Total Possible Quantum States When n = 2

AI Thread Summary
The discussion revolves around calculating the total number of quantum states for a particle with a principal quantum number n = 2. The allowed orbital quantum numbers are l = 0 and l = 1, with corresponding magnetic quantum numbers m_l of 0 for l = 0 and -1, 0, 1 for l = 1. After summing these states, the initial calculation suggested there were 6 states, which was then multiplied by 2 to account for spin, resulting in 12. However, the initial conclusion was incorrect, prompting a request for clarification. Ultimately, the participant indicated they resolved the issue independently.
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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.


Homework Equations





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..
 
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