#### Answer

The radius of the atom is $~~1.90~nm$

#### Work Step by Step

We can find the state $n$:
$E_n = \frac{13.6~eV}{n^2}$
$n^2 = \frac{13.6~eV}{E_n}$
$n = \sqrt{\frac{13.6~eV}{E_n}}$
$n = \sqrt{\frac{13.6~eV}{0.378~eV}}$
$n = 6$
We can find the radius:
$r_n = n^2~a_B$
$r_6 = (6)^2~(0.0529\times 10^{-9}~m)$
$r_6 = 1.90\times 10^{-9}~m$
$r_6 = 1.90~nm$
The radius of the atom is $~~1.90~nm$