Lecture 3 Quantum Mechanics and Wavefuntions

Question 1

Describe concept of the wavefunction and why it is used

Answer 1

How likely an electron is going to be in a particular place at a particular time. Ψ means wavefunction.

Question 2

What is the probability density according to the Born interpretation?

Answer 2

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

Question 3

Is Ψ^2 always positive?

Answer 3

Yes

Question 4

Is wavefunction always positive?

Answer 4

No, it can be positive or negative

Question 5

What is the probability if Ψ = 0 and what is this called

Answer 5

0, a node. It touches the x axis on graph

Question 6

What is the Schrodinger wave equation to describe behaviour of electron

Answer 6

H Ψ = E Ψ (doesn’t cancel) used to calculate behaviour of an electron

Question 7

Is solution of the schrodinger wave equation possible with any energy?

Answer 7

No, each allowed solution (wavefunction) of the schrodinger equation for the hydrogen atom defines an allowed atomic orbital

Question 8

In schrodinger wavefunction what is n? What numbers are allowed? What does it determine?

Answer 8

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

Question 9

What is the equation that relates wavelength of light to transitions between energy levels n?

Answer 9

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

Question 10

In schrodinger wavefunction what is l? What are it’s allowed values? What does it determine?

Answer 10

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.

Question 11

What are the orbitals in relation to l values?

Answer 11

l = 0 s l = 1 p l = 2 d l = 3 f

Question 12

When n = 1, what is l =? and what orbital would this result in?

Answer 12

l=0, s orbital

Question 13

When n = 2, what is l? and what orbital would this result in?

Answer 13

l=1, p orbital

Question 14

Why is there no 1p orbital?

Answer 14

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

Question 15

What is a degenerate orbital? Give an example

Answer 15

Orbitals of the same energy, e.g. 4s=4p=4d=4f

Question 16

What quantum number is mℓ? What are it’s allowed values? What does it determine?

Answer 16

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)

Question 17

When l=0, what values can mℓ be? How many possibilities does this make?

Answer 17

mℓ = 0 1 possibility for 1s orbital

Question 18

When l=1, what values can mℓ be? How many possibilities does this make?

Answer 18

mℓ= -1, 0, 1 3 possibilities for 2p orbitals

Question 19

When l=3, what values can mℓ be? How many possibilities does this make?

Answer 19

mℓ = -3, -2, -1, 0, 1, 2, 3 7 possibilities for 4f orbitals

Question 20

What does radial wavefunction graph map along each axis? What is the graph telling us?

Answer 20

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

Question 21

For a spherical shell, what do we plot against r? What will this tell us? (3 things)

Answer 21

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

Question 22

How to work out the number of radial nodes with reference to n and l with an example

Answer 22

n-l-1 2 for 3s, 1 for 2s and 2p, 0 for 1s, 2p 3d

Question 23

How do we arbitrarily define size of orbitals?

Answer 23

Surface of 90% of the total electron probability

Question 24

What do we plot to visualise electron orbitals?

Answer 24

Y squared, the angular probability

Question 25

Explain the significance of the overall shape and orientation depending only on l and ml, not n

Answer 25

All orbitals of same type have the same shape

Question 26

How to work out the number of angular nodes

Answer 26

=l

Question 27

How to work out total number of nodes

Answer 27

Angular + Radial

Question 28

What is the significance of working out the shape of electron orbitals?

Answer 28

Provides basis for structure and reactivity of all compounds

Question 29

Sketch shape and orientation of s orbitals

Answer 29