JEE PYQ: Atomic Physics Question 9
Question 9 - 2021 (17 Mar Shift 2)
A particle of mass $m$ moves in a circular orbit in a central potential field $U(r) = U_0 r^4$. If Bohr’s quantization conditions are applied, radii of possible orbitals $r_n$ vary with $n^{1/\alpha}$, where $\alpha$ is ____.
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Answer: 3
Solution
$F = \frac{-dU}{dr} = -4U_0r^3 = \frac{mv^2}{r}$. So $mv^2 = 4U_0r^4$, $v \propto r^2$. Using $mvr = \frac{nh}{2\pi}$, we get $r^3 \propto n$, so $r \propto n^{1/3}$. Thus $\alpha = 3$.
BETA
