Number of electrons with l=1 and m=0 in P-atom ground state

To determine the number of electrons with l=1 and m=0 in the ground state of a P-atom, we need to understand the electronic configuration of phosphorus (P) and the quantum numbers associated with the electrons.

Electronic configuration of Phosphorus (P)
The atomic number of phosphorus is 15, which means it has 15 electrons. The electronic configuration of phosphorus can be represented as: 1s^2 2s^2 2p^6 3s^2 3p^3.

Quantum numbers associated with electrons
Each electron in an atom is characterized by four quantum numbers: n, l, m, and s.
- The principal quantum number (n) determines the energy level or shell.
- The azimuthal quantum number (l) determines the subshell or orbital shape.
- The magnetic quantum number (m) determines the orientation of an orbital within a subshell.
- The spin quantum number (s) determines the spin orientation of an electron.

In the case of phosphorus, we are interested in finding the number of electrons with l=1 and m=0. This means we are looking for electrons in the p-subshell (l=1) with an orientation of 0 along the z-axis (m=0).

Determining the number of electrons with l=1 and m=0 in the ground state
In the ground state, the electrons of an atom occupy the lowest energy levels available. Following the Aufbau principle and Pauli exclusion principle, we fill the orbitals in order of increasing energy and with a maximum of two electrons per orbital.

In the case of phosphorus, the p-subshell has three orbitals: px, py, and pz. These orbitals have m values of -1, 0, and 1, respectively. Since we are interested in m=0, we focus on the pz orbital.

The pz orbital can hold a maximum of two electrons. Therefore, in the ground state of a phosphorus atom, there can be a maximum of two electrons with l=1 and m=0.

Summary
- The electronic configuration of phosphorus is 1s^2 2s^2 2p^6 3s^2 3p^3.
- The quantum numbers associated with electrons are n, l, m, and s.
- To find the number of electrons with l=1 and m=0 in the ground state, we focus on the p-subshell and the pz orbital.
- The pz orbital can hold a maximum of two electrons.
- Therefore, in the ground state of a phosphorus atom, there can be a maximum of two electrons with l=1 and m=0.

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