What is the ratio of the difference in energy between the first and second Bohr orbit to the differe — Atomic Structure Chemistry Question

💡 Solution & Explanation

The energy difference between orbits $n_1$ and $n_2$ is proportional to $(\frac{1}{n_1^2} - \frac{1}{n_2^2})$. Between $1^{st}$ and $2^{nd}$ orbits: $\Delta E_{1,2} \propto (\frac{1}{1^2} - \frac{1}{2^2}) = \frac{3}{4}$. Between $2^{nd}$ and $3^{rd}$ orbits: $\Delta E_{2,3} \propto (\frac{1}{2^2} - \frac{1}{3^2}) = \frac{1}{4} - \frac{1}{9} = \frac{5}{36}$. Ratio $= \frac{3/4}{5/36} = \frac{3}{4} \times \frac{36}{5} = \frac{27}{5}$.