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