Question

How many orbitals are in the 3d subshell?

Answer 1

Hint: We have to solve this problem by considering and calculating the relation between the quantum numbers.
- The magnetic quantum numbers (m) for $\text{l=2}$, $\text{m = -2 to 2}$

Complete step by step answer:
So in the question, it is given how many orbitals are there in the 3d subshell.
To show the question we should know the quantum numbers and the relation between these numbers with the shells and orbitals.
As it is asked about the 3d subshell, the orbitals we are talking about is about the third subshell i.e. with a n value 3, n = 3.
And the subshell is d.
- First let’s discuss the quantum numbers so that we can easily solve the question from the data given.
There are four quantum numbers which explains everything about the shells, subshells, orbitals and spin of an electron present in an atom. The four quantum numbers give the complete address of an electron in an atom.
The quantum numbers are:
- Principal quantum number which is represented as n, will give us all the data about the energy and the position of the electrons.
The principal quantum number gives the shell number in which the
The value of n ranges from n=0, 1, 2, 3 etc.
- Azimuthal quantum number which is represented using the letter l, which gives the subshell of the electrons and the azimuthal quantum number is related to n as,$\text{l=n-1}$
The value of l can be, l = 0, 1, 2, 3 etc.
The subshell with value l = 0 is the s subshell, with value l = 1 is the p subshell, l = 2, d subshell
- Magnetic quantum number (m) gives us the number of orbitals present in a subshell.
The value of m is related to l as, $\text{m=-l to +l}$
Therefore we could get the number of orbitals in a subshells if we know the n value or l value.
Here as we are concerned about 3d, the value of n is 3 and as the subshell is d, the value of l is 2
Therefore the value of m will be from -2 to +2 i.e. -2,-1, 0, 1, 2 in total of 5 orbitals.
There we could say that there are 5 orbitals in 3d subshell.

Note: The five subshells in 3d orbitals are:
-$d_{xy}$
-$d_{yz}$
-$d_{xz}$
-$d_{x^2-y^2}$
-$d_{z^2}$
The d-orbitals are having double-dumbbell shape.
And the filling of electrons in this orbitals too takes place according to three rules, Hund’s rule, Pauli exclusion principle and the Afbau principle.