For all hydrogen-like atoms and ions in their ground states, which...

For hydrogen-like atoms and ions in the ground state, the principal quantum number $n = 1$.

The radius of the orbit is given by $r = 0.529 \dfrac{n^2}{Z}$ \AA, which depends on the atomic number $Z$.

The energy of the atom is given by $E = -13.6 \dfrac{Z^2}{n^2}$ eV, which depends on $Z$.

The speed of the electron is given by $v = 2.18 \times 10^6 \dfrac{Z}{n}$ m/s, which depends on $Z$.

The orbital angular momentum of the electron in the ground state ($1s$ orbital, $l = 0$) is $\sqrt{l(l+1)} \dfrac{h}{2\pi} = 0$. According to Bohr's theory, the angular momentum is $\dfrac{nh}{2\pi} = \dfrac{h}{2\pi}$. In both models, it is independent of $Z$ and depends only on the quantum numbers $n$ or $l$.

Thus, the orbital angular momentum is identical for all hydrogen-like atoms and ions in their ground states.