Many Electron atoms

Question 1

What is the main problem with Schrodingers equation

Answer 1

Atoms with more than one electron cannot be solved by the Schrodinger equation
Atoms with more than one electron have electron-electron interactions

Question 2

What are the energies of the electron in orbital in hydrogen-like atoms

Answer 2

1s < 2s = 2p < 3s = 3p = 3d < 4s = 4p = 4d = 4f < ……
Energy only depends on number of orbit not type of orbital

Question 3

What is the difference between the energy of electrons, with atoms with 1 electron and atoms with more than one electron

Answer 3

1. As expected, only certain energies are allow
2. Each allowed solution is characterised by the same 3 quantum number as for hydrogen (n, l, ml)
3. Angular wavefunctions are however exactly the same as for hydrogen, so shapes of the s, p, d, f etc orbitals are the same
4. Unlike hydrogen, the energies depend on BOTH n and l. The energies (for a given n) are in the order: s < p < d < f < …

Question 4

The atomic septrum of hydrogen can be explained by
How does this atmoic spectrum come about

Answer 4

solutions to the Schrodinger equation
For the hydrogen atoms, the single electron is normally in the ground state (1s orbital). If the appropriate amount of energy is given to the electron, it will be raised to one of the excited states. The energy released when it moves back down to the ground state is measured by the atomic spetrum of hydrogen

Question 5

Give the order of orbital energies for atoms with more than one electron

Answer 5

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < …

Question 6

Why does the s orbital have less energy than the p orbital
Why does the p orbtial have less energy than the d orbital

Answer 6

• To explain the order of the energies of the orbitals we need to consider the radial probability functions
• For the 3s radial probability function, the electrons exist close to the nucleus than the 3p and 3d (penetration effect) so has an increased effective nuclear charge (Zeff)
• The outer electrons are normally shielded from the full effect of the nuclear charge (Z) by other electrons
• Hence the 3s electrons are bound more tightly than 3d

Question 6

How can we work out what Z eff is then?

Answer 6

Using slaters rules
Z eff= Z - S
Where Z is the number of protons and S is the shielding

Question 7

What are the 5 key Slater’s rules you need to know

Answer 7

1. The orbitals are divided into groups as follows: (1s) (2s 2p) (3s 3p) (3d) (4s 4p) (4d) (4f) (5s 5p) (5d) (5f)
2. The is no contribution to shielding (S) from electrons in groups to the right of the one being considered
3. There is a contribution of 0.35 added to S for each electron in the same group as the one being considered - except in the (1s) group where the contribution is 0.3
4. If the electrons being considered is a s or p orbital, then electrons in the next lowest shell (n-1) contribute 0.85 to shielding. Electrons in lower shells (n-2 and lower) contribute 1.00 to shielding
5. If the electrons being consider is in a d or f orbital, then all electrons below it in energy level contribute 1.00 to shielding

Question 8

For Iron, use Slater’s rules to work out Zeff for the 3s electron
(1s²) (2s² 2p⁶) (3s² 3p⁶) (3d⁶) (4s² 4p⁰)
Atomic number is 26, so Z = 26

Answer 8

S = (7 x 0.35) + (8 x 0.85) + (2 x 1.00)
Z*eff *= 26 - 11.25 = 14.75

Question 9

Can you use the solutions to the Schrodinger wave equation for hydrogen-like atoms to explain the periodic table

Answer 9

Yes - you can use the ‘Aufbau’ (building-up) principle:
To move from one element to the next, add one proton and x neutrons to the nucleus, and one electrons into the orbital of lowest energy which is available

Question 10

What is the spin quantum number (Ms)

Answer 10

It has allowed values of +1/2 and -1/2
Electrons are found to behave as though they were spinning. A particle can spin clockwise or anticlockwise
This spin is defined by the spin quantum number, and it can have only two values

Question 11

2 electrons exist is an orbit
Why is this the case

Answer 11

Each electron is completely specificed by the values for 4 quantum numbers: n, l, ml, and ms - Pauli Exclusion Principle
All electrons in a given orbtial have the same values for n, l and ml, and there is only two possible values for ms.
Therefore, there is a masimum of TWO electrons in any orbital and they must have opposite spins

Question 12

Why is Helium more stable than Hydrogen

Answer 12

Helium has a full 1s shell, however hydrogen doesn’t
It is very difficult to break up a full shell, helium is highly inert

Question 13

Why is Lithium less stable than Helium

Answer 13

Lithium only has 1 electron in the 2s shell so has a high tendency to loose it
Compared to Helium with a full 1s shell

Question 14

Why is beryllium more stable than lithium

Answer 14

Beryllium has a full 2s subshell, which means its harder to loose electrons
However berhyllium is not so stable as it 2 shell is not full filled but it is stull fairly unreactive

Question 15

What is Hund’s rule

Answer 15

The most stable electronic state is the one with the most parallel spins

Question 16

Fluorine’s chemistry is affected by its electronm configuration
1s² 2s² 2p⁵

Answer 16

It has a tendecyn to acquire the electron needed to obtain a full shell of electroms - same electron configuration of the noble gas neon

Question 17

Which electrons are affected by chemical reactions

Answer 17

Only the valence electrons

Question 18

The periodicity of chemical properties arises because

Answer 18

elements with the same number and type of valence electrons behave similarly

Question 19

In group 1 and 2
What is the general trend of atomic radius size

Answer 19

Atomic radius increases down the group
This is because there is more electron shells being added

Question 20

Group 13 does doesnt show such an obvious increase in atomic radius moving down the group
Why is this, use Gallium as your example

Answer 20

There is d-block contraction and a f-block contraction
This means that for Gallium for example, the d-block is now inbetween the s-block and p-block. When moving across the d-block a proton is being added to the nucleus causing nuclear charge to increase, while the increase in the singluar electron has a minimal effect because the d-block isn’t good a shielding
This pulls the outer electrons closer in towards the nucleus making its atomic radii smaller

Question 21

Group 13 does doesnt show such an obvious increase in atomic radius moving down the group
Why is this, use Thallium as your example

Answer 21

There is d-block contraction and a f-block contraction
For Thallium, the f-block (and d-block) is now inbetween the s-block and the p-block. The p-block is worse at shielding than the d-block, therefore the larger increase in nuclear charge, pulling the electrons closer to the nucleus, causing the atomic radius to be smaller

Question 22

What is the one thing to note about the shielding ability of the s and p-block; and the d and f-block

Answer 22

The s and p-block are really good at shielding
The d and f-block are not as good

Question 23

In period 1, what happens to the atomic radius as you move from left to right

Answer 23

The atmoic radius get small as you move to the right
This corresponds with the effective nuclear charge (Zeff) increasing to the right

Question 24

What is the trend in ionisation energy from Hydrogen to Argon

Answer 24

From hydrogen to helium there is a large increase in ionisation energy
Then from helium to lithum, there is a large decrease
Then from Lithium to Neon, there is a general increase
From Neon to Sodium, a large decrease
Then from sodium to Argon, there is a general increase