The de-Broglie wavelength associated with a particle of mass m and energy E is h / √ 2mE . The dimensional formula

Question

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 :

(1) \(\left[\mathrm{ML}^{-1} \mathrm{T}^{-2}\right]\)

(2) \(\left[\mathrm{ML}^{2} \mathrm{T}^{-1}\right]\)

(3) \(\left[\mathrm{MLT}^{-2}\right]\)

(4) \(\left[\mathrm{M}^{2} \mathrm{L}^{2} \mathrm{T}^{-2}\right]\)   

Answer 1

Correct option is : (2) \( \left[\mathrm{ML}^{2} \mathrm{T}^{-1}\right]\)   

\(\lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}}\) or \(\mathrm{E}=\mathrm{h} \nu\)

\(\left[\mathrm{ML}^{2} \mathrm{T}^{-2}\right]=\mathrm{h}\left[\mathrm{T}^{-1}\right]\)

\(\mathrm{h}=\left[\mathrm{ML}^{2} \mathrm{T}^{-1}\right]\)