Answer:
We
know that electrostatic potential energy between two electrons separated by
distance r is
\[U=\frac{ee}{4\pi {{\in }_{0}}r}\] \[\therefore \] units of \[\frac{{{e}^{2}}}{{{\in
}_{0}}}=U\times r=\left( M{{L}^{2}}{{T}^{-2}} \right)L\]
Also. energy of a photon,
\[E=h\upsilon
=\frac{hc}{\lambda }\]\[\therefore \] units of \[hc=E\times \lambda
=\left( M{{L}^{2}}{{T}^{-2}} \right)L\]
Now \[\frac{{{e}^{2}}}{{{\in }_{0}}hc}=\frac{\left(
M{{L}^{2}}{{T}^{-2}} \right)L}{\left( M{{L}^{2}}{{T}^{-2}} \right)L}=\left(
{{M}^{0}}{{L}^{0}}{{T}^{0}} \right)\], i.e., the given quantity is
dimensionless.
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