Answer
${\bf 2.28} \;\rm pm$
Work Step by Step
We know that the penetration distance is given by
$$ \eta = \frac{\hbar}{\sqrt{2m(U_0 - E)}} \tag 1$$
We are given that the helium atom's energy is $ 1.0 \; \rm{eV} $ below $ U_0 $, so that $U_0-E=1.0$ eV.
We are dealing with a helium atom, so we need to find the mass of a helium atom, which contains 4 protons, is given by
$ m_{\rm{_{He}}} =4M_{\rm _{He}}=4(1.67 \times 10^{-27}) \; \rm{kg}$
Substitute these known into (1);
$$
\eta = \frac{(1.055 \times 10^{-34})}{\sqrt{2 \times 4(1.67 \times 10^{-27}) (1)(1.602 \times 10^{-19})}}
$$
$$
\eta =\color{red}{\bf 2.28 \times 10^{-12}} \;\rm m
$$
