Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

JEE Main 20249 AprilEvening Shift

Exam: JEE Main
Year: 2024
Date: 9 April
Shift: Evening Shift
Subject: Physics
Chapter: Units and Dimensions

JEE Main 2024 · 9 April · Evening Shift · Physics · Units and Dimensions

The de-Broglie wavelength associated with a particle of mass m and...

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 :

Options

A $\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]$
B $\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$
C $\left[\mathrm{MLT}^{-2}\right]$
D $\left[\mathrm{M}^2 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]$

Correct answer

A. $\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]$

Step-by-step solution

\begin{aligned} & \lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}} \text{\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]\end{aligned}

Practice Units and Dimensions on Quantrex Academy →

More from Units and Dimensions

In a new system of units, the units of mass, length, time and current are 5 kg, 5 m, 5 s… JEE Advanced 2026 A new unit (α) of length is chosen such that it is equal to the speed of light in vacuum.… JEE Main 2026 Consider the equation H = (x^p ε^q E^r)/(t^s) , where H= magnetic field; E= electric… JEE Main 2026 The percentage error in the calculated volume of a sphere, if there is 2\% error in its… JEE Main 2026 Match List - I with List - II. List - I List - II A. Boltzmann constant I. [M^ -1 L^3T^… JEE Main 2026 The potential energy of a particle changes with distance x from a fixed origin as V = A x… JEE Main 2026 Match List-I with List-II. List-I List-II A. Meter (L) I. (hc)/(G) B. Second (S) II.… JEE Main 2026 L , C and R represents physical quantities inductance, capacitance and resistance… JEE Main 2026 Full Units and Dimensions list All JEE Main PYQs