The acceleration of an electron in the first orbit of the hydrogen atom (Z=1) is 

Speed of electron in first orbit $(n=1)$ of Hydrogen atom $(z=1)$

$\begin{array}{l}\mathrm{V}=\frac{{\mathrm{Ze}}^2}{2{\mathrm{\epsilon }}_0\mathrm{nh}}\\ \therefore \mathrm{V}=\frac{{\mathrm{e}}^2}{2{\mathrm{\epsilon }}_0\mathrm{h}}-----\left(1\right)\end{array}$ 

Radius  of Bohr first bit 

$\begin{array}{l}\mathrm{r}=\frac{{\mathrm{n}}^2{\mathrm{h}}^2{\mathrm{\epsilon }}_0}{{\mathrm{\pi me}}^2\mathrm{Z}}\\ \therefore {\mathrm{\epsilon }}_0=\frac{{\mathrm{r\pi me}}^2\mathrm{z}}{{\mathrm{h}}^2{\mathrm{n}}^2}(\mathrm{n}=1,\mathrm{z}=1)\end{array}$

$\therefore {\mathrm{\epsilon }}_{\mathrm{o}}=\frac{{\mathrm{r\pi me}}^2}{{\mathrm{h}}^2}$

Substituting this in the first equation

  $\mathrm{v}=\frac{{\mathrm{e}}^2}{2\frac{{\mathrm{r\pi me}}^2\mathrm{h}}{{\mathrm{h}}^2}}$

$\mathrm{v}=\frac{\mathrm{h}}{2\mathrm{\pi mr}}$

 $\Rightarrow {\mathrm{v}}^2=\frac{{\mathrm{h}}^2}{4{\mathrm{\pi }}^2{\mathrm{m}}^2{\mathrm{r}}^2}$

$\frac{{\mathrm{v}}^2}{\mathrm{r}}=\frac{{\mathrm{h}}^2}{4{\mathrm{\pi }}^2{\mathrm{m}}^2{\mathrm{r}}^3}$
Acceleration   $\mathrm{a}=\frac{{\mathrm{v}}^2}{\mathrm{r}}$

$\therefore \mathrm{a}=\frac{{\mathrm{h}}^2}{4{\mathrm{\pi }}^2{\mathrm{m}}^2{\mathrm{r}}^3}$