Given below are two statements :
Statement (I) : The dimensions of Planck's constant and angular momentum are same.
Statement (II) : In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant.
In the light of the above statements, choose the most appropriate answer from the options given below :

First recall the symbols:
  • Planck’s constant  $$h$$
  • Angular momentum of an electron in Bohr orbit  $$L$$

Checking Statement (I): “The dimensions of Planck's constant and angular momentum are same.”

Write dimensions of Planck’s constant.

Planck’s constant is energy $$\times$$ time.
Energy has dimension $$ML^{2}T^{-2}$$, therefore

$$[h] = ML^{2}T^{-2}\times T = ML^{2}T^{-1}$$

Write dimensions of angular momentum.

For a particle of mass $$m$$ moving with speed $$v$$ in a circle of radius $$r$$,
$$L = mvr$$

Dimensions: $$[L] = M(LT^{-1})L = ML^{2}T^{-1}$$

Thus $$[h] = [L] = ML^{2}T^{-1}$$, so Statement (I) is correct.

Checking Statement (II): “In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant.”

Bohr’s postulate states
$$mvr = n\frac{h}{2\pi},\qquad n = 1,2,3,\dots$$ $$-(1)$$

Equation $$-(1)$$ shows that angular momentum is an integral multiple of $$\dfrac{h}{2\pi}$$ (i.e. $$\hbar$$), not of $$h$$ itself. Hence Statement (II) is incorrect.

Conclusion: Statement (I) is correct, Statement (II) is incorrect. This matches Option C.

Therefore, the most appropriate answer is Option C.