Question

The ratio of the difference in energy between the first and the second Bohr orbit to that between second and third Bohr orbit is

Answer 1

For a Hydrogen spectrum, Bohr's model calculated the energy for an electron in a shell 'n' as:

$E\left(n\right)=\frac{-13.6}{n^2}$

For Hydrogen-atom:

$E_3=\frac{-13.6}{3^2}=\frac{-13.6}{9}=-1.5eV$

$E_2=\frac{-13.6}{2^2}=\frac{-13.6}{4}=-3.4eV$

$E_1=\frac{-13.6}{1^2}=-13.6eV$

$E_{21}=E_2-E_1=(-3.4)-(-13.6)=-3.4+13.6=10.2eV$

$E_{32}=E_3-E_2=(-1.5)-(-3.4)=-1.5+3.4=1.9eV$

$\frac{E_{21}}{E_{32}}=\frac{10.2eV}{1.9eV}=\frac{27}{5}$.