Verified answer

[tex]\\\:{ \color{red}{\maltese}}\:\:\:{\large { \underline{ \underline{\textsf{Question \: :}}}}}\\[/tex]

[tex]\sf The \: \: Bohr \: \: radius \: is \: \: given \: \: by \\ [/tex]

[tex] \sf \: \: a_0 = \frac{ \epsilon_0 {h}^{2} }{\pi \: m {e}^{2} } . \: Verify \: that \: the \: RHS \: has \: \\ [/tex]

[tex]\sf \: dimension \: of \: length.... \: \: \\\\ [/tex]

[tex]\\\:{ \color{purple}{\maltese}}\:\:\:{\large { \underline{ \underline{\textsf{Solution \: :}}}}}\\\\[/tex]

[tex] \sf \: \: The \: \: dimensions \: \: of \: \epsilon_0 \: \: can \: \: be \: \: derived \: \: from[/tex]

[tex] \sf \: \: the \: \: given \: \: formula; \\ \\ [/tex]

[tex] \sf \implies \: a_0 = \frac{ \epsilon_0 {h}^{2} }{\pi \: m {e}^{2} } \\ \\ [/tex]

[tex] \sf \implies\frac{A^{2}T^{0}{(ML^{2}T^{-1})}^{2}}{L^{2}ML^{-2}{(AT)}^{2}} \\ \\ [/tex]

[tex] \sf \implies\frac{ \: \: \: \: M ^{2} L^{2}T^{-2} \: \: \: \: \: }{ \: \: \: \: \: M ^{2} L^{3}T^{-2} \: \: \: \: \: \: } \\ \\ [/tex]

[tex] \sf \implies\frac{ \: \: [\: \: M ^{2} L^{2}T^{-2} \: \: \: ]\: \:}{ \: \: [\: \: \: M ^{2} L^{3}T^{-2} \: \: \: \:] \: \: } \\ \\ [/tex]

[tex] \sf \implies \: \: [ \: L \: ]\\ \\ [/tex]

[tex]{\therefore { \underline{ \sf { \: a_0 \: has \: dimensions \: \: of \: \: \: length ..!! }}}}[/tex]