A particle of mass m moves in a circular orbit in a central potential field ${\rm{U}}\left( {\rm{r}} \right) = \frac{1}{2}{\rm{k}}{{\rm{r}}^2}$. If Bohr’s quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number n as

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TuteeHUB · Accepted Answer

${{\rm{r}}_{\rm{n}}} \propto \sqrt {\rm{n}} ,{{\rm{E}}_{\rm{n}}} \propto \frac{1}{{\rm{n}}}$

TuteeHUB · Answer

rn ∝ n, En ∝ n

TuteeHUB · Answer

${{\rm{r}}_{\rm{n}}} \propto {{\rm{n}}^2},{{\rm{E}}_{\rm{n}}} \propto \frac{1}{{{{\rm{n}}^2}}}$

TuteeHUB · Answer

${{\rm{r}}_{\rm{n}}} \propto \sqrt {\rm{n}} ,{{\rm{E}}_{\rm{n}}} \propto {\rm{n}}$

1.	A particle of mass m moves in a circular orbit in a central potential field \({\rm{U}}\left( {\rm{r}} \right) = \frac{1}{2}{\rm{k}}{{\rm{r}}^2}\). If Bohr’s quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number n as
A.	rn ∝ n, En ∝ n
B.	\({{\rm{r}}_{\rm{n}}} \propto {{\rm{n}}^2},{{\rm{E}}_{\rm{n}}} \propto \frac{1}{{{{\rm{n}}^2}}}\)
C.	\({{\rm{r}}_{\rm{n}}} \propto \sqrt {\rm{n}} ,{{\rm{E}}_{\rm{n}}} \propto {\rm{n}}\)
D.	\({{\rm{r}}_{\rm{n}}} \propto \sqrt {\rm{n}} ,{{\rm{E}}_{\rm{n}}} \propto \frac{1}{{\rm{n}}}\)
Answer» D. \({{\rm{r}}_{\rm{n}}} \propto \sqrt {\rm{n}} ,{{\rm{E}}_{\rm{n}}} \propto \frac{1}{{\rm{n}}}\)

A particle of mass m moves in a circular orbit in a central potential field \({\rm{U}}\left( {\rm{r}} \right) = \frac{1}{2}{\rm{k}}{{\rm{r}}^2}\). If Bohr’s quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number n as

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