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.
(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
$r_{5}=(0.0529 \mathrm{~nm})(5)^{2}$
$r_{5}=1.3225 \mathrm{~nm}$
(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
$r_{5}=(0.0529 \mathrm{~nm})(5)^{2}$
$r_{5}=1.3225 \mathrm{~nm}$