Physics - Unit & Dimension Question with Solution | TestHub

$\because \mathrm{Capacitance} C=\frac{Q}{∆V}$

$\mathrm{Also}, \left[\frac{hc}{\lambda }\right]= \left[\frac{hc}{a_0}\right]= \left[\mathrm{Energy}\right]$.

$\therefore \left[C\right]= \frac{\left[Q\right]}{\left[∆V\right]}= \frac{\left[Q\right] \left[Q\right]}{\left[∆V\right] \left[Q\right]}$

$\because W=q∆V \Rightarrow \left[Q\right] \left[∆V\right]= \left[\mathrm{Energy}\right]$

$\therefore \left[C\right]= \frac{\left[Q^2\right]}{\left[\mathrm{Energy}\right]}= \frac{\left[Q^2\right] \left[a_0\right]}{\left[hc\right]}$

$\therefore \left[\mathrm{Capacitance}\right]= \frac{\left[Q^2\right] \left[a_0\right]}{\left[hc\right]}$

$\Rightarrow u= \frac{e^2 a_0}{hc}$