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1.Units, Dimensions and Measurement
hard
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:
A$\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$
B$\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]$
C$\left[\mathrm{MLT}^{-2}\right]$
D$\left[\mathrm{M}^2 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]$
(JEE MAIN-2024)
Solution
$\lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}} \text { or } \mathrm{E}=\mathrm{h} \nu$
${\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]=\mathrm{h}\left[\mathrm{T}^{-1}\right]}$
$\mathrm{h}=\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]$
${\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]=\mathrm{h}\left[\mathrm{T}^{-1}\right]}$
$\mathrm{h}=\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]$
Standard 11
Physics
Similar Questions
Match List $I$ with List $II$
| LIST$-I$ | LIST$-II$ |
| $(A)$ Torque | $(I)$ $ML ^{-2} T ^{-2}$ |
| $(B)$ Stress | $(II)$ $ML ^2 T ^{-2}$ |
| $(C)$ Pressure of gradient | $(III)$ $ML ^{-1} T ^{-1}$ |
| $(D)$ Coefficient of viscosity | $(IV)$ $ML ^{-1} T ^{-2}$ |
