To find the total number of allowed states, first, write down the allowed orbital quantum numbers l<span>, and then write down the number of allowed values of </span>m<span>l for each orbital quantum number. Sum these quantities, and then multiply by 2 to account for the two possible orientations of spin.</span>
Quantum states for n=5
l......ml
0 , 0................................1
1 , -1, 0, +1................................ 3
2 , -2, -1, 0, +1, +2................................5
3 , -3, -2, -1, 0, +1, +2, +3................................ 7
4 , -4,-3, -2, -1, 0, +1, +2, +3,+4 ................................9
2*(1+3+5+7+9)=
2*5^2 = 50 allowed states
