Concept:

Bohr Model of Hydrogen Atom

• Bohr proposed a model for the hydrogen atomin which asingle electron revolves around a stationary nucleus of positive charge Ze(called hydrogen-like atom).
• A moving electron in its circular orbit behaves like a particle-wave.
• As a result, standing waves are produced and thetotal distance traveled by a wave is an integral number of wavelengths.

​This gives the relation:\(2πr_k = \frac{kh}{mv_k}\)= kλ ----(1)

Where rkis the radius of the kthorbit, andλ is the wavelength.

Also Thede Broglie wavelengthis given by:

λ =\(\frac{h}{mv_k}\) ----(2)

​Where vkis the velocity of the electron in kthorbit.

From (1) and (2) we get:

\(2πr_k = \frac{kh}{mv_k}\)

⇒\(mv_kr_k =\frac{kh}{2π}\)⇒\(m\omega_k =\frac{kh}{2π}\)

∴Angular momentum=\(m\omega_k =\frac{kh}{2π}\)

Explanation:

So, the angular momentum is given by

\(L =m\omega_k = mvr =\frac{kh}{2π}\)

k and h are constant

So, we can say that

L∝ h / 2π

So,\(\frac h {2\pi}\)is the correct option.