MHT CET · Physics · Atomic Physics
The force acting on the electrons in hydrogen atom (Bohr's theory) is related to the principle quantum number 'n' as
- A \(n^{-2}\)
- B \(n^{4}\)
- C \(n^{-4}\)
- D \(n^{2}\)
Answer & Solution
Correct Answer
(C) \(n^{-4}\)
Step-by-step Solution
Detailed explanation
Now \(F=\frac{m v^{2}}{r} \)
\( v \propto \frac{1}{n} \text { and } r \propto n^{2} \)
\( F \propto \frac{1}{n^{2}} \times \frac{1}{n^{2}} \)
\( F \propto n^{-4}\)
\(\therefore \mathrm{F} \propto \frac{1}{\mathrm{n}^{2}} \times \frac{1}{\mathrm{n}^{2}}\)
\(\therefore \mathrm{F} \propto \mathrm{n}^{-4}\)
\( v \propto \frac{1}{n} \text { and } r \propto n^{2} \)
\( F \propto \frac{1}{n^{2}} \times \frac{1}{n^{2}} \)
\( F \propto n^{-4}\)
\(\therefore \mathrm{F} \propto \frac{1}{\mathrm{n}^{2}} \times \frac{1}{\mathrm{n}^{2}}\)
\(\therefore \mathrm{F} \propto \mathrm{n}^{-4}\)
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