Question

The magnitude of total energy of nth orbit in Bohr model is \(\left|E_{n}\right|\) and angular momentum is L_n. What is the relation between them?

Answer 1

E_n = \(\frac{Z^{2} e^{4} m}{8 \varepsilon_{0}^{2} n^{2} h^{2}}\) ………….. (1)
From Bohr’s second postulate
L_n = \(\frac{n h}{2 \pi}\) ……………….. (2)
From relation (2), nh = 2πL_n
Putting value of nh in equation (1),
\(\left|E_{n}\right|=\left[\frac{Z^{2} e^{4} m}{8 \varepsilon_{0}^{2}}\right] \frac{1}{\left(2 \pi L_{n}\right)^{2}}\)