Question

what is the maximum number of electrons that can have the quantum numbers n = 3, ℓ = 2, mℓ = 1?

Explanation:

Step1: Recall electron spin quantum number

The spin quantum number \(m_s\) can have two values: \(+\frac{1}{2}\) and \(-\frac{1}{2}\).

Step2: Determine the number of electrons

Given \(n = 3\), \(\ell=2\), \(m_{\ell}=1\). For a given set of \(n\), \(\ell\), \(m_{\ell}\), the number of electrons is determined by the spin quantum number. Since there are 2 possible values of \(m_s\) for each combination of \(n\), \(\ell\), \(m_{\ell}\).

Answer:

\(2\)