Electrons: Bonding, Electronic structure

Question 1

What does the Schrödinger equation describe?

Answer 1

The solutions to many particles (Many electrons and many nuclei in solid)

Question 2

Define the Schrödinger equation

Answer 2

HΨ = EΨ

where Ψ is the wavefunction describing the positions and spin states of all degrees of freedom the electrons and nuclei in the system.
The terms in the H = kinetic term (with inputs of the electron and nuclear masses) as PE dominated by Coulomb interaction term between all the electrons and nuclei

Question 3

What are the four quantum numbers?

Answer 3

|n, l, l_z, σ_z,⟩

Question 4

What is the n, quantum number?

Answer 4

n is the principal quantum number

Where n is the radius of shell

n=1,2,…

Question 5

What is the l, quantum number?

Answer 5

l is the angular momentum

l is the shape
l = 0,1,….n-1
s,p,d,f which corresponds to 2(2l+l

Question 6

What is the l_z, quantum number?

Answer 6

l_z is the z component of angular momentum
The relative orientation of the orbital
l_z=-l..,l

Question 7

What is the σ_z, quantum number?

Answer 7

σ_z is the z-component of spin

σ_z=-1/2 or +1/2

Question 8

How do you decide which orbitals are filled?

Answer 8

First consider, the pauli exclusion Principle: no two electrons in a system can have the same quantum numbers.(Because electrons are fermions)

Then the afbau principle: shells should be filled starting with the lowest energy state. An entire shell is filled before another shell is started.

Also the madelung’s or klechkovsky’s rule: The energy ordering is from lowest value of n+l to the largest; and when two shells have the same value of n+l, fill the one with the smallest n first.

Question 9

What is the ordering rule that shells should be filled?

Answer 9

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, . . . .

The fill up diagonal diagram

Question 10

Do some atoms violate some rules?

Answer 10

There are a few atoms that violate this ordering (Madelung’s) rule.
One example is copper which typically fills the 3d shell by “borrowing”
an electron from the (putatively lower energy) 4s shell.

Question 11

Why is there similarities between certain elements(?

Answer 11

Elements in the same column of the periodic table (with a few
exceptions) have the same number of electrons in the outermost
shells, and hence have similar chemical properties.

Question 12

Why are electrons more tightly bound to the nucleus of atoms on the right of the periodic table than the left?

Answer 12

The idea of screening and effective nuclear charge explains a number
of the periodic trends going across the rows of the periodic
table.

Question 13

How is the effective nuclear charge reduced?

Answer 13

One electron will shield the other from the nucleus, yielding a reduced “effective nuclear charge”

Question 14

What are the key trends in the periodic table?

Answer 14

The binding energy of the outermost electrons increases as we go from left
to right in the rows of the periodic table—i.e., as we put more electrons
in the outermost shells the effective charge of the nucleus increases,
since electrons at the same radius screen each other from the nucleus
ineffectively.

The
radius of atoms drops going left to right in the periodic table, the energy
required to ionize an atom increases going left to right, and the energy
gained by adding an electron (the electron affinity) also increases going
left to right

Question 15

Bonding flashcards

Answer 15

Watch lecture while doing this!