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JEE Mains · Physics · STD 12 - 12. atoms
A particle of mass \(m\) moves in a circular orbit in a central potential field \(U\left( r \right) = \frac{1}{2}k{r^2}\). If Bohr’s quantization conditions are applied, radii of possible orbits and energy levels vary with quantum number \(n\) as
- A \({r_n} \propto \sqrt n ,{E_n} \propto n\)
- B \({r_n} \propto \sqrt n ,{E_n} \propto \frac{1}{n}\)
- C \({r_n} \propto n,{E_n} \propto n\)
- D \({r_n} \propto {n^2},{E_n} \propto \frac{1}{{{n^2}}}\)
Answer & Solution
Correct Answer
(A) \({r_n} \propto \sqrt n ,{E_n} \propto n\)
Step-by-step Solution
Detailed explanation
\(\mathrm{U}=\frac{1}{2} \mathrm{kr}^{2}\) Force, \(F=-\frac{d U}{d r}=-k r\) For circular motion \(\frac{\mathrm{mv}^{2}}{\mathrm{r}}=\mathrm{kr}\) .... \((i)\) And \({ mvr }=\frac{n h}{2 \pi}\) .... \((ii)\)…
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