Wavefunctions
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What is the equation for a wavefunction?
Normalisation constant (A) x angular x radial x exponential
What does the negative exponential decay represent?
The dependence of the wavefunction from the distance to the nucleus
What is the angular part of the wavefunction?
It depends on the direction
What is the radial part of the wavefunction?
It depends only on the distance to the nucleus r and not on the direction
What value is used if either of the radial or angular parts are missing?
1
What does the angular part describe?
Shape and orientation
Which quantum number is the number of nodes?
ι
How many angular nodes does a 1s orbital have?
ι = 0 s orbitals are spherical and have no direction dependence
How many angular nodes does a 2p orbital have?
ι = 1 They have different orientations in space
How many angular nodes does a 3d orbital have?
ι=2 Has 2 planes
What does the radial part describe?
the effective size of the orbital
How do you calculate the number of radial nodes?
The total number of nodes (n-1) minus the number of angular nodes ι
Why don’t you look at A or the exponential decay in the wavefunction equation?
They are effectively constant
How many radial nodes does a 1s orbital have?
0
How many radial nodes does a 2s orbital have?
1
How many radial nodes does a 3s orbital have?
2
The number of radial nodes…
Increases with n
What is electron density proportional to?
The distance from the nucleus Proportional to the number of points at which the electron can be at a particular value of r
What is radial probability function?
Electron density at a distance r from the nucleus is proportional to 4πr²φ²
Where in an s orbital is there the most electron density in R²?
The outermost lobe of the orbital
Do 2p orbitals have any radial nodes?
No
Do 2p orbitals have any angular nodes?
Yes When x=o, y=o or when z=o
When is there a change of phase?
When you cross a node
What do orbital energies depend on for multi electron atoms?
Quantum numbers n and ι