Units & Dimensions

JEE Main level, single correct, medium

52 of 149

Question 52 of 149

The de-Broglie wavelength associated with a particle of mass mm and energy EE is h/2mEh / \sqrt{2 m E}. The dimensional formula for Planck's constant is :

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Answer: (A) [ML2 T−1]\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]

λ=h2mE or E=hν[ML2 T−2]=h[T−1]h=[ML2 T−1]\begin{aligned} & \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]\end{aligned}

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