The radius of third stationary orbit of electron for Bohr's atom is...

From Bohr's atomic model, it follows that

${r}_{n} = \dfrac{{n}^{2}}{Z}{r}_{1} . . . \left(1\right)$

Following equation (1), it can be written that

$\dfrac{{r}_{4}}{{r}_{3}} = \dfrac{{4}^{2}}{{3}^{2}} ⇒ {r}_{4} = \dfrac{16}{9}R$