JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
The de-Broglie wavelength associated with a particle of mass \(m\) and energy \(E\) is \(\mathrm{h} / \sqrt{2 m E}\) The dimensional formula for Planck's constant is _______.
- A \(\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]\)
- B \(\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]\)
- C \(\left[\mathrm{MLT}^{-2}\right]\)
- D \(\left[\mathrm{M}^2 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]\)
Answer & Solution
Correct Answer
(B) \(\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]\)
Step-by-step Solution
Detailed explanation
\(\lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}} \text { or } \mathrm{E}=\mathrm{h} \nu\) \({\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]=\mathrm{h}\left[\mathrm{T}^{-1}\right]}\) \(\mathrm{h}=\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]\)
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