Unit 1: Structure of Matter Sections: 2.1-2.3, 7, PES Copyright © The McGraw-Hill Companies, Inc.  Permission required for reproduction or display.

Democritus Greek era All matter consists of very small, indivisible particles, which he named atomos

Law of conservation of mass Lavoisier Law of conservation of mass 16 X 8 Y + 8 X2Y

Proust Law of definite proportions

Dalton’s Atomic Theory 1. Elements are composed of extremely small particles called atoms. 2. All atoms of a given element are identical, having the same size, mass and chemical properties. The atoms of one element are different from the atoms of all other elements. 3. Compounds are composed of atoms of more than one element. In any compound, the ratio of the numbers of atoms of any two of the elements present is either an integer or a simple fraction. 4. A chemical reaction involves only the separation, combination, or rearrangement of atoms; it does not result in their creation or destruction.

Law of Multiple Proportions

Review of Concepts The atoms of elements A (blue) and B (orange) form two compounds shown here. Do these compounds obey the law of multiple proportions?

The speed (u) of the wave = l x n Maxwell Properties of Waves Wavelength (l) is the distance between identical points on successive waves. Amplitude is the vertical distance from the midline of a wave to the peak or trough. Frequency (n) is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s). The speed (u) of the wave = l x n

Review of Concept Which of the waves shown has (a) the highest frequency (b) the longest wavelength (c) the greatest amplitude?

proposed that visible light consists of electromagnetic waves. Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves. Speed of light (c) in vacuum = 3.00 x 108 m/s All electromagnetic radiation l x n = c

Practice Exercise 7.1 What is the wavelength (in meters) of an electromagnetic wave whose frequency is 3.64x107 Hz?

Cathode Ray Tube J.J. Thomson, measured mass/charge of e- (1906 Nobel Prize in Physics)

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(a) A cathode ray produced in a discharge tube traveling from the cathode (left) to the anode (right). The ray itself is invisible, but the fluorescence of a zinc sulfide coating on the glass causes it to appear green. (b) The cathode ray is bent downward when a bar magnet is brought toward it. (c) When the polarity of the magnet is reversed, the ray bends in the opposite direction.

Thomson’s Model

Types of Radioactivity α β ϒ (uranium compound)

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Mystery #1, “Heated Solids Problem” Plank Mystery #1, “Heated Solids Problem” When solids are heated, they emit electromagnetic radiation over a wide range of wavelengths. Radiant energy emitted by an object at a certain temperature depends on its wavelength. Energy (light) is emitted or absorbed in discrete units (quantum). E = h x n Planck’s constant (h) h = 6.63 x 10-34 J•s E = hc / λ Because ν = c/λ h = 6.63 x 10-34 J•s

Practice Exercise 7.2 The energy of a photon is 5.87x10-20 J. What is its wavelength (in nanometers) ?

Photon is a “particle” of light Einstein Mystery #2, “Photoelectric Effect” hn Light has both: wave nature particle nature KE e- Photoelectric effect phenomenon in which electrons are ejected from the surface of certain metals exposed to light of at least a certain minimum frequency (threshold frequency) Photon is a “particle” of light

Review of Concept A clean metal surface is irradiated with light of three different wavelengths λ1, λ2, and λ3. The kinetic energies of the ejected electrons are as follows: λ1: 2.9×10−20 J; λ2: aprox 0; λ3: 4.2×10−19 J. Which light has the shortest wavelength and which has the longest wavelength?

Thomson’s charge/mass of e- = -1.76 x 108 C/g Millikan’s Experiment Measured mass of e- (1923 Nobel Prize in Physics) e- charge = -1.60 x 10-19 C Thomson’s charge/mass of e- = -1.76 x 108 C/g e- mass = 9.10 x 10-28 g

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(1908 Nobel Prize in Chemistry) Rutherford’s Experiment (1908 Nobel Prize in Chemistry) particle velocity ~ 1.4 x 107 m/s (~5% speed of light) atoms positive charge is concentrated in the nucleus proton (p) has opposite (+) charge of electron (-) mass of p is 1840 x mass of e- (1.67 x 10-24 g)

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Rutherford’s Model of the Atom atomic radius ~ 100 pm = 1 x 10-10 m nuclear radius ~ 5 x 10-3 pm = 5 x 10-15 m “If the atom is the Houston Astrodome, then the nucleus is a marble on the 50-yard line.”

Atomic Number, Mass Number, and Isotopes Atomic number (Z) = number of protons in nucleus Mass number (A) = number of protons + number of neutrons = atomic number (Z) + number of neutrons Isotopes are atoms of the same element (X) with different numbers of neutrons in their nuclei Mass Number X A Z Element Symbol Atomic Number H 1 H (D) 2 H (T) 3 U 235 92 238

The Isotopes of Hydrogen

Practice Exercise 2.1 How many protons, neutrons, and electrons are in the following isotope of copper: Cu? What is the atomic number of an element if one of its isotopes has 117 neutrons and a mass number of 195? Which of the following two symbols provides more information? O or O. 63 17 8

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Line Emission Spectrum of Hydrogen Atoms Energize the sample Line Emission Spectrum of Hydrogen Atoms

n (principal quantum number) = 1,2,3,… Bohr Model of the Atom (1913) e- can only have specific (quantized) energy values light is emitted as e- moves from one energy level to a lower energy level En = −RH ( ) 1 n2 n (principal quantum number) = 1,2,3,… RH (Rydberg constant) = 2.18 x 10-18J

Bohr Planetary Model Emission spectrum of Hydrogen supports the notion that energy is quantized and PES gives further evidence that those energy levels are divided into subshells

E = hn E = hn

( ) ( ) ( ) Ephoton = DE = Ef - Ei 1 Ef = -RH n2 1 Ei = -RH n2 1 nf = 2 ni = 3 nf = 1 ni = 3 Ef = -RH ( ) 1 n2 f Ei = -RH ( ) 1 n2 i nf = 1 ni = 2 i f DE = RH ( ) 1 n2

Practice Exercise 7.4 What is the wavelength of a photon (in nanometers) emitted during a transition from the ni = 6 state to the nf = 4 state in the hydrogen atom?

Review of Concept Which transition in the hydrogen atom would would emit light of a shorter wavelength? (a) ni = 5 nf = 3 or (b) ni = 4 nf = 2

Photoelectron Spectroscopy PES Further evidence to support bohr model

Standing Waves

Why is e- energy quantized? De Broglie (1924) Why is e- energy quantized? reasoned that e- is both particle and wave. 2pr = nl l = h mv v = velocity of e- m = mass of e-

Practice Exercise 7.5 Calculate the wavelength (in nanometers) of a H atom (mass = 1.674x10-27 kg) moving at 7.00x102 cm/s.

Heisenberg Uncertainty principle

Schrodinger Wave Equation In 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e- Wave function (y) describes: . energy of e- with a given y . probability of finding e- in a volume of space y2 Schrodinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems. y is a function of four numbers called quantum numbers

Schrödinger Quantum Mechanical Model

Principal quantum number n distance of e- from the nucleus n=1 n=2 n=3

Angular Momentum quantum number Shape of the “volume” of space that the e- occupies Where 90% of the e- density is found for the 1s orbital Sublevels: s orbital p orbital d orbital f orbital

Magnetic quantum number orientation of the orbital in space

s orbital (1 orientation: sphere)

p orbital (3 orientations: dumbbells)

d orbital (5 orientations: double dumbbells)

f orbital (7 orientations)

Electron Spin quantum number

Coulomb’s Law The force between two charged particles is proportional to the magnitude of each of the two charges (q1 and q2) and inversely proportional to the square of the distance between them (r) *The force is along the straight line joining them *Combine equations 1 & 2, then solve for force:

( ) Energy of orbitals in a single electron atom 1 En = -RH n2 Energy only depends on principal quantum number n n=3 n=2 En = -RH ( ) 1 n2 n=1

Energy of orbitals in a multi-electron atom Energy depends on energy level and orbital shape

Shielding Effect Why is the 2s orbital lower in energy than the 2p? “shielding” reduces the electrostatic attraction Energy difference also depends on orbital shape

Electron configuration is how the electrons are distributed among the various atomic orbitals in an atom. number of electrons in the orbital 1s1 principal quantum number n Sublevel (shape) Orbital diagram 1s1 H

“Fill up” electrons in lowest energy orbitals (Aufbau principle)

Order of orbitals (filling) in multi-electron atom 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s

Outermost subshell being filled with electrons

Pauli exclusion principle - no two electrons in an atom can have the same four quantum numbers. Each seat is uniquely identified (E, R12, S8). Each seat can hold only one individual at a time. Existence (and energy) of electron in atom is described by its unique wave function y.

Paramagnetic Diamagnetic unpaired electrons all electrons paired 2p 2p

The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule).

Practice Exercise Calculate the total number of electrons that can be present in the principal level for which n = 4. An oxygen atom has a total of eight electrons. Write the ground state electron configuration and orbital diagram. The ground-state electron configuration of an atom is 1s22s22p63s23p3. What is the same/different for the three 3p electrons?

Noble Gas Configuration Ex: Aluminum e− configuration: 1s22s22p63s23p1 preceding noble gas is Ne: 1s22s22p6 noble gas configuration: [Ne] 3s23p1

Practice Exercise Write the noble gas configuration and the noble gas orbital diagram for sulfur (S). Identify the atom that has the following ground-state electron configuration: [Ar]4s23d6

Chadwick (1935 Noble Prize in Physics) H atoms: 1 p; He atoms: 2 p mass He/mass H should = 2 measured mass He/mass H = 4 a + 9Be 1n + 12C + energy neutron (n) is neutral (charge = 0) n mass ~ p mass = 1.67 x 10-24 g

mass p ≈ mass n ≈ 1840 x mass e-