Atomic orbitals in many electron atoms
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What is orthogonality?
The need for all independent parts in order to describe the whole atom
When will two wavefunctions φ₁ and φ₂ be orthogonal?
If their overlap integral is zero
What is an overlap integral?
Values of 2 wavefunctions are multiplied at each point and all these values are added up
What are the differences between the H atom and the polyelectronic atom?
• Different energies for the orbitals in different atoms • Energy of orbitals on the H atom only depend on n but for polyelectronic atoms, the energy depends on n and l • Orbitals from polyelectronic atoms are smaller than that of the H atom due to more attraction to nucleus
What are the three rules called for determining electron configuration for polyelectronic atoms?
• Pauli exclusion principle • Aufbau principle • Hund’s rule
What is the Pauli exclusion principle?
Every electron in an atom must have a unique set of quantum numbers
What is the 4th quantum number for each electron ?
Spin quantum number
What is the spin quantum number?
Related to the intrinsic magnetic movement of an electron
What are the two possible spin values of an electron?
• 1/2 + 1/2
What symbol does spin quantum number have?
ms
What are the two different arrangements of electrons in the same atom?
Spin parallel ↑↑ Spin paired ↑↓
What are the two different arrangements of electrons in the same atom?
Spin parallel ↑↑ Spin paired ↑↓
What is the most important consequence of the Pauli exclusion principle?
An orbital cannot contain more than 2 electrons
How must the electrons in the same atom be arranged in order to have different ms values?
Spin paired↑↓
What is the Aufbau principle?
The ground state electron configuration of an atom is found by putting each electron in turn into the available lowest energy
How are electrons added into each separate degenerate orbital?
added into orbitals as spin parallel until all have one electron and then added in to form spin paired
What is Hund’s rule?
The ground state electron configuration of an atom is the arrangement with the maximum number of spin parallel electrons