Step 1: Understand the hunt.
We are looking for the one statement that is false, so we verify each against atomic-structure rules.
Step 2: Check the azimuthal quantum number.
The quantum number $l$ fixes orbital shape ($s,p,d,f$), so that statement is true.
Step 3: Check the energy formula.
For hydrogen-like atoms $E_n \propto \dfrac{1}{n^2}$, so energy magnitude is inversely proportional to $n^2$; true.
Step 4: Count nodes for 3s carefully.
Total nodes $= n-1$. For $3s$, $n=3$ gives \[ \text{total nodes} = 3-1 = 2 \] not three. We can even split it: radial nodes $=n-l-1=3-0-1=2$ and angular nodes $=l=0$, summing to $2$. This statement is therefore false.
Step 5: Check the He$^+$ radius.
Since $r_n \propto \dfrac{n^2}{Z}$, for $n=1$ the radius scales as $1/Z$; He$^+$ has $Z=2$, giving half the hydrogen radius; true.
Step 6: Pick the odd one out.
Only the 3s node claim breaks a rule, so it is the incorrect statement. \[ \boxed{\text{3s orbital has 2 nodes, not 3}} \]