Question

Which of the following is an integral multiple of $\dfrac{h}{2\pi}$ in Bohr's model of an hydrogen atom?

• A. Radius of an atom
• B. Kinetic energy
• C. Potential energy
• D. Angular momentum

Hint:

Bohr quantisation: angular momentum is n h over 2 pi.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Bohr's postulate says that the electron moves only in orbits where its angular momentum is quantised:
\[ L=mvr=n\frac{h}{2\pi},\quad n=1,2,3,\dots \]

Step 2: Check the options
(A) The radius varies as \(n^2\), so it is not an integral multiple of \(h/2\pi\).
(B) Kinetic energy varies as \(1/n^2\).
(C) Potential energy varies as \(-1/n^2\).
(D) Angular momentum is exactly \(n\dfrac h{2\pi}\).

Step 3: Conclusion
Only the angular momentum is an integral multiple of \(\dfrac h{2\pi}\), option (D).

Final Answer:
Bohr's rule fixes the angular momentum at n h over 2 pi, option (D). \[ \boxed{\text{Angular momentum}} \]