Question:

A particle of mass m moves in a circular orbit in a central potential field U(r) = 1/2kr². If Bohr's quantization condition is applied, radii of possible orbitals and energy levels vary with quantum number n as:

rₙ∝√n, Eₙ∝1/n

rₙ∝√n, Eₙ∝n

rₙ∝n², Eₙ∝1/n²

rₙ∝n, Eₙ∝n

The correct option is D
rₙ∝√n, Eₙ∝n
F = dV/dR = kr = mv²/r
mvr = nħ/2π
r²∝n
r∝√n
E = 1/2kr² + 1/2mv²∝r²∝n