Many Electron atoms Flashcards
What is the main problem with Schrodingers equation
Atoms with more than one electron cannot be solved by the Schrodinger equation
Atoms with more than one electron have electron-electron interactions
What are the energies of the electron in orbital in hydrogen-like atoms
1s < 2s = 2p < 3s = 3p = 3d < 4s = 4p = 4d = 4f < ……
Energy only depends on number of orbit not type of orbital
What is the difference between the energy of electrons, with atoms with 1 electron and atoms with more than one electron
- As expected, only certain energies are allow
- Each allowed solution is characterised by the same 3 quantum number as for hydrogen (n, l, ml)
- Angular wavefunctions are however exactly the same as for hydrogen, so shapes of the s, p, d, f etc orbitals are the same
- Unlike hydrogen, the energies depend on BOTH n and l. The energies (for a given n) are in the order: s < p < d < f < …
The atomic septrum of hydrogen can be explained by
How does this atmoic spectrum come about
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
Give the order of orbital energies for atoms with more than one electron
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < …
Why does the s orbital have less energy than the p orbital
Why does the p orbtial have less energy than the d orbital
- 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
How can we work out what Z eff is then?
Using slaters rules
Z eff= Z - S
Where Z is the number of protons and S is the shielding
What are the 5 key Slater’s rules you need to know
- The orbitals are divided into groups as follows: (1s) (2s 2p) (3s 3p) (3d) (4s 4p) (4d) (4f) (5s 5p) (5d) (5f)
- The is no contribution to shielding (S) from electrons in groups to the right of the one being considered
- 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
- 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
- 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
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
S = (7 x 0.35) + (8 x 0.85) + (2 x 1.00)
Z*eff *= 26 - 11.25 = 14.75
Can you use the solutions to the Schrodinger wave equation for hydrogen-like atoms to explain the periodic table
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
What is the spin quantum number (Ms)
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
2 electrons exist is an orbit
Why is this the case
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
Why is Helium more stable than Hydrogen
Helium has a full 1s shell, however hydrogen doesn’t
It is very difficult to break up a full shell, helium is highly inert
Why is Lithium less stable than Helium
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
Why is beryllium more stable than lithium
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
What is Hund’s rule
The most stable electronic state is the one with the most parallel spins
Fluorine’s chemistry is affected by its electronm configuration
1s² 2s² 2p⁵
It has a tendecyn to acquire the electron needed to obtain a full shell of electroms - same electron configuration of the noble gas neon
Which electrons are affected by chemical reactions
Only the valence electrons
The periodicity of chemical properties arises because
elements with the same number and type of valence electrons behave similarly
In group 1 and 2
What is the general trend of atomic radius size
Atomic radius increases down the group
This is because there is more electron shells being added
Group 13 does doesnt show such an obvious increase in atomic radius moving down the group
Why is this, use Gallium as your example
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
Group 13 does doesnt show such an obvious increase in atomic radius moving down the group
Why is this, use Thallium as your example
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
What is the one thing to note about the shielding ability of the s and p-block; and the d and f-block
The s and p-block are really good at shielding
The d and f-block are not as good
In period 1, what happens to the atomic radius as you move from left to right
The atmoic radius get small as you move to the right
This corresponds with the effective nuclear charge (Zeff) increasing to the right
What is the trend in ionisation energy from Hydrogen to Argon
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
