Question

If the value of kinetic energy of an electron in $1st$ orbit of a hydrogen atom is $2.18\times {10}^{-18}J$, then what will be the energy of the electron in $5th$ orbit?

Answer 1

Energy of electron is given by:

$E_n=\frac{13.6\times z}{n^2}$

$⟹E_n\propto \frac{1}{n^2}$

$⟹\frac{E_1}{E_5}=\frac{5^2}{1^2}$

$⟹E_5=\frac{E_1}{25}=\frac{2.18\times {10}^{-18}}{25}=8.72\times {10}^{-20}J$

So, the energy of electron in 5th orbit is $8.72\times {10}^{-20}$ J.