According to the Bohr model, the radius of the nth orbit ($r_n$) is given by the expression $r_n = n^2 a_0$, where $a_0$ is the radius of the ground state orbit (Bohr radius) and $n$ is the principal quantum number . For the ground state, $n = 1$. The first excited state corresponds to $n = 2$. Therefore, the radius of the first excited state is $r_2 = (2)^2 a_0 = 4a_0$, which is four times the ground state radius.