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Let $R_1$ be the radius of the second stationary orbit and $R_2$ be the radius of the fourth stationary orbit of an electron in Bohr's model. The ratio $\frac{R_1}{R_2}$ is:
Detailed Solution
In Bohr's model $r=0.529\frac{n^2}{Z}$ Å, so $r\propto n^2$. $\frac{R_1}{R_2}=\frac{2^2}{4^2}=\frac{1}{4}=0.25$.