Q70 / 75 · JEE Main 2025 (4 Apr Shift 2) · Physics

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 :

  • A
    Both Statement I and Statement II are correct
  • B
    Statement I is incorrect but Statement II is correct
  • Correct answer
    C
    Statement I is correct but Statement II is incorrect
  • D
    Both Statement I and Statement II are incorrect

Solution

$\begin{aligned}<br/>& \mathrm{E}=\mathrm{hf} \\ & \mathrm{ML}^2 \mathrm{~T}^{-2}=[\mathrm{h}] \times\left[\mathrm{T}^{-1}\right] \\ & {[\mathrm{h}]=\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]} \\ & \mathrm{L}=[\mathrm{MVR}]=\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right] \\ & \mathrm{L}=\frac{\mathrm{nh}}{2 \pi}<br/>\end{aligned}$
L is integral multiple of $\frac{\mathrm{h}}{2 \pi}$

Hence, the correct answer is option: 'C'.

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