Bohr's model of hydrogen atom.

We know that

$E_{k}=\dfrac{{\left(mv\right)}^{2}}{2m}$ , where $E_{k}$ is Kinetic Energy.

Using $mvr=\dfrac{nh}{2\pi} \Longrightarrow mvr=n\hbar$ , we have,

$\left(\sqrt{2mE_{k}}\right)r=n\hbar$

$\Longrightarrow E_{k}=\dfrac{n^{2}\hbar^{2}}{2mr^{2}}$

Since, the question is asked for 4th Bohr orbit of hydrogen,

$\therefore r_{4}=a_{0}\times\dfrac{4^{2}}{1} \Longrightarrow r_{4}=16a_{0} \quad\quad\quad\quad \small\color{#3D99F6}{\because r_{n}=a_{0}\times\dfrac{n^{2}}{Z}}\small\color{#3D99F6}{\text{where n=orbit number, Z=atomic number of single electronic species}}$

So,

$E_{k}=\dfrac{\left(4^{2}\right)\hbar^{2}}{2m\left({16a_{0}}^{2}\right)}$

$\Longrightarrow E_{k}=\boxed{\dfrac{\hbar^{2}}{32m{a_{0}}^{2}}}$