The quantum state of a particle can be specified by giving a complete set of quantum numbers (n, l, m_l, m_s). How many different quantum states are possible if the principal quantum number is n = 4? 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_1 for each orbital quantum number. Sum these quantities, and then multiply by 2 to account...