According to Bohr's model of the hydrogen atom, the radius of the $n$-th stationary state (orbit) is directly proportional to the square of the principal quantum number ($n$). The relationship is given by the expression: $r_n = n^2 r_1$ where $r_1$ (or $a_0$) is the radius of the first orbit (ground state).

Given:

• Radius of ground state ($n=1$), $r_1 = 0.53$ Å
• First excited state corresponds to $n = 2$ (since the ground state is $n=1$).

Calculation: $r_2 = (2)^2 \times 0.53 \text{ Å}$ $r_2 = 4 \times 0.53 \text{ Å}$ $r_2 = 2.12 \text{ Å}$