Total Possible Quantum States When n = 2

Click For Summary
SUMMARY

The total number of quantum states for a principal quantum number of n = 2 is calculated by considering the allowed orbital quantum numbers (l) and their corresponding magnetic quantum numbers (m_l). For n = 2, the allowed values of l are 0 and 1, with m_l values of 0 for l = 0 and -1, 0, 1 for l = 1. This results in a total of 6 states, which, when multiplied by 2 to account for the two possible spin orientations, yields a final total of 12 quantum states. The initial calculation of 6 states was incorrect as it did not account for the spin multiplicity.

PREREQUISITES
  • Understanding of quantum mechanics terminology, specifically quantum numbers.
  • Familiarity with the principal quantum number and its implications.
  • Knowledge of orbital quantum numbers and their allowed values.
  • Basic grasp of spin quantum numbers and their significance in quantum states.
NEXT STEPS
  • Study the implications of quantum numbers in atomic structure.
  • Learn about the Pauli exclusion principle and its effect on quantum states.
  • Explore the concept of spin and its role in quantum mechanics.
  • Investigate the relationship between quantum states and electron configurations in atoms.
USEFUL FOR

Students of quantum mechanics, physics educators, and anyone interested in the foundational principles of atomic structure and quantum states.

xinlan
Messages
61
Reaction score
0

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..
 
Physics news on Phys.org
it's ok.. I got it.. :)
 
can you show me?!
 

Similar threads

Undergrad Are certain combinations of quantum numbers (basis vectors) forbidden?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Does putting a hydrogen atom in a box mix angular momentum states?
  • · Replies 2 ·
Replies
2
Views
2K
What are the possible quantum states of an electron relaxing from n=4 to n=3?
  • · Replies 1 ·
Replies
1
Views
1K
Why Are There More Energy Levels in Silicon's 3p4p Configuration Than in 3p²?
  • · Replies 4 ·
Replies
4
Views
2K
Help Calculating probability between 2 limits for the ground state
  • · Replies 28 ·
Replies
28
Views
2K
Understand some quantum numbers in a problem
  • · Replies 7 ·
Replies
7
Views
2K
Electron excited from the ground state to a quantum state
  • · Replies 5 ·
Replies
5
Views
1K
Validity of Two-Fermion System Wavefunction with Quantum Numbers a and b
  • · Replies 2 ·
Replies
2
Views
1K
Is My Quantum Well Probability Calculation Correct?
  • · Replies 9 ·
Replies
9
Views
2K
Graduate Spin-orbital combination and the exclusion principle
  • · Replies 18 ·
Replies
18
Views
2K