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

$$\lambda = \frac{h}{\sqrt{2mE}}$$, so $$h = \lambda\sqrt{2mE}$$.

Dimensions: $$[\lambda] = [L]$$, $$[m] = [M]$$, $$[E] = [ML^2T^{-2}]$$.

$$[h] = [L] \cdot [M \cdot ML^2T^{-2}]^{1/2} = [L] \cdot [M^2L^2T^{-2}]^{1/2} = [L][MLT^{-1}] = [ML^2T^{-1}]$$.

The correct answer is Option 1: $$[ML^2T^{-1}]$$.

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