Given relation

The de-Broglie wavelength is $\lambda = \frac{h}{\sqrt{2mE}}$

Write dimensions of each quantity

• Wavelength: $[\lambda] = [L]$
• Mass: $[m] = [M]$
• Energy: $[E] = [ML^2T^{-2}]$

Find dimensions of $\sqrt{2mE}$

Since 2 is dimensionless, $[mE] = [M]\,[ML^2T^{-2}] = [M^2L^2T^{-2}]$

Therefore, $[\sqrt{mE}] = [M L T^{-1}]$

Use the de-Broglie formula to find $[h]$

From $\lambda = \frac{h}{\sqrt{2mE}}$ we get $[h] = [\lambda]\,[\sqrt{2mE}]$

So, $[h] = [L]\,[MLT^{-1}] = [ML^2T^{-1}]$

Match with the options

$[h] = [ML^2T^{-1}]$

This corresponds to Option C.

Verification with stored answer

Stored correct answer: C

Derived answer: C

Hence, the derived answer agrees with the stored answer.