Chapter 13 Quantum-Mechanical Model -explains how e- exist in atoms and how close those e- determine the chemical and physical properties of elements -already studied much of this: -metals vs. non-metals -noble gases inert -charges on ions

-electrons and light have much in common Wave Nature of Light electromagnetic radiation (waves)- a type of energy embodied in oscillating electric and magnetic fields -waves move at a constant speed of 3.00X108m/s -this is the speed of light (c) -takes a particle of light 1/7 of a second to circle Earth -this is why you see fireworks before you hear the bang and why you see lightning before you hear thunder -sound travels about 340m/s

origin

electromagnetic waves amplitude- height of a wave from the origin to the crest or from origin to trough -determines the intensity or brightness of the light, greater amplitude = greater intensity wavelength- (λ) - distance between two adjacent crests (units= m, cm, nm) frequency- (ν) - # of wave cycles that pass through a given point per unit time (units= cycles / sec or 1/s or s-1 or hertz- Hz) -each complete wave cycle begins at the origin and returns to the origin

-frequency is directly proportional to the speed at which the wave is traveling- the faster the wave, the higher the frequency -frequency and wavelength are inversely proportional

c = νλ c = speed of light (3.00 x 108m/s) ν = frequency (1/s, s-1, Hz) λ = wavelength (m, cm, nm(10-9)) λ = c/ν ν = c/λ

visible light- light that can be seen by the human eye -wavelength determines the color of the visible light -can see colors when white light is passed through a prism -red, orange, yellow, green, blue, indigo, violet -red light has the longest wavelength (750nm) -violet has shortest (400nm)

electromagnetic spectrum- includes all wavelengths of electromagnetic radiation (radio, microwaves, infrared, visible, UV rays, X-rays, and gamma rays) page 285 figure 7.5 left side = low energy, low frequency, long wavelength right side = high energy, high frequency, short wavelength

Types of electromagnetic radiation: radio waves- longest wavelengths, 105, transmits signals for radios, cell phones, TV microwaves- used for radar and microwaves infrared radiation (IR)- the heat you feel when you place your hand near a hot object visible light- light you can see UV rays- from the sun X-rays- used to image bones and internal organs gamma rays (γ)- produced by the sun or in space, very dangerous because of high energy

Particle Nature of Light photoelectric effect- metals emit electrons when light shines on them *especially the alkali metals -used in solar calculators -Einstein proposed that light energy must come in packets photon/quantum- particles/packets of light -he also said that the amount of energy in a photon depends on its frequency

E = hν E = energy in joules h = Planck’s constant = 6 E = hν E = energy in joules h = Planck’s constant = 6.626 x 10 -34J∙s ν = frequency (1/s, s-1, Hz) -since ν = c/λ, the energy of a photon can also be expressed as: E = hc λ -to find number of photons = Epulse / Ephoton

-electrons emit light when they are excited by the passage of an electric discharge through an element atomic emission spectrum- range of wavelengths emitted by a particular element that can be used to identify an element ex- neon lights- each noble gas will give a specific color (He= pink, Ne= orange/red, Xe= blue, Kr= whitish) ex- fireworks- each element present will give a particular color (Na= yellow, Sr= red, Ca= orange) page 292

-Neils Bohr said that e- travel around the nucleus in circular orbits (energy levels) *e- are at fixed distances from nucleus *radiation was emitted or absorbed only when an electron jumped from one level to another

Louis de Broglie -stated that a single electron traveling through space has a wave nature -its wavelength is related to its kinetic energy λ = h/mv v = h/mλ λ = wavelength h = Planck’s constant (6.626x10-34 J·s) m = mass of electron (9.11x10-31kg) v = velocity (m/s) **1J = 1kg·m2/s2

Example- Calculate the wavelength of an electron traveling with a speed of 2.65x106m/s λ = h/mv (6.626x10-34 kgm2/s2·s) (9.11x10-31kg)(2.65x106m/s) =2.74 x 10-10m

Heisenberg’s Uncertainty Principle -states that it is impossible to know both the velocity and position of a particle at the same time -Remember where electrons are found in an atom!! -surrounding the nucleus in electron clouds or energy levels For Practice 7.4 page 297 Pg 315: 43, 44, 51, 52, 53, 54

Quantum Mechanics and the Atom Principal Quantum Number (n) -the energy level -determines the overall size and energy of an orbital (where electrons are held) -n can be equal to 1, 2, 3, 4, 5, 6, 7 -distance electron is from the nucleus increases as n increases

Angular Momentum Quantum Number (l) -determines the shape of the orbital -shapes are s, p, d, or f -when given a value of n, l can be any integer including zero up to n - 1 ex: n = 1 l = 0 ex: n = 2 l = 0, 1 -to avoid confusion between n and l, values of l are often assigned as letters

Value of l Shape of orbital l = 0 s l = 1 p l = 2 d l = 3 f Back to examples: #1: n = 1 l = 0 is in first energy level with s orbitals #2: n = 2 l = 0, 1 is in the second energy level with s and p orbitals

Atomic Orbital Shapes s-orbital -spherically shaped -one shape, one orbital -lowest energy orbital p-orbital -peanut/dumb bell shaped -three shapes, three orbitals d-orbital -clover shaped -five shapes, five orbitals

f-orbitals -flower shaped -7 shapes, 7 orbitals energy level # of sublevels Type of sublevel n = 1 1 1s n = 2 2 2s,2p n = 3 3 3s, 3p, 3d n = 4 4 4s, 4p, 4d, 4f

ex: how many orbitals in 3d. 5 how many orbitals in 4s ex: how many orbitals in 3d? 5 how many orbitals in 4s? 1 how many orbitals in 2p? 3 how many orbitals in 2s? how many orbitals in the third energy level? 9 1 from s, 3 from p, 5 from d

-Orbitals with the same value of n are said to be in the same principle level -Orbitals with the same value of n and l are said to be in the same sublevel Magnetic Quantum Number (ml) -specifies the orientation of the orbital -equal to integer values, including zero ranging from -l to +l ex: l = 0 ml = 0 ex: l = 1 ml = -1 0 +1

ex: What are the quantum numbers and names of the orbitals in the n = 4 principle level? How many orbitals exist? n = 4 l ml values orbitals 0 0 4s 1 -1 0 +1 4p 2 -2 -1 0 +1 +2 4d 3 -3 -2 -1 0 +1 +2 +3 4f **16 total orbitals Try For Practice 7.5 page 303 Example 7.6 page 303 For Practice 7.6 page 303

electron configuration- how e- are arranged around the nucleus Rules for e- configs: Aufbau Principle -electrons enter orbitals of lower energy first s → p → d → f -atomic orbitals are represented as boxes s = 1 box (1 orbital) p = 3 boxes (3 orbitals) d = 5 boxes (5 orbitals) f = 7 boxes (7 orbitals)

Pauli-Exclusion Principle -an atomic orbital can hold at most 2 e- -electrons are represented as arrows -spins are opposite -first electron is ↑ -second electron is ↓ -number of e- must equal number of arrows

Hund’s Rule -one electron enters each orbital of equal energy until orbitals contain one electron, then they can hold two e- -it is more stable to have partially filled orbitals than empty orbitals