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**1. Homework Statement**

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. Homework 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..