According to Bohr's theory of H-atom, for the electron in the nth permissible orbit : |
\(\text{Linear momentum} \propto \frac{1}{n}\) \(\text{Angular Momentum} \propto n\) \(\text{Kinetic Energy } \propto \frac{1}{n^2}\) All of the above |
All of the above |
The correct answer is option 4. All of the above. \(\text{Angular Momentum Quantization }\) \(\text{mvr = }\frac{nh}{2\pi}\text{----------→(1)}\) \(\text{Centripetal force:}\) \(\frac{k(e)e}{r^2}\text{ = }\frac{mv^2}{r}\text{----------→(2)}\) \(v^2r\text{ = }\frac{ke^2}{m}\) \(\text{Substituting equation (1) in (2), we get}\) \(\text{v = }\frac{2\pi ke^2}{nh}\) \(\text{Energy: E = 13.6}\frac{Z^2}{n^2}\text{----------→(3)}\) \(\text{Linear Momentum :}\) \(\text{mvr = }\frac{nh}{2\pi r}\text{----------→(4)}\) \(\text{From the concept attached :}\) \(\text{r } \propto n^2\text{----------→(5)}\) \(\text{Hence, mv } \propto \frac{1}{n}\) \(\text{and, U = 2K.E. }\) \(E \propto \frac{1}{n^2}\) |