Answer
$38$ electrons
Work Step by Step
In the electron configuration of an atom, different orbitals can hold a specific number of electrons. When we consider the given designations:
- \(1p\) orbital: $n=1$, $l=1$, but for $n=1$, $l$ can only be 0, so there are 0 electrons.
- \(6d_{x^{2}-y^{2}}\) orbital: Can hold a maximum of 2 electrons.
- \(4f\) orbital: Can hold a maximum of 14 electrons.
- \(7p_{y}\) orbital: Can hold a maximum of 2 electrons.
- \(2s\) orbital: Can hold a maximum of 2 electrons.
- \(n=3\) orbitals: In the third energy level, the \(s\), \(p\), and \(d\) orbitals can hold a maximum of 2, 6, and 10 electrons respectively, so we get 18 electrons.
By adding up the maximum number of electrons that can occupy each of these orbitals, we get a total of 38 electrons that can have the given designations.
