Instead of angular momentum quantization a sudent posits that energy is quantized as E = - E 0 / n E 0 0 and n is a positive integer. Which of the following options is correct?

Question

Instead of angular momentum quantization a sudent posits that energy is quantized as E = - E 0 / n E 0 > 0 and n is a positive integer. Which of the following options is correct?, The radius of the electron orbit is r ∝ n, The speed of the electron is v ∝ n, The angular speed of the electron is ω ∝ 1 / n, The angular momentum of the electron is ∝ n

MARKS App · Accepted Answer

F e = m v 2 r ⇒ m v 2 r = k ( Z e ) ( e ) r 2 1 2 m v 2 = K Z e 2 2 r … i (Kinetic energy) Potential energy = K q 1 q 2 r = K ( Z e ) ( - e ) r … ii Total energy = K E + P E = - K Z e 2 2 r = - E 0 n ∴ r ∝ n As kinetic energy = K Z e 2 2 r ⇒ K E ∝ 1 n or v 2 ∝ 1 n ⇒ v 2 ∝ 1 n L = m v r L ∝ v r L ∝ 1 n ( n ) ∝ n ⇒ L ∝ n

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