Question

How many electrons can have the quantum number set n = 5 and ml = 1?

Answer 1

For solving this question, we should have the knowledge of quantum numbers and the filling of electrons in the orbital. The two quantum number given in the question are principal quantum number denoted by “n” and magnetic quantum number denoted by “${m_l}$”

Complete step by step answer:
There are three quantum numbers which help to determine the orbital. The three quantum numbers are Principal quantum number, Azimuthal quantum number or angular quantum number and magnetic quantum number. The principal quantum number is denoted by n which describes the size of the orbital. The angular quantum number or the azimuthal quantum number is denoted by l which describes the shape of the orbital. The magnetic quantum number is denoted by ${m_l}$ which describes the orientation of the space of the particular orbital. There is one other quantum number which helps to know the angular momentum of the electron known as spin quantum number which is denoted by ${m_s}$

Number	Symbol	Possible values
Principal quantum number	n	1, 2, 3, 4……
Angular quantum number	l	0, 1, 2, 3, (n-1)
Magnetic quantum number	${m_l}$	-l, …..-1, 0, 1,…..1
Spin Quantum number	${m_s}$	+1/2,-1/2

Here, we have given two quantum numbers principal quantum number and magnetic quantum number.
n = 5 and ${m_l}$ is 1.
For n = 5,
l = (0, 1, 2, 3, 4)
${m_l}$= 1
${m_s}$= $\pm \dfrac{1}{2}$
n =5;I = 1; ${m_l}$=1; ${m_s}$= $\pm \dfrac{1}{2}$
n =5;I = 2; ${m_l}$=1; ${m_s}$= $\pm \dfrac{1}{2}$
n =5;I = 3; ${m_l}$=1; ${m_s}$= $\pm \dfrac{1}{2}$
n =5;I = 4; ${m_l}$=1; ${m_s}$= $\pm \dfrac{1}{2}$
As in one orbital (${m_l} = 1$) two electrons can be occupied each with opposite spin per subshell ( l).
So total 8 electrons can be shared by the two quantum numbers.

Note: The principal quantum number tells you about the energy level where the electrons are located which is equivalent to the period in which the chemical element is placed in the periodic table.