Question

The following parameter is same for all hydrogen like atoms and ions in their ground state.

• A. Radius of the orbit
• B. Speed of the electron
• C. Energy of the atom
• D. Orbital angular momentum of the electron

Hint:

For hydrogen-like atoms, radius, speed and energy depend on atomic number \(Z\), but angular momentum is quantized as \[ L=\frac{nh}{2\pi}. \] For ground state, \(n=1\), so \(L=\dfrac{h}{2\pi}\).

Answer 1

The Correct Option is D

Step 1: Recall Bohr's quantization rule.
mvr = nh/(2π). For ground state n = 1, so angular momentum = h/(2π), independent of Z.

Step 2: Check Z-dependence of other quantities.
Radius ∝ 1/Z, velocity ∝ Z, energy ∝ Z² — all depend on Z.

Step 3: Final Answer:
Orbital angular momentum of the electron.