Question

How many electrons in an atom may have the following quantum number? $n = 3,l = 0$

Answer 1

Hint : We must know that $n$stands for principal quantum number and $l$stands for azimuthal quantum number.The azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital.

Complete step by step solution :
Let’s start with discussing quantum numbers; Quantum numbers are the set of numbers which help us determine the position and energy levels of electrons in an atom. There are four quantum numbers which are principle, azimuthal, magnetic and spin quantum numbers.
The Principal quantum number is denoted by $n$ and it ranges from 1 to infinity.
The Azimuthal quantum number is denoted by $l$ and it ranges from 0 to (n-1).
Magnetic quantum number is denoted by $m$ and it ranges from -1 to 1.
Spin quantum number is denoted by $s$and its value is$- \dfrac{1}{2},\dfrac{1}{2}$.
The Principal quantum number tells the maximum possible number of electrons that can be present in the designated shell. It is given by the formula$2{\text{ }} \times {\text{ }}{n^2}$. In this question we are given $n = 3$ so in this shell $2{\text{ }} \times {\text{ }}{3^2} = {\text{ }}18$ electrons will be present in total.
Azimuthal quantum number tells in which subshell s, p, d, and f this electron is, in our question $l = 0$ is given which means that the electron is in s subshell.
Since it’s the s subshell and in the s subshell only 2 electrons are possible, so the number of electrons having quantum number $n = 3,l = 0$ is 2.

Note : Determining the number of electrons in each shell or subshell is of almost importance as it helps us identify the position of the electrons in the atom. This also helps us understand how many shells and subshells there are in a particular principle quantum.