The de-Broglie wavelength associated with a particle of mass and energy is The dimensional formula for Planck's constant is

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Solution

Q.
The de-Broglie wavelength associated with a particle of mass $m$ and energy $E$ is $h / \sqrt{2 m E} .$ The dimensional formula for Planck's constant is [2024]

1 $[M L^{- 1} T^{- 2}]$

2 $[M L^{2} T^{- 1}]$

3 $[M L T^{- 2}]$

4 $[M^{2} L^{2} T^{- 2}]$

Ans.
(2)

Given $λ = \frac{h}{\sqrt{2 m E}}$

$\Rightarrow h = λ \sqrt{2 m E}$ or $h = λ p$

So dimensional formula of Planck's constant

$[h] = [l e n g t h] [M a s s \times v e l o c i t y]$

$= [L^{1}] [M^{1} L^{1} T^{- 1}] = [M L^{2} T^{- 1}]$

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