The dimensions of {e^2}/(4pi varepsilon _0 hc | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The given expression is $\frac{e^2}{4\pi \varepsilon _0 hc}$.We know that the Coulomb force is given by $F = \frac{1}{4\pi \varepsilon _0} \frac{e

Vedclass · Accepted Answer

$[M^0 L^0 T^0]$

Vedclass · Answer

(A) The given expression is $\frac{e^2}{4\pi \varepsilon _0 hc}$.We know that the Coulomb force is given by $F = \frac{1}{4\pi \varepsilon _0} \frac{e^2}{r^2}$,so the dimensions of $\frac{e^2}{4\pi \varepsilon _0}$ are $[F][r^2] = [MLT^{-2}][L^2] = [ML^3T^{-2}]$.Planck's constant $h$ has dimensions $[ML^2T^{-1}]$.The velocity of light $c$ has dimensions $[LT^{-1}]$.Therefore,the dimensions of the expression are $\frac{[ML^3T^{-2}]}{[ML^2T^{-1}][LT^{-1}]} = \frac{[ML^3T^{-2}]}{[ML^3T^{-2}]} = [M^0 L^0 T^0]$.This quantity is known as the fine-structure constant,which is a dimensionless quantity.

The dimensions of ${e^2}/(4\pi \varepsilon _0 hc)$,where $e, \varepsilon _0, h,$ and $c$ are electronic charge,electric permittivity,Planck's constant,and velocity of light in vacuum respectively,are:

Similar Questions

The velocity of a particle depends upon time as $v = a + bt + ct^2$. If the velocity is in $m/s$,the unit of $a$ will be:

What is the spring constant of a spring? Write its unit and dimensional formula.

Dimensions of Gyromagnetic ratio are

Dimensions of kinetic energy are

Vedclass Test Series

Exam Paper Generator

Online Exam Module