The formula to calculate the radius of the nth orbit in a hydrogen atom is given by the equation:

$r_n = r_0 \times n^2$

where,
$r_n$ is the radius of the nth orbit,
$r_0$ is the radius of the innermost orbit (known as the Bohr radius), and
$n$ is the orbit number.

Given that the radius of the innermost orbit ($r_0$) is $$5.3 \times 10^{-11} \mathrm{~m}$$ or equivalently $$0.53 \mathop A\limits^o$$, and we're interested in finding the radius of the third orbit ($n = 3$).

So,

$$r_3 = 0.53 \times (3)^2$$ $\mathop A\limits^o$

$r_3 = 0.53 \times 9$ $\mathop A\limits^o$

$r_3 = 4.77$ $\mathop A\limits^o$

Therefore, the radius of the third allowed orbit of the hydrogen atom is 4.77 $\mathop A\limits^o$.