Question

What is the total number of orbitals in the shell to which the g-subshell first arises?
A. $9$
B. $16$
C. $25$
D. $36$

Answer 1

To solve this question, you should have knowledge about the quantum numbers. The g-subshell has azimuthal quantum number equal to $4$. To find out the number of orbitals in a shell, use ${{n}^{2}}$.

Complete step by step answer:
We should know that, the three quantum numbers (i.e. principal quantum number {denoted by ‘n’}, azimuthal quantum number {denoted by ‘l’} and magnetic quantum number {denoted by ‘m’}) that describe an orbital are generally integers which lies as $0,1,2,3,$ and so on. The principal quantum number cannot be zero and thus the allowed values of n are $1,2,3,4,$ and so on. While the azimuthal quantum number can be any integer between $0$ and $n-1$. Different sublevels have different azimuthal quantum numbers. Such as, the “l” value of s sublevel is $0$. The principal quantum number can be calculated from azimuthal quantum number by $l+1$ formula.
Orbital are spaces that have a high probability of containing an electron. In other words; we can say that, orbital is an area where the electrons live. One orbital can contain a maximum of two electrons only. Each sublevel has a different number of orbitals such as, s sublevel has one orbital and therefore it will have only two electrons. The number of orbitals associated with the principal quantum number ‘n’ is given by ${{n}^{2}}$.
Here, as per the question g-subshell is given. The azimuthal quantum number of g-subshell is $4$.
So, the minimum value of n for g-subshell will be $l+1=4+1=5$.
Therefore, the number of orbitals in a shell with $n=5$ will be ${{n}^{2}}={{5}^{2}}=25$.
So, the total number of orbitals in the shell to which the g-subshell first arises is $25$.

Hence, the correct option is C.

Note: The principal quantum number just designates the size of the orbital or energy level while the azimuthal quantum number specifies the shape of the orbital and the magnetic quantum number shows the orientation of the orbital.