Chapter 2 Atomic Orbitals, energy, shape, and electron density

Rydberg constant

-2.18 x 10^-18 J/electron

Hydrogen ionization energy

-2.18x10^-18 J (1/infinity^2-1/1^2)--> -2.18x10^-18 J(0-1)= 0

To calculate ionization energy

-2.18x10^-18 J (1/nf^2-1/ni^2) This is actually Bohr's equation that determines the electrons energy when it moves up or down an orbit.

SPDF

0123

Rules for Wavefunction

1. must be finite in magnitude. Any value of Ψ that is infinite results in Ψ^2 to be infinite at those points. And the probability has to be from 0 to 100% 2. Ψ must be single-valued. 3. Ψ must be a smooth and continuous function

There are

18 electron fillings when you're doing the electron configuration

Molecular order filling

1s,2s,2p,3s,3p,4s,3d,4p,5s,4d,5p,6s,4f,5d,7s,5f,6d,7p

What is the HOMO and LUMO of ground-state carbon?

2p

Bohr radius equation

5.29x10^-11 m, this is when n=1

What is the difference between a shell and a subshell?

A shell is like 1 and 2, the 2nd shell has subshells we have a 2s orbital and a 2p orbital

Excited State

Atoms can undergo absorption of electromagnetic radiation upon which an electron can be promoted to a higher energy orbital. These states do not follow the aufbau principle

Why are 2p orbitals higher in energy than 2p?

Because 2s orbitals penetrate closer to the nucleus which means the electrons in 2s experience a stronger attraction to the nucleus, pulling them down, and making the 2p orbitals have a higher energy than the 2s

Why is Helium 1s closer to nucleus than Hydrogen?

Because more protons will lead to a smaller radius than and a higher probability of finding the electron.

Electrons prefer to be unpaired rather than paired

Because that would give them a bigger magnetic spin number, +1/2 + +1/2= 1

The 4s orbital is higher in energy than the 3d

Because when you fill the 3d shell, the 4s goes to a higher energy although it is filled before.

When n=1

Bohr's model has the lowest possible energy state

Radii

Distance from the nucleus, defined by n

r, θ, and Ψ

Give position of electron, r depends on n and theta is angular portion

magnetic quantum number ml

Gives the orientation of the orbital in space; in other words, the value of m describes whether an orbital lies along the x-, y-, or z-axis on a three-dimensional graph

Hamiltonian operator

Has kinetic and potential components. For an electron, the kinetic energy term accounts for the motion of the electron around the nucleus. The potential energy term involves the Coulombic interaction between the positive nucleus and negative electron.

frontier orbitals

Homo and Lumo

Schrodinger Equation

HΨ=EΨ Determines what energy of an electron is and where the electron density is. The equation states that when the Hamiltonian operator is applied to the wavefunction, Ψ, the total energy E of the electron can then be calculated.

Remember

In Spartan, whenever the atom or molecule has an unpaired electron the orbital energy diagram is split into two labeled a and b, which correspond to the two spins α and β (+1/2 and -1/2). So the bLUMO for hydrogen is a 1s orbital and the aLUMO is a 2p orbital.

Know that

Neutrons and protons form the nucleus at the center of the atom Electrons are arranged around the nucleus There is an attractive force between the negatively charged electrons and the positively charged neutrons.

Important

Notice how the amount of possible L values is equal to the quantum number. ex) n=2, the possible values for L are 0 and 1, which are 2 values

Hund's Rule

Place electrons in a way that will maximize spin #

Ψ^2

Probability Density of finding an electron in a region of space

in the absence of the angular component

R= Ψ

Order of subatomic particles

Smallest to largest: electron, neutron, proton

Exceptions to the Aufbau Principle

Some elements such as Chromium, copper,niobium,silver, nitrate

What makes up the Ψ?

a radial function R and an angular function Y.

monatomic ion

an ion formed from a single atom. ex) when a fluorine atom forms the fluoride ion, it gains one electron: F (1s22s22p5) + e- → F- (1s22s22p6)

Wavefunction is composed of

angular component and radial component

Bohr proposed that

angular momentum and radii become quantized in energy levels.

Electrons that have a common value of n

are said to be within the same shell

All states n>1

called the excited states

The energy difference between 2 electrons or states

can be calculated by taking the difference between 2 energies.

DXZ orbital

crosses the z axis vertically and it points towards the x axis which is to the right and down.

The principal quantum number n

determines the most likely distance an electron is away from the nucleus, as well as the highest point in the radial distribution plot.

The angular momentum number L

determines the shape of the orbital

Bohr believed

electrons travel around the nucleus in orbits, and that each orbit had an energy associated with it.

Angular Nodes

equal to the L quantum number, it is shown by the space in between the lobes. is caused by the change of sign of the angular wavefunction.

Bohr's equation

has a negative sign to imply the attractive force between an electron and protons within the nucleus

How I interpreted graph on LBLF

it had to be s b/c its penetrating closer to the nucleus.

Small HOMO LUMO gap

less stable

DXY orbital

looks like someone sleeping

Cations

lose electrons, positive charge

For transition metals

metals, monatomic ions are formed by first removing s electrons prior to removing d electrons. For example, if we consider iron ([Ar]4s23d6), we would remove electrons from the 4s first because it is the higher one in energy.

Bohr Model

model of an atom that shows electrons in circular orbits around the nucleus

Radial Nodes

n-L-1

Anions

negatively charged, gain electrons

Pauli Exclusion Principle

no two electrons in the same atom can have the same set of four quantum numbers

In a SINGLE electron

orbitals are degenerate (same energy level) b/c they're not interacting w any other electrons, this applies to hydrogen

n must be a

positive integer

subshells

spdf

Aufbau Principle

states that each electron occupies the lowest energy orbital available

Nitrogen configuration

the 2s^2 and 2p^2 are shielded by the inner 1s^2 electrons from the nucleus

As n increases

the Bohr radius increases

As n increases (in context with energy)

the energy of the electron increases and it is pushed away from the nucleus. As n approaches infinity, the electron is no longer attached to the nucleus and the energy levels start to overlap.

Probability density

the likelihood that an electron will be found in a particular region of space

Bohr Radius

the nearest distance an electron can be from the nucleus, which means the electron cannot crash into the nucleus.

Compared to the rest of the atom

the nucleus is smaller and contains most of the atom's mass

As the radius increases

the orbital energy increases

node

the point where the wavefunction changes sign from positive to negative.

What happens when the electron gets farther from the nucleus?

the principal quantum number goes up and the energy increases and the electron is less stable because the electron is farther away from the nucleus.

It is acceptable for Ψ

to have a positive or negative value.