JEE MAIN - Physics (2025 - 4th April Evening Shift - No. 20)
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 :
Both Statement I and Statement II are correct
Statement I is correct but Statement II is incorrect
Both Statement I and Statement II are incorrect
Statement I is incorrect but Statement II is correct
Explanation
$$\begin{aligned}
&\begin{aligned}
& \mathrm{E}=\mathrm{hf} \\
& \mathrm{ML}^2 \mathrm{~T}^{-2}=[\mathrm{h}] \times\left[\mathrm{T}^{-1}\right] \\
& {[\mathrm{h}]=\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]} \\
& \mathrm{L}=[\mathrm{MVR}]=\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right] \\
& \mathrm{L}=\frac{\mathrm{nh}}{2 \pi}
\end{aligned}\\
&\mathrm{L} \text { is integral multiple of } \frac{\mathrm{h}}{2 \pi}
\end{aligned}$$
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