Question

The energy of electron in the ground state of hydrogen atom is $-13.6eV$. The energy required for the transition from $n$ = 2 to $n$=3 will be :

• A. $2eV$
• B. $4eV$
• C. $1.89eV$
• D. $2.89eV$

Answer 1

The correct option is C $1.89eV$

The energy of electron in the $n^{th}$ state of hydrogen atom is:

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

The energy of electron in the ground state ($n=1$) of hydrogen atom is $-13.6eV$.

The energy required for the transition from n = 2 to n=3 i.e. Excitation energy required to excite an electron from state $n=2$ to $n=3$ is:

$\Delta E=\frac{E_1}{n_3^2}-\frac{E_1}{n_2^2}$

$\Delta E=(-13.6)[\frac{1}{3^2}-\frac{1}{2^2}]$

$\Delta E=-13.6\left[\frac{-5}{36}\right]$

$\Delta E=1.89eV$