What Causes 2n^2 Vacancies in Atomic Orbitals?

  • Context: Graduate 
  • Thread starter Thread starter motoroller
  • Start date Start date
Click For Summary
SUMMARY

The discussion centers on the calculation of vacancies in atomic orbitals, specifically the formula 2n^2, where n represents the principal quantum number. The factor of two accounts for the degeneracy of s orbitals, while the first factor of n arises from the angular momentum quantum number (L), which can take values from 0 to n-1, yielding n states. The second factor of n is attributed to the magnetic quantum number (m_l), which ranges from -l to +l, further contributing to the total number of vacancies in atomic orbitals.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with quantum numbers: principal (n), angular momentum (l), and magnetic (m_l)
  • Knowledge of atomic structure and electron configurations
  • Basic grasp of degeneracy in quantum states
NEXT STEPS
  • Study the implications of quantum numbers on electron configurations
  • Explore the concept of degeneracy in atomic orbitals
  • Learn about the role of angular momentum in quantum mechanics
  • Investigate the relationship between quantum numbers and atomic stability
USEFUL FOR

Students and professionals in physics, particularly those focusing on quantum mechanics and atomic theory, as well as educators teaching atomic structure concepts.

motoroller
Messages
29
Reaction score
0
Having a mental block, I should know the answer but can't remember!

Why are there 2n^2 vacancies for each value of n in an atom?

The factor of two is due to degeneracy in s, and one factor of n comes from angular orbitals, 0<=L<=(n-1), which gives n states (2L+1=n), but where does the second factor of n come from?
 
Physics news on Phys.org
Magnetic quantum number: -l \leq m_l \leq +l
 

Similar threads

Undergrad Orbitals and selection rules in a synchrotron
  • · Replies 18 ·
Replies
18
Views
2K
Graduate 2nd Quantization states
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Exploring the Lamb Shift: G-Factor & Angular Momentum
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Does putting a hydrogen atom in a box mix angular momentum states?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Addition of angular momenta
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Ground state energy of cube-like potential wells
  • · Replies 3 ·
Replies
3
Views
2K
High School (N+1) enhancement of spontaneous emission, why not (N+1/2)
  • · Replies 17 ·
Replies
17
Views
3K
Undergrad Why is the total number of quantum states = 2n^2 for some n?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Number of particles in canonical ensemble
  • · Replies 9 ·
Replies
9
Views
2K
Graduate Solving the Radial Equation for the Dirac Hydrogen Atom Solution
  • · Replies 10 ·
Replies
10
Views
4K