Question 175: Units , Dimensions and Error Analysis

Question

If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity ${1 \over {4\pi {\varepsilon _0}}}{{|e{|^2}} \over {hc}}$ has dimensions of :

Accepted Answer

Given
e = electronic charge
c = speed of light in free space
h = Planck's constant
We know, E = ${{hc} \over \lambda }$
and $F = {1 \over {4\pi {\varepsilon _0}}}{{{q^2}} \over {{d^2}}}$ $ \Rightarrow $ ${{{q^2}} \over {4\pi {\varepsilon _0}}} = F{d^2}$
${1 \over {4\pi {\varepsilon _0}}}{{{e^2}} \over {hc}} $
= ${{F{d^2}} \over {E\lambda }}$
= ${{Fd.d} \over {E\lambda }}$
= ${d \over \lambda }$
$ = $ dimensionless
$ = \left[ {{M^0}{L^0}{T^0}} \right]$

Answer

$[ML{T^{ - 1}}]$

Answer

$[ML{T^0}]$

Answer

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

Answer

$[L{C^{ - 1}}]$

Units , Dimensions and Error Analysis

If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity {1 \over {4\pi {\varepsilon _0}}}{{|e{|^2}} \over {hc}} has dimensions of :

Choose the correct answer: