Posted by Anonymous on Monday, October 29, 2012 at 1:06am.
Here are the rules.
n can be any whole number over zero; i.e., 1, 2, 3, 4, etc.
l ("ell") can be any whole number beginning with zero, 1, 2, 3, etc with a maximum of n-1.
m_{l} = - ell to + ell in whole numbers;i.e., if ell is 2 then m_{l} can be -2,-1,0,+1,+2.
m_{s} may have two values only; i.e., +1/2 or -1/2
Your job is to take these rules and apply them to each of the above and find those that are allowed. To give you a fast start
#1 is allowed.
#2 is not allowed. Why not? If N is 4, then l CAN be 2 (l can have values in this case of 0,1,2,3) so 2 is allowed. However, m_{l} CANNOT be 3 because m_{l} may take values from -l to +l (in whole numbers) which will allow -2,-1,0,+1,and +2 but not +3.
4 and 5
hjgtgy