What is the maximum number of electrons in an atom that can have these quantum numbers? a Maximum number of electrons = b Maximum number of electrons

Note: that quantum number are based on the idea that electron are found on the orbital and can be located by a specific address just like a mailing address and one electron can reside in one location,so each specific address has only one electron in it

Principal Quantum Number (n):

This can be defined as the magnitude of an orbital , it is also known as the energy level (n = 1,2,3,4)

Angular Quantum Number (I) :

This can be the shape of an orbital , it is also known as sub-level

I = 0 : the electron is on the s sub-level

I = 1 : the electron is on the p sub-level

I = 2 : the electron is on the d sub-level

I = 3 : the electron is on the f sub-level

Magnetic Quantum Number (mI) :

This can be defined as the atomic orbital in each sub-level it ranges from -I < mI < I

This means that if your I = 2 the then your ml ranges from -2 to +2 denoted like this

-2 < ml < 2

Spin Quantum Number (ns):

This can be defined as the spin of an electron whether is upward or downward and note that only one electron can occupy an upward or downward position in each orbital, this is what i was trying to state above that only one electron can be found in a specific address.

If we think of the principal quantum number as a country a lot of different person can live in one country same as a lot of different electron can live in the principal quantum number.

So if your address is 498 Walter lane then only you can be found in that address just as only one electron can be found in specific address(An upward or a downward spin position in an orbital).

Considering part A of the question

n = 3 this means that the electron must be on the Third energy level

and for ml = -2 we can deduce that it represents one orbital which can have max 2 electrons

2 electrons can have a principal quantum number of 3 and magnetic quantum number of -2

Considering part B of the question

n = 4 this means that we are on the 4th energy level and I = 3 means we are in the f sub-level

Generally the f sub-level has 7 atomic orbitals and each atomic orbital can have two electron(located on the downward and upward spin position in the atomic orbital).

So 14 electron can have a principal quantum number of n = 4 and l = 3

Considering part C

n = 5 this means that we are on the 5th energy level and l = 3 so we are on the f sub-level and an ml of 2 represents one orbital which can have max 2 electrons(located on the downward and upward spin position in the atomic orbital)

Hence only 2 electron can have n =5 , l = 3 and ml = 2

Considering part D

n = 4 this means we are on the 4th energy level I = 1 which means we are on the p sub- level and with ml = 0 which represents an atomic orbital and we know that atomic orbital can have maximum of 2 electrons one on the upward spin position and the second in the downward spin position.

Hence only 2 electrons can have n = 4 , I = 1 and ml = 0