Question

the ratio of energy of 3rd and 4th orbit of hydrogen atom

Answer 1

Given: 3rd and 4th orbit of the hydrogen atom.

To find: We have to find the ratio of energy.

Solution:

The energy expression for the hydrogen atom is given as-

$E=\dfrac{-13.6}{n^2}$.

For the 3rd Bohr orbit n=3 and the energy, expression can be written as-

$E_3=\dfrac{-13.6}{3^2}\\E_3=\dfrac{-13.6}{9}$.

For the 4th Bohr orbit n=4 and the energy, expression can be written as-

$E_4=\dfrac{-13.6}{4^2}\\E_4=\dfrac{-13.6}{16}$.

Thus, the ratio of energy is as follows-

$\frac{E_3}{E_4} = \frac{ \frac{ - 13.6}{9} }{ \frac{ - 13.6}{16} } \\ \frac{E_3}{E_4} = \frac{16}{9}$

The ratio of the energy of the 3rd and 4th orbit of a hydrogen atom is 16:9.