Question

what is the maximum number of electrons in the atom that can have the following quantum numbers

1). n=3 and magnetic quantum= -2
2). n =4 and l=3
3). n= 5, l=3, and magnetic quantum=2
4). n=4, l=1 and magnetic quantum=0

Answer 1

Question 1. n=3 means it contains 3 shells. Then its azimuthal quantum number will be 0 to n-1. That is 0 to 2. 0 for S, 1 for P. 2 for d orbital respectively. Then, magnetic quantum number m= -l to +l. (ie from -2,-1,0,1,2)

The magnetic quantum number here is -2. So it represent dxy orbital. (five orbitals are dxy,dyz,dxz,dx²-y²,dz²) So 2 electron can be filled dxy.

Question 2. n=4, l can be from 0 to n-1. So 0 (s),1 (p), 2 (d), 3 (f). here asked one is l=3 so f orbital. So total of 14 electrons can be filled f orbitals.

Question 3. n=5, l=3, m=2 So it is an f orbital., But only one f orbital from 7 f- orbitals mentioned, so again only 2 electron can be found in m=2.

Question 4. n=4, l=1, m=0. P is orbital ( l=1) and only 3 shapes are there in p orbitals. ie, Px, Py, and Pz. So if the m=0, then it will be Py orbital. So again 2 electron can be filled here.