The dimensions of \(e^{2} / 4 \pi \epsilon_{0} h c\) , where e, \varepsilon_0, h and c are electronic charge, electric permittivity, Planck’s constant and velocity of light in vacuum respectively
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\(\left[e\right] = \left[AT\right],\) \(\epsilon_0 = \left[M^{-1} L^{-3} T^{4} A^{2}\right],\) \(\left[h\right] = \left[ML^{2}T^{-1}\right]\)
and [c] = [L T^{-1}]
\(\left[\frac{e^{2}}{4 \pi \epsilon_{0} h c}\right]=\left[\frac{A^{2} T^{2}}{M^{-1} L^{-3} T^{4} A^{2} \times M L^{2} T^{-1} \times L T^{-1}}\right]\)
\(= \left[ M^{0} L^{0} T^{0} \right]\)
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