Question

The energy of an electron in the nth orbit is given by en= 13.6/n^2 ev. Calculate the energy required to excite an electron from ground state to the second excited state.

Answer 1

Answer: The energy required to excite an electron from ground state to the second state is 10.2 eV.

Explanation:

It is given in the problem that the  energy of an electron in the nth orbit is given by en= 13.6/n^2 ev.

Calculate the energy required to excite an electron from ground state to the second excited state.

$E_{n}=E_{1}-E_{2}$                           ....... (1)

Here,$E_{2}$ is the energy in the second excited state and $E_{2}$  is the energy in the ground state.

Calculate the energy of an electron in the ground state is;

$E_{n}=\frac{13.6}{n^2} eV$

Put n=1.

$E_{n}=\frac{13.6}{(1)^2} eV$

$E_{1}=\frac{13.6}{(1)^2} eV$

Calculate the energy of an electron in the second  state is;

$E_{n}=\frac{13.6}{n^2} eV$

Put n=2.

$E_{n}=\frac{13.6}{(2)^2} eV$

$E_{1}=\frac{13.6}{(2)^2} eV$

Put $E_{1}=\frac{13.6}{(1)^2} eV$ and  $E_{1}=\frac{13.6}{(2)^2} eV$ in the equation (1).

$E_{n}=E_{1}-E_{2}$

$E_{n}=\frac{13.6}{1^2}-\frac{13.6}{2^2}$

$E_{n}=10.2 eV$

Therefore, the energy required to excite an electron from ground state to the second state is 10.2 eV.