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Use Bohr's postulate to prove that the radius of nth orbit in a hydrogen atom is proportional to n2. |
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Answer» As the electron revalues in an stationary orbit, Thus centrifugal force acting on the electron to balanced by the coulombic force Fcentrifugal = Fcoulomb \(\frac{mv^2}{r_n}=\frac{kl^2}{{r_n}^2}\) \(r_n=\frac{kl^2}{m{v_n}^2}\) We take \(m\,v_nr_n= \frac{nh}{2\pi}\) \(\because V_n = \frac{nh}{2\pi mr_n}\) Then, \(r_n = \frac{kl^2}{m{v_n}^2}\) \(r_n = \frac{kl^2}{m}.\frac{(2\pi mr_n)^2}{n^2h^2}\) \(r_n = \frac{kl^2 4\pi^2m^2{r_n}^2}{m\,n^2h^2}\) \(r_n = \frac{n^2h^2}{kl^24\pi^2m}\) \(r_n \propto n^2\) |
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