Question

question (2 points)
how many electrons could have the following set of quantum numbers?
1st attempt
(a) n = 3, ℓ = 2
electrons
(b) n = 5, ℓ = 3, m_ℓ = - 3
electrons

Explanation:

Step1: Recall electron - capacity per orbital

Each orbital can hold a maximum of 2 electrons. The number of orbitals in a sub - shell is given by $2\ell + 1$.

Step2: Calculate number of orbitals for (a)

For $n = 3$ and $\ell=2$, the number of orbitals in the sub - shell is $2\ell + 1=2\times2 + 1 = 5$. Since each orbital can hold 2 electrons, the number of electrons is $2\times5=10$.

Step3: Analyze quantum numbers for (b)

For $n = 5$, $\ell = 3$, and $m_{\ell}=-3$, we have specified a particular orbital. Since each orbital can hold a maximum of 2 electrons, the number of electrons with these quantum numbers is 2.

Answer:

(a) 10
(b) 2