If e is the electronic charge, c is the speed of light in free...

e

is the electronic charge,

c

is the speed of light in free space and

h

is Planck's constant, the quantity

\dfrac{1}{4\pi{ε}_{0}}\dfrac{{\left|e\right|}^{2}}{hc}

has dimensions of :

Options

A $\left[{MLT}^{0}\right]$
B $\left[{M}^{0}{L}^{0}{T}^{0}\right]$
C $\left[{MLT}^{- 1}\right]$
D $\left[{LC}^{- 1}\right]$

Correct answer

B. $\left[{M}^{0}{L}^{0}{T}^{0}\right]$

Step-by-step solution

F = \dfrac{1}{4\pi{ϵ}_{0}}\dfrac{{e}^{2}}{{r}^{2}} $$ E = \dfrac{hc}{\lambda} $$ \left[\dfrac{{e}^{2}}{4\pi{ε}_{0}} \times \dfrac{1}{hc}\right] = \dfrac{F{r}^{2}}{E\lambda} = $\left({M}^{0}{L}^{0}{T}^{0}\right)$

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