Chem chapter 2 refresh

Schrodinger’s equation

allows us to calculate the probability of finding an electron with a particular amount of energy at a particular location in the atom- solutions produce wave functions

orbital

a probability distribution map of a region where the electron is likely to be found

quantum numbers

solutions to schrodinger’s equation wave functions- n, l , m1, ms

principle quantum number

n; characterizes the energy of electron in a particular orbital

• determines the overall size and energy of an orbital

  • larger n = more energy and larger orbital

energies of electrons description

an electron’s energy is made more negative as a result of its interaction with nucleus- electrons have E=0 when they escape the atom

results of increasing principle quantum number

as n gets larger, the amount of energy between orbitals gets smaller and the energy of the orbital becomes greater (less negative)

energy of an orbital equation

En = -2.18×10^-18(1/n²)

angular momentum quantum number

L; determines the shape of the orbital

• can have integer values from 0 to n-1

• s, p, d, f

magnetic quantum number

mL; specifies the direction in space orbital is aligned relative to other orbitals

• values are integers from -L to +L including 0

• gives number of orbitals

spin quantum number

ms; describes the spin behavior of an electron

• all electron spins are equal in magnitude but differ in orientation

  • +1/2 = spin up, -1/2 = spin down

describing orbital relationships

orbitals with same value of n are in same principle energy level

orbitals with same levels of n and L are in same sublevel

general rules for energy levels

number of sublevels within level = n

number of orbitals within a sublevel = 2L +1

number of orbitals within a level = n²

electron transition and photon relationship

when an electron is excited, it transitions from orbital in lower energy level to higher, and when an electron relaxes, it goes from higher energy level to lower energy level

• photon of light released when electron relaxes whose energy equals the energy difference between orbitals

energy transition equation

E = -2.18×10^-18(1/n_f²- 1/n_i²)

rydberg formula

1/lambda = 1.097×10⁷(1/n_f²- 1/n_i²)- wavelength of photon released

nodes

points in radial distribution function where probability = 0

radial distribution function

represents the total probability at a certain distance from nucleus- maximum at most probable radius

probability density

the probability of finding an electron at a particular point in space- decreases further away from nucleus

radial distribution function

total probability of finding an electron within a thin spherical shell at distance r from nucleus

• probability decreases with distance from nucleus but volume of shell increases

s orbital

• lowest energy orbital in principle energy state

• spherical shaped

• L = 0

• number of nodes = n-1

p orbitals

• each energy state above n=1 has three p orbitals (m1 = -1, 0 , 1)

• second lowest energy orbitals in principle energy state

• each of 3 orbitals points along a different axis; px, py, pz

• two lobed

• L = 1

• one node at nucleus; total of n nodes

d orbitals

each energy state above n = 2 has 5 d orbitals

• mainly 4 leaf clover shaped except one with a 2 lobed orbital and a ring/collar

• L = 2

f orbitals

• L = 3

• each principle energy state above n = 3 has 7 f orbitals

• mainly 8 lobed but some have 2 lobed orbital with collar

phase of orbitals

sign of wave function is called a phase

• when orbitals interact, they can be in phase (same sign) or out of phase (opposite signs)