The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth stationary orbit will be:

<p>The radius of the nth stationary orbit in the Bohr model of an atom is directly proportional to the square of its principal quantum number n and inversely proportional to the atomic number Z. This relationship is represented by the formula $r_n = \frac{n^2h^2}{4\pi^2kme^2Z},$ where :</p> <ul> <li> <p>$n$ is the principal quantum number,</p> </li> <li> <p>$h$ is Planck's constant,</p> </li> <li> <p>$k$ is the Coulomb constant,</p> </li> <li> <p>$m$ is the mass of the electron,</p> </li> <li> <p>$e$ is the charge of the electron, and</p> </li> <li> <p>$Z$ is the atomic number of the nucleus (for hydrogen, Z=1).</p> </li> </ul> <p>To find the radius of the fourth orbit ($r_4$), in comparison to the third orbit ($r_3$), we apply the formula with $n=4$ for the fourth orbit and $n=3$ for the third orbit, and simplify as follows:</p> <p>$$\begin{aligned} & \frac{r_4}{r_3} = \frac{(4^2)h^2}{4\pi^2kme^2Z} \div \frac{(3^2)h^2}{4\pi^2kme^2Z} = \frac{(4^2)}{(3^2)} \\\\ & = \frac{16}{9} \end{aligned}$$ <p>Thus, the radius of the fourth stationary orbit is $\frac{16}{9}$ times the radius of the third stationary orbit, $R$. Therefore, $r_4 = \frac{16}{9} R$.</p>