Lecture 3 Quantum Mechanics and Wavefuntions Flashcards
Describe concept of the wavefunction and why it is used
How likely an electron is going to be in a particular place at a particular time. Ψ means wavefunction.
What is the probability density according to the Born interpretation?
Imagine a small box centred around co-ordinates of (x,y,z) in space. The probability of finding the electron in that box is proportional to the square of the wavefunction at that point
Is Ψ^2 always positive?
Yes
Is wavefunction always positive?
No, it can be positive or negative
What is the probability if Ψ = 0 and what is this called
0, a node. It touches the x axis on graph
What is the Schrodinger wave equation to describe behaviour of electron
H Ψ = E Ψ (doesn’t cancel) used to calculate behaviour of an electron
Is solution of the schrodinger wave equation possible with any energy?
No, each allowed solution (wavefunction) of the schrodinger equation for the hydrogen atom defines an allowed atomic orbital
In schrodinger wavefunction what is n? What numbers are allowed? What does it determine?
Principal Quantum Number. Allowed values 1,2,3,4,5 NOT 0. Determines energy of an allowed solution of wave function, for 1e- atoms such as Hydrogen. Also determines overall size of orbital
What is the equation that relates wavelength of light to transitions between energy levels n?
1/λ = Rh (1/(n1^2)-1/(n2^2) When λ = wavelength, Rh = 1.097X10^7 m^-1 Rydberg’s Constant, and n are integers such that n1 is less than n2
In schrodinger wavefunction what is l? What are it’s allowed values? What does it determine?
l is the Orbital Angular Momentum Quantum Number. Allowed values are 0,1,2,3,4…as long as it’s (n-1). It determines shape of the orbital but NO effect on energy for one-electron atoms.
What are the orbitals in relation to l values?
l = 0 s l = 1 p l = 2 d l = 3 f
When n = 1, what is l =? and what orbital would this result in?
l=0, s orbital
When n = 2, what is l? and what orbital would this result in?
l=1, p orbital
Why is there no 1p orbital?
As l has to be n-1, and n cannot be 0, it begins as n=1, this means the only value l can be is 0 which only creates an s orbital
What is a degenerate orbital? Give an example
Orbitals of the same energy, e.g. 4s=4p=4d=4f
What quantum number is mℓ? What are it’s allowed values? What does it determine?
It is the Magnetic Quantum Number. It’s values are integers starting as -L to +L with total of 2L + 1 values for any L. -L, -L+1, -L+2…-1, 0, 1….+L-2, +L,1, +1. It determines the orientation in space of the orbital, it has no effect on the energy of the electron unless in a magnetic field (which acts as a direction bias)
When l=0, what values can mℓ be? How many possibilities does this make?
mℓ = 0 1 possibility for 1s orbital
When l=1, what values can mℓ be? How many possibilities does this make?
mℓ= -1, 0, 1 3 possibilities for 2p orbitals
When l=3, what values can mℓ be? How many possibilities does this make?
mℓ = -3, -2, -1, 0, 1, 2, 3 7 possibilities for 4f orbitals
What does radial wavefunction graph map along each axis? What is the graph telling us?
On y is wavefunction (R) against x which is distance from the nucleus (r) in pm. It is telling us the probability of finding the electron at a given distance from the nucleus
For a spherical shell, what do we plot against r? What will this tell us? (3 things)
4πr^2R^2 (4πr^2 is area of a sphere) It will tell us likely size of the orbitals, as n increases for a given value of l (specific type of orbital) size increases There is a small but greater than 0 chance of finding the electron far from the nucleus, so it’s hard to accurately define size There are certain distances where there is 0 possibility of the electron being, these are called nodes
How to work out the number of radial nodes with reference to n and l with an example
n-l-1 2 for 3s, 1 for 2s and 2p, 0 for 1s, 2p 3d
How do we arbitrarily define size of orbitals?
Surface of 90% of the total electron probability
What do we plot to visualise electron orbitals?
Y squared, the angular probability
