Answer
$0\%$
Work Step by Step
We know that the probability of tunneling is given by
$$
P_{\text{tunnel}} = e^{-2w\eta}\tag 1
$$
Where $ w $ is the width of the barrier, and $\eta$ is the penetration distance which is given by:
$$
\eta = \frac{\hbar}{\sqrt{2m(U_0 - E)}}
$$
where $ U_0 - E = E_0 $ since the electrons inside metals are bound by a certain energy called the work function $ E_0 $ which is the energy required to release an electron from the metal.
$$
\eta = \frac{\hbar}{\sqrt{2mE_0}}
$$
Plug the known;
$$
\eta = \frac{(1.05 \times 10^{-34})}{\sqrt{2(9.11 \times 10^{-31} )(4.3 \times 1.6 \times 10^{-19} )}}=\bf 9.38 \times 10^{-11}\;\rm m
$$
Substitute all the known into (1);
$$
P_{\text{tunnel}} = e^{-2(50 \times 10^{-9}) / (9.38 \times 10^{-11})} = e^{-1066}
$$
$$
P_{\text{tunnel}} \approx \color{red}{\bf 0\%}
$$
Thus, the probability of tunneling between the aluminum pieces is essentially zero.
