Question

What will be the sum of all possible values of l and m for n=5.

Answer 1

Answer:

n=5

l=0,1,2,3,4

m=-4,-3,-2,-1,0,1,2,3,4

Sum of positive values of l and m for n(5)=1+2+3+4+1+2+3+4=20

Answer 2

Given: n= 5 where n is principal quantum number of an atom

To find: Sum of all possible values of l and m

Explanation: For any value of n, the value of azimuthal quantum number (l) ranges from 0 to n-1. In this case the value of n= 5. Therefore, the value of l ranges from 0 to 4.

Therefore, possible values of l= 0,1,2,3,4

For any value of l, the value of n ranges from -l to +l. In this case, the value of n can range from -4 to +4.

Therefore, possible values of m= -4,-3,-2,-1,0,1,2,3,4

Sum of values of l= 0+1+2+3+4= 10

Sum of values of m= (-4)+(-3)+(-2)+(-1)+0+1+2+3+4=0

Total sum= 10+0= 10

Therefore, the sum of all possible values of l and m for n= 5 is 10.