Question

The maximum number of electrons in a subshell is:

$$A.{\text{ }}2\left( {2l + 1} \right) \\\ B.{\text{ }}2l + 1 \\\ C.{\text{ }}2l \\\ D.{\text{ }}2l - 1 \\\$$

Answer 1

In order to solve the given problem we will first understand the basic structure of the atom on the basis of the quantum model of the atom and further we will relate the number of atomic level, number of orbitals, number of electrons and the number of subshells with the different quantum numbers. Thereafter on the basis of the quantum model we will try to derive the number of electrons in a subshell on the basis of the number of subshells.

Complete step by step answer:
Only such discrete energy quantities, called energy levels, may be embraced by a quantum mechanical device or particle that is bound, that is, spatially confined.
Energy levels (also known as shells of electrons) are set distances from an atom's nucleus where electrons can be contained. In an atom, electrons are small, negatively charged particles that pass at the centre of the positive nucleus. Energy levels are a little like the staircase steps.
In quantum mechanics there are 4 types of quantum numbers; they are principal quantum number, azimuthal quantum number, magnetic quantum number and spin quantum number.
The principal quantum number relates with the energy levels and the azimuthal quantum number relates with the number of subshells in the energy level.
The principal quantum number is represented as “n” and the azimuthal quantum number is represented as “l” in the quantum model.
“n” is the number of energy levels in the atom.
Each energy level has different number of subshells which is given as follows:
$l = 0$ to $l = \left( {n - 1} \right)$ .
For each of the subshells we have a different number of total orbitals which is increasing as the azimuthal number increases.
The number of orbitals are as follows:

$$s \Rightarrow 1{\text{ orbitals}} \\\ p \Rightarrow 3{\text{ orbitals}} \\\ d \Rightarrow 5{\text{ orbitals}} \\\ .......... \\\$$

The number of orbitals related to the subshell is given as:
${\text{Number of orbitals}} = 2l + 1$
Also we know that each orbitals can have a maximum of 2 electrons in it. So the total number of electrons is twice the number of orbitals.
Therefore the number of electrons is:
$= 2\left( {2l + 1} \right)$
Hence, the maximum number of electrons in a subshell is $2\left( {2l + 1} \right)$ .
So, the correct answer is “Option A”.

Note: In order to solve such types of problems students must be aware of the quantum model of the atom and should also know about the various relations between the different quantum numbers and the physical structure of the atom. To explain the direction and the movement of an electron in an atom, quantum numbers may be used. The quantum numbers, when combined, of all the electrons in a given atom must conform with the Schrodinger equation.