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

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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.

List $I$	List $II$
$A$. Spring constant	$I$. $(T^{-1})$
$B$. Angular speed	$II$. $(MT^{-2})$
$C$. Angular momentum	$III$. $(ML^2)$
$D$. Moment of inertia	$IV$. $(ML^2T^{-1})$

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

Match List $I$ with List $II$:
List $I$ List $II$
$A$. Spring constant $I$. $(T^{-1})$
$B$. Angular speed $II$. $(MT^{-2})$
$C$. Angular momentum $III$. $(ML^2)$
$D$. Moment of inertia $IV$. $(ML^2T^{-1})$

Choose the correct answer from the options given below:

Which one of the following does not have the same dimensions?

An object is moving through a liquid. The viscous damping force acting on it is proportional to its velocity. The dimension of the constant of proportionality is:

The dimensional formula of a physical quantity is $[M^{a} L^{b} T^{c}]$. Then,that physical quantity is:

What is the dimension of a physical quantity? Explain using a suitable example.

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