Question

in a ground state atom of al how many electrons total will have the quantum number \\( \ell = 0 \\)?

Explanation:

Step1: Determine the electron configuration of Al

Al (aluminum) has an atomic number of 13. The electron configuration of Al in the ground state is \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{1}\).

Step2: Identify orbitals with \(l = 0\)

The quantum number \(l\) represents the azimuthal quantum number. When \(l = 0\), the orbital is an \(s\) - orbital.
In the electron configuration \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{1}\), the \(s\) - orbitals are \(1s\), \(2s\), and \(3s\).

Step3: Calculate the number of electrons in \(s\) - orbitals

For the \(1s\) orbital, the number of electrons \(n_1=2\); for the \(2s\) orbital, \(n_2 = 2\); for the \(3s\) orbital, \(n_3=2\).
The total number of electrons in \(s\) - orbitals (where \(l = 0\)) is \(N=n_1 + n_2+n_3\).
Substitute the values: \(N=2 + 2+2\).

Answer:

6