Schrodinger Wave Equation

Question 1

What is the Schrodinger wave equation used for?

Answer 1

Determining the energy levels for electrons.

Question 2

What is a wavefunction?

Answer 2

A mathematical function that varies with position.

Question 3

What does each wavefunction describe?

Answer 3

A different orbital type with a characteristic energy.

Question 4

What is the purpose of the wavefunction squared?

Answer 4

The wavefunction alone is not a measurable quantity, whereas the wavefunction squared is. It represents the electron density per unit volume.

Question 5

What does dt measure?

Answer 5

How electron density varies as one moves through space in small volume amounts - this gives us orbital shape.

Question 6

When was the SWE solved and what was the outcome?

Answer 6

In 1927 the equation was solved and it showed that the Bohr radius of 0.529 angstroms was the most likely distance from the nucleus of finding an electron in a hydrogen atom.

Question 7

What is n?

Answer 7

Principle quantum number, determines the energy.

Question 8

What is l?

Answer 8

Secondary quantum number, gives orbital type.

Question 9

What is ml?

Answer 9

Magnetic quantum number, gives the orbital orientations for each l value.

Question 10

What is R(r)?

Answer 10

The radial wavefunction and examines how the wavefunction changes as r varies. (r=distance from nucleus).

Question 11

What is Y(theta, thing)?

Answer 11

The angular wavefunction and determines the overall orbital shape.

Question 12

What is a node?

Answer 12

When the wavefunction has a value of zero.

Question 13

What are the two types of node?

Answer 13

A radial node and a nodal plane.

Question 14

What does the radial wavefunction tell us?

Answer 14

How the wavefunction behaves as a function of distance from the nucleus only.

Question 15

What does R(r)^2 tell us?

Answer 15

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

Question 16

Whys is R(r)^2 not that useful?

Answer 16

Does not take into account the amount of space (volume elements/places) available for the electron and can be misleading.

Question 17

What is the radial distribution function?

Answer 17

The probability of finding an electron in a spherical shell of thickness dr at a distance r from around the nucleus.

Question 18

What does the maximum in the rdf tells us?

Answer 18

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

Question 19

What is a key difference between s orbitals and all other orbitals in terms of R(r)?

Answer 19

S orbitals have a positive value of R(r) at the nucleus whereas all other orbitals have a value of R(r) of zero at the nucleus.

Question 20

Despite the 2s orbital having a greater rdf. max than the 2p orbital, why is a 2p electron more likely to be found further away from the nucleus than the 2s?

Answer 20

The 2s penetrates the 2p, so the 2s electron can sometimes get closer to the nucleus than the 2p electron. The energy of the 2p orbital is therefore greater than the 2s orbital, and the 2s fills before the 2p.

Question 21

How does the angular wavefunction vary for the pz orbital?

Answer 21

It is only dependent on theta and not phi.

Question 22

How does the angular wavefunction vary for the px and py orbitals?

Answer 22

The vary with both parts of the angular wavefunction but in different ways.

Question 23

What is a boundary surface?

Answer 23

Depictions of orbitals where there is 95% probability of finding an electron/where electron density is located.

Question 24

What are angular nodes?

Answer 24

When the angular wavefunction is equal to zero. They can be planes or cones and do not depend on r.

Question 25

Why must orbital approximations be used when looking at more than 1-electron systems?

Answer 25

The SWE cannot be solved if more than one electron is present.

Question 26

What is a radial node?

Answer 26

A distance from the nucleus (r) where the radial wavefunction is equal to zero.

Question 27

What is the orbital approximation?

Answer 27

Wf (1,2,3,4…N) = Wf1 x Wf2 x Wf3….n