Question

give all the possible values of the four quantum numbers of an electron in the following orbital: 4p n : l : m_l : m_s : write your answer in a fractional form.

Explanation:

Step1: Determine the principal quantum number (n)

For the orbital \(4p\), the principal quantum number \(n\) is given by the number before the orbital letter. So, \(n = 4\).

Step2: Determine the azimuthal quantum number (l)

The orbital type is \(p\), and for \(p\) orbitals, the azimuthal quantum number \(l = 1\) (since \(s\) orbitals have \(l = 0\), \(p\) have \(l = 1\), \(d\) have \(l = 2\), \(f\) have \(l = 3\), etc.).

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

The magnetic quantum number \(m_l\) can take values from \(-l\) to \(+l\) including zero. For \(l = 1\), the possible values of \(m_l\) are \(-1\), \(0\), \(+1\).

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

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

Answer:

• \(n\): \(4\)
• \(l\): \(1\)
• \(m_l\): \(- 1,0, + 1\)
• \(m_s\): \(\frac{1}{2}\) or \(-\frac{1}{2}\)