# What are the possible quantum numbers for the 6d orbital?

Nov 13, 2015

Here's what I got.

#### Explanation:

In order for an electron to reside in the d-subshell of any energy level, starting with the third one, it must have a distinct value for its angular momentum quantum number, $l$.

More specifically, the only value of $l$ that describes the d-subshell is $l = 2$.

In the case of the 6d-subshell, the principal quantum number ,$n$, which gives you the energy level on which the electron can be found, is equal to $6$.

Now, any d-subshell will contain a total of $5$ orbitals given by the values of the magnetic quantum number, ${m}_{l}$.

For a d-subshell, ${m}_{l}$ can take the following values

m_l = {-2; -1; 0; 1; 2}

Now, the spin quantum number, ${m}_{s}$, can only take two possible values

${m}_{s} = - \frac{1}{2} \to$ describes an electron with spin-down
${m}_{s} = + \frac{1}{2} \to$ describes an electron with spin-up

So, to sum this up, the electrons located in the 6d-subshell will have

• $n = 6 \to$ the sixth energy level
• $l = 2 \to$ the d-subshell
• m_l = { -2; -1; 0; 1; 2} -> the five d-orbitals found in the d-subshell
• ${m}_{s} = \pm \frac{1}{2} \to$ either spin-up or spin-down