Question

The energy associated with the first orbit in the hydrogen atom is –2.18 × ${10}^{–18}$ J $ato{m}^{–1}$ . What is the energy associated with the fifth orbit?

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

Answer 1

Energy associated with the fifth orbit of hydrogen atom is calculated as:
$E_5=\frac{-(2.18\times {10}^{-18})}{(5{)}^2}=\frac{-2.18\times {10}^{-18}}{25}{E}_5=-8.72\times {10}^{-20}J$

Radius of Bohr’s $n^{th}$ orbit for hydrogen atom is given by, $r_n=\left(0.0529nm\right)n^2$
For, n = 5
$r_5=\left(0.0529nm\right)(5{)}^2$
$r_5=1.3225nm$