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

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

In Bohr's model of a hydrogen-like atom (nuclear charge \( Ze \)), the orbital angular momentum is quantised as \( L = nh/2\pi \), which does not contain \( Z \). The other quantities depend on \( Z \):

    \( L_n = n\,h/2\pi \)
    \( v_n \propto Z/n \)
    \( r_n \propto n^{2}/Z \)
    \( E_n = -13.6\,Z^{2}/n^{2}\ \mathrm{eV} \)

In the ground state \( n = 1 \), so every hydrogen-like atom has \( L = h/2\pi \), while the energy, speed and radius change from one atom to another.

NCERT (2026-27):
Bohr Model of the Hydrogen Atom – “… (ii) Bohr’s second postulate defines these stable orbits. This postulate states that the electron revolves around the nucleus only in those orbits for which the angular momentum is some integral multiple of h/2π where h is the Planck’s constant (= 6.6 × 10⁻³⁴ J s). Thus the angular momentum (L) of the orbiting electron is quantised. That is

    \( \displaystyle L = \frac{n h}{2\pi} \qquad (12.5) \) ”