Question

what is the maximum number of electrons that can have the following set of quantum numbers?
$n = 2, l = 1, m_l=-1$.

Explanation:

Step1: Recall Pauli Exclusion Principle

According to Pauli Exclusion Principle, no two electrons in an atom can have the same set of four quantum numbers. The four quantum numbers are \(n\) (principal quantum number), \(l\) (azimuthal quantum number), \(m_l\) (magnetic quantum number), and \(m_s\) (spin quantum number). Here, \(n = 2\), \(l=1\), \(m_l=- 1\) are given. The spin quantum number \(m_s\) can have two values: \(m_s=+\frac{1}{2}\) and \(m_s =-\frac{1}{2}\).

Step2: Calculate the number of electrons

Since for the given \(n = 2\), \(l = 1\), \(m_l=-1\), the only variable quantum number is \(m_s\) which has two possible values.

Answer:

\(2\)