{array}$

Here the negative sign refers that the energy of the electron in the atom is lower than the energy of a free electron at rest, which is taken as zero.

Therefore, The energy of an electron in the ground state of a hydrogen atom can be calculated by using the formula given by the Bohr model, and here the energy has been found to be $-13.6\mathrm{eV}.$