# The energy associated with the first orbit in the hydrogen atom

Question.

(i) The energy associated with the first orbit in the hydrogen atom is $-2.18 \times 10^{-18} \mathrm{~J}$ atom $^{-1}$. What is the energy associated with the fifth orbit?

(ii) Calculate the radius of Bohr’s fifth orbit for hydrogen atom.

Solution:

(i)Energy associated with the fifth orbit of hydrogen atom is calculated as:

$E_{5}=\frac{-\left(2.18 \times 10^{-18}\right)}{(5)^{2}}=\frac{-2.18 \times 10^{-18}}{25}$

$E_{5}=-8.72 \times 10^{-20} \mathrm{~J}$

(ii) Radius of Bohr's $n^{\text {th }}$ orbit for hydrogen atom is given by, $r_{n}=(0.0529 \mathrm{~nm}) n^{2}$

For, n = 5

$r_{5}=(0.0529 \mathrm{~nm})(5)^{2}$

$r_{5}=1.3225 \mathrm{~nm}$