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 α , where α is _______ .

Question

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 α , where α is _______ .,

MARKS App · Accepted Answer

F = - d U d r = - 4 U 0 r 3 = m v 2 r m v 2 = 4 U 0 r 4 V ∝ r 2 r 3 ∝ n ⇒ r ∝ n 1 / 3 = 3

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