Question

give all the possible values of the four quantum numbers of an electron in the following orbital:
3s
n:
1:
m_l:
m_s: write your answer in a fractional form.

Explanation:

Step1: Determine the principal quantum number \(n\)

The orbital is \(3s\). The principal quantum number \(n\) represents the energy level. For the \(3s\) orbital, \(n = 3\).

Step2: Determine the azimuthal quantum number \(l\)

The azimuthal quantum number \(l\) has values from \(0\) to \(n - 1\). For \(s\) - orbital, \(l=0\).

Step3: Determine the magnetic quantum number \(m_l\)

The magnetic quantum number \(m_l\) has values from \(-l\) to \(+l\). Since \(l = 0\), \(m_l=0\).

Step4: Determine the spin quantum number \(m_s\)

The spin quantum number \(m_s\) can have values \(\frac{+1}{2}\) or \(\frac{-1}{2}\)

Answer:

\(n = 3\), \(l = 0\), \(m_l=0\), \(m_s=\frac{+1}{2}\) or \(\frac{-1}{2}\)