For an electron in the ground state of a hydrogen atom, what are the values of the orbital quantum number $l$ and the magnetic quantum number $m_{l}$ ?

medium 3 marks Class 12 · Physics · Atoms

Answer

l = 0, m_{l} = 0

The correct answer is $l = 0, m_{l} = 0$ — With $l = 0$ , the only possible $m_{l}$ is $0$ .

Step-by-step solution

Ground state corresponds to principal quantum number $n = 1$ .
Orbital quantum number $l$ can take values $0 \leq l \leq n - 1$ .
For $n = 1$ , the only allowed value is $l = 0$ .
For a given $l$ , the magnetic quantum number $m_{l}$ ranges from $- l$ to $+ l$ in integer steps.
With $l = 0$ , the only possible $m_{l}$ is $0$ .

Common mistake: Assigning

l = 1

m_{l} = \pm 1

to the ground state.

Concept tested: Quantum numbers for hydrogen ground state