At most, how many 4d electrons can an atom have? Of these what is the maximum number that
can have ms= -1/2?

A 5f electron has what value of quantum number l? What values of ml may it have?

Also please explain how you got the answers so I can understand?

Thank you so much!

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1. To do these you need to know the rules and that will do it.
n can have any whole number from 1 --- to infinity.
l(ell) has integral values of 0 to n-1; i.e., 0,1,2,3,....n-1
msubl is -ell to +ell as min to max with inters between, including zero.
msubs can have -1/2 or +1/2 only.

Examples:
n = 1
So ell can be zero only.
msubell = 0
msubs = -1/2 or =+1/2

The s orbital has ell = 0
The p orbital has ell = 1
The d orbital has ell = 2
The f orbital has ell = 3
etc.

The number of orbitals is 2*(ell)+1 which means there is only 1 s orbital; i.e.k (2*0 + 1) = 1
Likewise, there are 3 p orbitals, 5 d orbitals, 7 f orbitals
Each orbital can hold a maximum of 2 electrons; one will have +1/2 spin and the other -1/2 spin.
So your question about the 4d orbitals. There are 5 4d orbitals, each may have 2 electrons, so if the 4d orbitals are completely filled you may have as many as 10 electrons. Since one of those electrons in each "box" is +1/2 and the other is -1/2, you may have as many as 5 4d orbitals with ms = -1/2.

I'll leave the 4f question for you. Please follow up if you don't understand and ask specific questions. I know this can be confusing but you have ab out 3 or 4 rules; knowing those rules lets you handle any of these questions.

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