Question

What is the maximum number of electrons in the $ 4d $ subshell?

Answer 1

Hint: To calculate the maximum number of electrons that can be accommodated (present) in subshell we first need to know about the concept of the four quantum numbers. The four quantum numbers are principal quantum number, magnetic quantum number, azimuthal quantum number and spin quantum number. Based on these we can calculate the maximum number of electrons in a subshell.

Complete answer:
We know that four quantum numbers are present which are principal quantum number, magnetic quantum number, azimuthal quantum number and spin quantum number.
The Principal quantum number gives the value of the shell in which an electron is present and it is denoted by “n”.
An Azimuthal quantum number, denoted by “l” gives the value of the subshell and can have value from $ 0 $ to $ (n - 1) $ .
Magnetic quantum number which is denoted by “m” can have a value from $ - l $ to $ + l $ .
Spin quantum numbers can have values $ - \dfrac{1}{2} $ or $ + \dfrac{1}{2} $ .
We also know that there can be a maximum of two electrons in an orbital according to the Pauli Exclusion Principle.
Now, the given orbital is $ 4d $ .
In which we can identify that the value of n is $ 4 $ and the value of azimuthal quantum number, l is $ 2 $ .
Number of orbitals for the d subshell can be $ - l $ to $ + l $ which is $ - 2to + 2 $ .
Therefore, there are a total of $ 5 $ orbitals.
Hence, maximum electrons in these five orbitals are:
 $ = 2 \times 5 $
 $ = 10 $
Hence, there can be a maximum ten electrons in the $ 4d $ subshell.

Note:
We should note that there cannot be more than two electrons in an orbital of the subshell and this can be explained on the basis of Pauli Exclusion Principle which states that no two electrons should have the same value of all the four quantum numbers. It also helps in calculating the number of orbitals, electrons and magnetic moment too.