1. The problem statement, all variables and given/known data The quantum state of a particle can be specified by giving a complete set of quantum numbers (n, l, m_s, m_l) . How many different quantum states are possible if the principal quantum number is n = 2? To find the total number of allowed states, first write down the allowed orbital quantum numbers l, and then write down the number of allowed values of m_l for each orbital quantum number. Sum these quantities, and then multiply by 2 to account for the two possible orientations of spin. 2. Relevant equations 3. The attempt at a solution since n = 2 then l = 0,1 m_l for l = 0 --> 0 m_l for l = 1 --> -1,0,1 then I added them up, which is 6 and then multiply it by 2, which is 12. but I got wrong.. please help me.. thanks..