Question

How many atomic orbitals are there in the g subshell ?

Answer 1

Hint: An orbital is defined as the function which describes the wave-characteristics of an electron. It is also considered as a space where the probability of the presence of electrons is highest. Whereas, a subshell is defined as the path which the electrons follow inside the shell.

Complete step by step answer:
a subshell is a sub division of electron shells which is divided by electron orbitals. The subshells of an atom are named as s, p, d, f and g each having its own set of orbitals. Each of the shells also consist of a different set of subshells.
In the first shell, there is only 1 subshell that is s. In the second subshell, there are two subshells which are s and p and so on.
Inside a particular subshell, the numbers of orbitals are also always fixed. This number can be calculated by the quantum numbers. Quantum numbers are those numbers which helps us to find the energy level associated with each of the electrons in an atom. There are mainly four types of Quantum Numbers- Principal quantum number$(n)$ , Azimuthal quantum number$(l)$ , spin quantum number$({m_s})$ and magnetic quantum number$({m_l})$.Depending on this quantum numbers we can find out the number of orbitals present in the g subshell of an atom.
The Azimuthal quantum number $(l)$ tells us in which subshell the electron is located. For g-subshell the value of $l$ is 4.
The magnetic quantum number$({m_1})$ tells us the type of orbitals the subshell contains. The value ranges from $ - l$ to $ + l$. For this case, it will be $ - 4$ to $ + 4$ .
Therefore the orbitals contained in the g subshell are {$ - 4, - 3, - 2, - 1,0, + 1, + 2, + 3, + 4$}=9. Hence the number of orbitals present are 9.
We can find the same in an alternative way also, by the equation ${m_1} = 2l + 1$. We can put the value of $l = 4$ then the equation becomes $2.4 + 1$ =$9$ .

So the number of orbitals present in the g subshell is 9.

Note: There are still questions about the existence of the g-subshell as it has not been seen in any element so far. The existence of it is solely based on mathematical deductions.