Atomic Orbitals

Question 1

How can p orbitals be described in terms of energy, given that they have the same energy?

Answer 1

Degenerate.

Question 2

What is meant by saying that d orbitals have 5-fold degeneracy?

Answer 2

All five d orbitals in the same shell have the same energy.

Question 3

What values can the principle quantum number, n, take?

Answer 3

Integer values.

Question 4

In a one electron system what is the value of n alone responsible for describing?

Answer 4

The energy of the electron.

Question 5

What values can the angular momentum quantum number, l, take?

Answer 5

n-1.

Question 6

What is the equation for angular momentum?

Answer 6

(h/2π) x sqrt(lx(l+1))

Question 7

What letter corresponds with l=0

Answer 7

s

Question 8

What letter corresponds with l=1

Answer 8

p

Question 9

What letter corresponds with l=2

Answer 9

d

Question 10

What letter corresponds with l=3

Answer 10

f

Question 11

What letter corresponds with l=4

Answer 11

g

Question 12

What letter corresponds with l=5

Answer 12

h

Question 13

What values can the magnetic quantum number, m_l, take?

Answer 13

From -l to +l.

Question 14

What does the magnetic quantum number describe?

Answer 14

The orientation of the orbital’s angular momentum.

Question 15

What does the angular momentum quantum number describe?

Answer 15

The magnitude of the orbital’s angular momentum.

Question 16

As well as the three quantum numbers, what other value can be used to describe an electron?

Answer 16

Spin.

Question 17

What is the fixed value of spin for an electron?

Answer 17

1/2

Question 18

What does m_s define?

Answer 18

The alignment of an electron’s spin.

Question 19

What is the symbol for wavefunction?

Answer 19

Psi.

Question 20

Psi squared gives you what?

Answer 20

A probability density - a measure of the probability of finding an electron at a given position.

Question 21

For what systems is it possible to solve the Schrödinger equation exactly, giving atomic orbitals?

Answer 21

One electron systems.

Question 22

What is the equation for the energy of a wavefunction?

Answer 22

E_n= -((m_e x e^4)/(8ε_o x h^2)) x (z^2/n^2)

Where m_e = mass of the electron
ε_o = vacuum permittivity.
e=elementary charge
z= nuclear charge.

Question 23

Why is the equation for energy of a wavefunction only dependent on n?

Answer 23

It is for a one-electron system, so energy is only dependent on n.

Question 24

The constants in the equation for the energy of a wavefunction can be grouped to give what constant? What does the equation simplify to?

Answer 24

The Rydberg Constant (R_H).

R_H x (z^2/n^2)

Question 25

What is an important point about the results of the Schrödinger equation?

Answer 25

The energies are negative, and tend towards zero the larger n gets.

Question 26

In terms of the Schrödinger equation, what is the ionisation energy?

Answer 26

The energy required to promote an electron from the lowest energy level to zero energy.

Question 27

Should Polar or Cartesian coordinates be used to describe the position of an electron?

Answer 27

Polar

Question 28

What values can the angle θ take?

Answer 28

From 0 to π (180 degrees).

Question 29

What values can the angle φ take?

Answer 29

From 0 to 2π (360 degrees).

Question 30

What diagram can be used to show how the wavefunction varies with different values of θ and φ?

Answer 30

3D isosurface plots.

Question 31

What is a disadvantage of 3D isosurface plots?

Answer 31

Do not give a measure of the probability of finding an electron in a given position.

Question 32

What do the contours join up in a contour plot?

Answer 32

Areas of equal values of wavefunction (psi).

Question 33

Does a density plot show the probability of finding an electron at a given position, and if so how?

Answer 33

Yes. The darker it is, the higher the value of psi and the higher the probability of finding an electron at that point.

Question 34

What is the Radial Distribution Function (RDF)?

Answer 34

The sum of the electron density in a thin shell at a set distance, r, from the nucleus.

Question 35

What information is given by the RDF?

Answer 35

The probability of finding an electron in a thin shell of thickness δr, at radius r from the nucleus.

Question 36

What is RDF the product of?

Answer 36

ψ^2 x r^2.

Question 37

What is the Bohr radius (a_0)?

Answer 37

The radius at which the electron is most likely to be found.

Question 38

How can the number of radial nodes be calculated?

Answer 38

n-1-l

Question 39

How can the number of angular nodes be calculated?

Answer 39

It is equal to l

Question 40

How can the total number of nodes be calculated?

Answer 40

n-1

Question 41

What is unusual about the 3d_z^2 orbital's angular node?

Answer 41

It is a nodal cone rather than a nodal plane.

Question 42

Why is the orbital approximation used rather than the Schrödinger equation for multi-electron systems?

Answer 42

Repulsion between electrons is an extra factor that must be taken into account, so the Schrödinger equation can't be solved exactly.

Question 43

What assumptions are made in the orbital approximation?

Answer 43

From the point of view of one electron, the effect of all the other electrons can be averaged out to give a modified potential that is spherically symmetrical and centred on the nucleus.

Question 44

As a result pf screening, what is the effective nuclear charge (z_eff) for electrons in the 1s orbital?

Answer 44

About 2.7

Question 45

As a result pf screening, what is the effective nuclear charge (z_eff) for electrons in the 2s orbital?

Answer 45

About 1.3

Question 46

By what percentage of the charge of a proton do electrons in the 1s orbital screen each other by?

Answer 46

30%

Question 47

Explain why the 2s orbital is lower in energy than the 2p orbital?

Answer 47

It penetrates the 1s orbital to a greater extent than the 2p orbital on a graph of RDF.

Question 48

Why is the 4s orbital lower in energy than the 3d orbital in many multi-electron systems?

Answer 48

Greater nuclear charge contracts the orbitals so the 4s orbital penetrates lower orbitals to a sufficient extent that, on average, the electrons in this orbital experience greater effective nuclear charge than those in the 3d orbital.