MHT CET · Physics · Atomic Physics
The force acting on the electron in hydrogen atom (Bohr' theory) is related to the principle quantum number ' \(n\) ' as
- A \(\mathrm{n}^4\)
- B \(\mathrm{n}^{-4}\)
- C \(\mathrm{n}^2\)
- D \(\mathrm{n}^{-2}\)
Answer & Solution
Correct Answer
(B) \(\mathrm{n}^{-4}\)
Step-by-step Solution
Detailed explanation
The centripetal force of the rotating electron is given by \(F=\frac{m^2}{r}\)
But, according to Bohr, \(\mathrm{v} \propto \frac{1}{\mathrm{n}}\) and \(\mathrm{r} \propto \mathrm{n}^2\)
i.e. \(\mathrm{F} \propto \frac{\mathrm{v}^2}{\mathrm{r}^2}\)
\(\Rightarrow \mathrm{F} \propto \frac{1}{\mathrm{n}^2 \mathrm{n}^2}\)
\(\mathrm{F} \propto \frac{1}{\mathrm{n}^4}\)
But, according to Bohr, \(\mathrm{v} \propto \frac{1}{\mathrm{n}}\) and \(\mathrm{r} \propto \mathrm{n}^2\)
i.e. \(\mathrm{F} \propto \frac{\mathrm{v}^2}{\mathrm{r}^2}\)
\(\Rightarrow \mathrm{F} \propto \frac{1}{\mathrm{n}^2 \mathrm{n}^2}\)
\(\mathrm{F} \propto \frac{1}{\mathrm{n}^4}\)
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