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