MARY - Topic 4

Question 1

What is the Schrödinger wave equation used for?

Answer 1

To determine energy levels for electrons. It uses the idea of an electron acting as a wave that alters with position.

Question 2

What is a wavefunction?

Answer 2

A mathematical function which varies with position. Each different wavefunction describes a different orbital type with a characteristic energy.

Question 3

What do the different parts of the equation mean?

Answer 3

1 = KE of wavefunction
2 = Potential Energy

= E(Total) for electron @ point x,y,z in space.

Question 4

What can the Schrödinger wave equation be solved for?

Answer 4

Only 1-electron systems, where it gives all the energy levels possible for that electron.

Question 5

What is the wavefunction squared/the probability per unit volume?

Answer 5

The probability of an electron being in a certain volume of space.

Question 6

What are the different quantum numbers?

Answer 6

n = Principal Quantum Number (determines the energy shell)
l = Secondary Quantum Number (gives the types of orbitals possible for a given 'n')
ml = Magnetic Quantum Number (orbital orientations for each l value)

Question 7

What are the spherical (polar) coordinates?

Answer 7

(r, θ, φ ) = in radian units

1 = distance from nucleus
2 = deviation from the z axis
3 = deviation from x axis.

Question 8

What can the wavefunction be factorised into?

Answer 8

Wavefunction (x,y,z) = Wavefunction (r, θ, φ ) = R(r) x Y(θ, φ )

R(r) = radial wavefunction and shows how the wavefunction varies as r changes (distance from nucleus)
Y(θ, φ ) = angular wavefunction and shows the overall orbital shape.

Question 9

What happens when the wavefunction = 0?

Answer 9

It is a node.

Question 10

What are the two types of nodes?

Answer 10

Radial Node = when R(r) = 0

Angular Node = when Y(θ, φ ) = 0

Question 11

What does R(r) contain information on?

Answer 11

How the wavefunction behaves as a function of distance (r) from the nucleus

Question 12

When are there no radial nodes?

Answer 12

The first time an orbital appears.

Question 13

How do you work out the number of nodes?

Answer 13

n-(l+1)

Question 14

What happens to s-orbitals?

Answer 14

Only s-orbitals start with R(r) > 0

Question 15

What is R(r)squared?

Answer 15

The electron density at a specific point in space, as a function of distance (r) from the nucleus only.

Question 16

What is the problem with R(r)squared?

Answer 16

It doesn’t take into account the amount of space available for the electron, and can be misleading.

Question 17

What is the radial distribution function?

Answer 17

It describes the probability of finding an electron in a spherical shell of thickness, as a distance (r) from around the nucleus.

Question 18

What does the maximum in the rdf tell us?

Answer 18

The most probable distance from the nucleus of finding an electron.

Question 19

What happens to the R(r) value at the nucleus?

Answer 19

S-orbitals have +ve R(r) values at the nucleus, all other orbital types have an R(r) value of 0 at the nucleus.

Question 20

What is penetration with orbitals?

Answer 20

The s orbital penetrates the p and d orbitals, so although r @ rdf max is on the s orbital pattern, and furthest away from nucleus, the penetration can mean that an electron in s orbital can get closer to the nucleus.

Question 21

What happens to the angular wavefunction?

Answer 21

s-orbitals have a fixed angular wavefunction, so s-orbitals are spherical.
p, d and f orbitals angular wavefunctions do vary so they aren’t spherical.