Chapter 4 Models of the Atom by Christopher G. Hamaker Illinois State University © 2014 Pearson Education, Inc. 1

Dalton Model of the Atom John Dalton proposed that all matter is made up of tiny particles. These particles are molecules or atoms. Molecules can be broken down into atoms by chemical processes. Atoms cannot be broken down by chemical or physical processes.

Chemistry Connection: John Dalton Dalton began teaching at the age of 12 and developed an interest in science. He was especially interested in meteorology and kept a lifelong daily journal of atmospheric conditions. Although he was color blind, Dalton was able to make many great contributions to chemistry, including his model of the atom and the law of definite proportions.

Chemistry Connection: John Dalton, Continued According to the law of definite composition, the mass ratio of carbon to oxygen in carbon dioxide is always the same. Carbon dioxide is composed of one carbon atom and two oxygen atoms. Similarly, two atoms of hydrogen and one atom of oxygen combine to give water. Dalton proposed that two hydrogen atoms could substitute for each oxygen atom in carbon dioxide to make methane with one carbon atom and four hydrogen atoms. Indeed, methane is CH4!

Dalton Atomic Theory A Summary of Dalton Atomic Theory: An element is composed of tiny, indivisible, indestructible particles called atoms. All atoms of an element are identical and have the same properties. Atoms of different elements combine to form compounds. Compounds contain atoms in small whole number ratios. Atoms can combine in more than one ratio for form different compounds.

Dalton Atomic Theory, Continued The first two parts of atomic theory were later proven incorrect. We will see this later. Proposals 3, 4, and 5 are still accepted today. The Dalton theory was an important step in the further development of atomic theory.

Thomson Model of the Atom Toward the end of the 1800s, evidence was seen that atoms were divisible. Two subatomic particles were discovered. Negatively charged electrons, e–. Positively charged protons, p+. An electron has a relative charge of –1, and a proton has a relative charge of +1.

Thomson Model of the Atom, Continued J. J. Thomson proposed a subatomic model of the atom in 1903. Thomson proposed that the electrons were distributed evenly throughout a homogeneous sphere of positive charge. This was called the plum pudding model of the atom.

Thomson Model of the Atom, Continued Originally, Thomson could only calculate the mass-to-charge ratio of a proton and an electron. Robert Millikan determined the charge of an electron in 1911. Thomson calculated the masses of a proton and electron: An electron has a mass of 9.11 × 10–28 g. A proton has a mass of 1.67 × 10–24 g.

Rutherford Model of the Atom Rutherford’s student fired alpha particles at thin gold foils. If the plum pudding model of the atom was correct, α particles should pass through undeflected. However, some of the alpha particles were deflected backward.

Rutherford Model of the Atom, Continued Most of the alpha particles passed through the foil because an atom is largely empty space. At the center of an atom is the atomic nucleus, which contains the atom’s protons. The alpha particles that bounced backward did so after striking the dense nucleus.

Rutherford Model of the Atom, Continued Rutherford proposed a new model of the atom: The negatively charged electrons are distributed around a positively charged nucleus. An atom has a diameter of about 1 × 10–8 cm and the nucleus has a diameter of about 1 × 10–13 cm. If an atom were the size of the Superdome, the nucleus would be the size of a marble.

Rutherford Model of the Atom, Continued Based on the heaviness of the nucleus, Rutherford predicted that it must contain neutral particles in addition to protons. Neutrons, n0, were discovered by James Chadwick. A neutron is about the size of a proton without any charge.

Atomic Notation Each element has a characteristic number of protons in the nucleus. This is the atomic number, Z. The total number of protons and neutrons in the nucleus of an atom is the mass number, A. We use atomic notation to display the number of protons and neutrons in the nucleus of an atom:

Using Atomic Notation An example: Si The element is silicon (symbol Si). The atomic number is 14; silicon has 14 protons. The mass number is 29; the atom of silicon has 29 protons + neutrons. The number of neutrons is A – Z = 29 – 14 = 15 neutrons. 29 14

Isotopes All atoms of the same element have the same number of protons. Most elements occur naturally with varying numbers of neutrons. Atoms of the same element that have a different number of neutrons in the nucleus are called isotopes. Isotopes have the same atomic number, but different mass numbers.

Isotopes, Continued We often refer to an isotope by stating the name of the element followed by the mass number. Protium is Deuterium is How many protons and neutrons does an atom of lead-206 have? The atomic number of Pb is 82, so it has 82 protons. Pb-206 has 206 – 82 = 124 neutrons. H 1 H 2 1

Simple and Weighted Averages A simple average assumes the same number of each object. A weighted average takes into account the fact that we do not have equal numbers of all the objects. A weighted average is calculated by multiplying the percentage of the object (as a decimal number) by its mass for each object and adding the numbers together.

Average Atomic Mass Since not all isotopes of an atom are present in equal proportions, we must use the weighted average. Gallium has two isotopes: 69Ga, with a mass of 68.926 amu and 60.11% abundance. 71Ga, with a mass of 70.925 amu and 39.89% abundance. The average atomic mass of copper is: (68.926 amu)(0.6011) + (70.925 amu)(0.3989) = 69.72 amu

The Periodic Table We can use the periodic table to obtain the atomic number and atomic mass of an element. The periodic table shows the atomic number, symbol, and atomic mass for each element.

Chemistry Connection: Heavy Water Heavy water still has the formula H2O, but the hydrogen atoms are the isotope hydrogen-2. Hydrogen-2 is often referred to as deuterium, and is given the symbol D. Heavy water (D2O) is slightly more dense than light water (H2O), and has slightly higher melting and boiling points. Heavy water is used in nuclear reactors to slow down neutrons released during the fission process.

The Wave Nature of Light Light travels through space as a wave, similar to an ocean wave. Wavelength is the distance the light wave travels in one cycle. Frequency is the number of wave cycles completed in each second. Light travels at a constant speed: 3.00 × 108 m/s.

Wavelength Versus Frequency The longer the wavelength of light, the lower the frequency. The shorter the wavelength of light, the higher the frequency.

Light—A Continuous Spectrum Light usually refers to radiant energy that is visible to the human eye. The visible spectrum is the range of wavelengths between 400 and 700 nm. Radiant energy that has a wavelength lower than 400 nm and greater than 700 nm cannot be seen by the human eye.

Radiant Energy Spectrum The complete radiant energy spectrum is an uninterrupted band, or continuous spectrum. The radiant energy spectrum includes many types of radiation, most of which are invisible to the human eye.

Radiant Energy Spectrum Calculate the wavelength of light, in nm, of light with a frequency of 3.52 x 1014 s-1.

Photoelectric Effect Electrons ejected from a metal’s surface when exposed to light of certain frequency Einstein proposed that particles of light are really photons (packets of light energy) and deduced that Ephoton = h

Photoelectric Effect Only light with a frequency of photons such that h equals the energy that binds the electrons in the metal is sufficiently energetic to eject electrons. If light of higher frequency is used, electrons will be ejected and will leave the metal with additional kinetic energy. (what is the relationship between energy and frequency?) Light of at least the threshold frequency and of greater intensity will eject more electrons.

Quantum Theory The quantum concept states that energy is present in small, discrete bundles. For example: A tennis ball that rolls down a ramp loses potential energy continuously. A tennis ball that rolls down a staircase loses potential energy in small bundles. The loss is quantized.

Quantum Theory Energy of a single quantum of energy where E = energy (in Joules) h = Planck’s constant 6.63 x 1034 J  s  = frequency

Photoelectric Effect Calculate the energy (in joules) of a photon with a wavelength of 700.0 nm

Emission Line Spectrum When an electrical voltage is passed across a gas in a sealed tube, a series of narrow lines is seen. These lines are the emission line spectrum. The emission line spectrum for hydrogen gas shows three lines.

Photoelectric Effect Calculate the wavelength (in nm) of light with energy 7.83 x 1019 J per photon. In what region of the electromagnetic radiation does this light fall? Ultraviolet region

Bohr Model of the Atom Niels Bohr speculated that electrons orbit about the nucleus in fixed energy levels. Electrons are found only in specific energy levels, and nowhere else. The electron energy levels are quantized.

Evidence for Energy Levels Bohr realized that this was the evidence he needed to prove his theory. The electric charge temporarily excites an electron to a higher orbit. When the electron drops back down, a photon is given off. The red line is the least energetic and corresponds to an electron dropping from energy level 3 to energy level 2.

“Atomic Fingerprints” The emission line spectrum of each element is unique. We can use the line spectrum to identify elements using their atomic fingerprint.

Line Spectra of Hydrogen The Rydberg equation: Balmer (initially) and Rydberg (later) developed the equation to calculate all spectral lines in hydrogen

Energy Transitions Calculate the energy needed for an electron to move from n = 1 to n = 4. Note: final  initial levels

Critical Thinking: Neon Lights Most “neon” signs don’t actually contain neon gas. True neon signs are red in color. Each noble gas has its own emission spectrum, and signs made with each have a different color.

Energy Levels and Sublevels It was later shown that electrons occupy energy sublevels within each level. These sublevels are given the designations s, p, d, and f. These designations are in reference to the sharp, principal, diffuse, and fine lines in emission spectra. The number of sublevels in each level is the same as the number of the main energy level.

Energy Levels and Sublevels, Continued The first energy level has one sublevel designated 1s. The second energy level has two sublevels designated 2s and 2p. The third energy level has three sublevels designated 3s, 3p, and 3d.

Electron Occupancy in Sublevels The maximum number of electrons in each of the energy sublevels depends on the sublevel: The s sublevel holds a maximum of 2 electrons. The p sublevel holds a maximum of 6 electrons. The d sublevel holds a maximum of 10 electrons. The f sublevel holds a maximum of 14 electrons. The maximum electrons per level is obtained by adding the maximum number of electrons in each sublevel.

Electrons per Energy Level

Electron Configurations Electrons are arranged about the nucleus in a regular manner. The first electrons fill the energy sublevel closest to the nucleus. Electrons continue filling each sublevel until it is full, and then start filling the next closest sublevel. A partial list of sublevels in order of increasing energy is as follows: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d …

Filling Diagram for Energy Sublevels The order does not strictly follow 1, 2, 3, etc. For now, use Figure 4.16 to predict the order of sublevel filling.

Writing Electron Configurations The electron configuration of an atom is a shorthand method of writing the location of electrons by sublevel. The sublevel is written followed by a superscript with the number of electrons in the sublevel. For example, if the 2p sublevel contains two electrons, it is written 2p2. The electron sublevels are arranged according to increasing energy.

Writing Electron Configurations, Continued First, determine how many electrons are in the atom. Bromine has 35 electrons. Arrange the energy sublevels according to increasing energy: 1s 2s 2p 3s 3p 4s 3d … Fill each sublevel with electrons until you have used all the electrons in the atom: Br: 1s2 2s2 2p6 3s2 3p6 4s2 3d 10 4p5 The sum of the superscripts equals the atomic number of bromine (35).

Quantum Mechanical Model of the Atom An orbital is the region of space where there is a high probability of finding an atom. In the quantum mechanical atom, orbitals are arranged according to their size and shape. The higher the energy of an orbital, the larger its size. All s orbitals have spherical shapes.

Shapes of p Orbitals Recall that there are three different p sublevels. All p orbitals have dumbbell shapes. Each of the p orbitals has the same shape, but each is oriented along a different axis in space.

Location of Electrons in an Orbital The orbitals are the region of space in which the electrons are most likely to be found. An analogy for an electron in a p orbital is a fly trapped in two bottles held end to end.

Shapes of d Orbitals Recall that there are five different d sublevels. Four of the d orbitals have a clover-leaf shape and one has a dumbbell and doughnut shape.

Chapter Summary Atoms are composed of protons, neutrons, and electrons. The protons and neutrons are located in the nucleus, and the electrons are outside the nucleus. Atoms are mostly empty space. The number of protons is referred to as the atomic number for the atom.

Chapter Summary, Continued All atoms of the same element have the same number of protons. Isotopes are atoms with the same number of protons, but differing numbers of neutrons. The mass number for an isotope is the total number of protons plus neutrons. The atomic mass of an element is the weighted average of the masses of all the naturally occurring isotopes.

Chapter Summary, Continued Light has properties of both waves and particles. The particles of light are referred to as photons. The energy of photons is quantized. Electrons exist around the nucleus of atoms in discrete, quantized energy levels. Electrons fill energy sublevels, starting with the lowest energy sublevel and filling each successive level of higher energy.