All the hydrogen-like atoms in their ground states have the same

The correct answer is Option (1) → orbital angular momentum of the electron

For a hydrogen-like atom (one electron, atomic number Z):

Energy in ground state: $E = -13.6 Z^2 \, \text{eV}$ → depends on Z

Radius in ground state: $r = \frac{a_0}{Z}$ → depends on Z

Speed of electron: $v = Z \alpha c$ → depends on Z

Orbital angular momentum: $L = \sqrt{l(l+1)}\hbar$, and for ground state $n=1$, $l=0$

Thus $L = 0$ → same for all hydrogen-like atoms in ground state.

Final Answer:

Orbital angular momentum of the electron