Question

The maximum number of electrons in a subshell is given by the expression:
A. \[4l+2\]
B. \[4l-2\]
C. \[2l+1\]
D. \[2{{n}^{2}}\]

Answer 1

Hint: To solve these types of questions we must keep in mind that each orbital can occupy at most 2 electrons in number. Now, if we want to determine the maximum number of electrons in a subshell then we just need to find the number of orbitals in that particular subshell and multiply it by 2, it will give us the maximum number of electrons present in that subshell.

Complete answer:
A subshell with azimuthal quantum number l has \[(2l+1)\]number of orbitals. Each orbital can occupy at most 2 electrons. Hence, the maximum number of electrons in a given subshell with azimuthal quantum number l is given by \[2(2l+1)\].
Here, the value of the azimuthal quantum number \[l\] can vary from 0 to \[\left( n-1 \right)\]where n is principal quantum number, depending on the value of principal quantum number.

Thus value of l for the following is:
s subshell \[l=0\] maximum number of electrons in s subshell \[=2(2l+1)=2(2\times 0+1)=2\]
p subshell: \[l=1\] maximum number of electrons in p subshell \[=2(2l+1)=2(2\times 1+1)= 6\] and so on.

Note: The principal quantum number is the quantum number denoted by n and which indirectly describes the size of the electron orbital. It is always assigned an integer value for example, \[n=1,2,3..,\] but its value may never be 0. The principal quantum number has the greatest effect on the energy of the electron.
The azimuthal quantum number is a quantum number for an atomic orbital that is used to determine its orbital angular momentum and also describes the shape of the orbital. It is denoted by l. The azimuthal quantum number is the second of a set of quantum numbers which describe the unique quantum state of an electron along with other quantum numbers. The values of azimuthal quantum number are from zero to \[n-1\].