Chapter 5

1. Chapter 5 Models of the Atom Vanessa N. Prasad-Permaul Valencia College CHM1025 Chapter 5

2. 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. Chapter 5

3. Dalton Model • 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! Chapter 5

4. 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 to form different compounds. Chapter 5

5. 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. Chapter 5

6. Subatomic Particles • About 50 years after Dalton’s proposal, 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. Chapter 5

7. Thomson Model of the Atom • 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. Chapter 5

8. Mass of Subatomic Particles • 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. Chapter 5

9. Types of Radiation • There are three types of radiation: • Alpha (a) • Beta (b) • Gamma (g) • Alpha rays are composed of helium atoms stripped of their electrons (helium nuclei). • Beta rays are composed of electrons. • Gamma rays are high-energy electromagnetic radiation. Chapter 5

10. Rutherford Gold Foil Experiment • 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. Chapter 5

11. Explanation of Scattering • 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 did so after striking the dense nucleus. Chapter 5

12. Rutherford Model of the Atom • 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 Astrodome, the nucleus would be the size of a marble. Chapter 5

13. Subatomic Particles Revisited • Based on the heaviness of the nucleus, Rutherford predicted that it must contain neutral particles in addition to protons. • Neutrons, n0, were discovered about 30 years later. A neutron is about the size of a proton without any charge. Chapter 5

14. 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: mass number (p+ and n0) Sy A symbol of the element Z atomic number (p+) Chapter 5

15. 29 14 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. Chapter 5

16. Solution We can draw a diagram of an atom by showing protons and neutrons in the nucleus surrounded by electrons. (a) Since the atomic number is 9 and the mass number is 19, the number of neutrons is 10 (19 – 9). If there are 9 protons, there must be 9 electrons. Example 5.1Atomic Notation Given the atomic notation for the following atoms, draw a diagram showing the arrangement of protons, neutrons, and electrons. (a) (b) (b) Since the atomic number is 47 and the mass number is 109, the number of neutrons is 62 (109 – 47). If there are 47 protons, there must be 47 electrons.

17. Practice Exercise Concept Exercise Given the following diagram, indicate the nucleus using atomic notation. Can atoms of different elements have the same atomic number? Exercise 5.1 Atomic Notation

18. 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. Chapter 5

19. Co C 60 14 37 6 Isotopes, Continued • We often refer to an isotope by stating the name of the element followed by the mass number. • Cobalt-60 is • Carbon-14 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. Chapter 5

20. Example 5.2Nuclear Composition of Isotopes State the number of protons and the number of neutrons in an atom of each of the following isotopes. (a) (b) mercury-202 Solution • The subscript value refers to the atomic number (p+), and the superscript value refers to the mass number (p+ and n0). • Thus, has 17 p+ and 20 n0 (37 – 17 = 20). • (b) In the periodic table, we find that the atomic number of mercury is 80. Thus, the atomic notation, , indicates 80 p+ and 122 n0 (202 – 80 = 122).

21. Practice Exercise Concept Exercise Can atoms of different elements have the same mass number? State the number of protons and the number of neutrons in an atom of each of the following isotopes. (a) (b) uranium-238 Exercise 5.2 Nuclear Composition of Isotopes

22. 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. Chapter 5

23. Average Atomic Mass • Since not all isotopes of an atom are present in equal proportions, we must use the weighted average. • Copper has two isotopes: • 63Cu, with a mass of 62.930 amu and 69.09% abundance. • 65Cu, with a mass of 64.928 amu and 30.91% abundance. • The average atomic mass of copper is: (62.930 amu)(0.6909) + (64.928amu)(0.3091) = 63.55 amu Chapter 5

24. Solution We can find the atomic mass of silicon as follows: 28Si: 27.977 amu 0.9221 = 25.80 amu 29Si: 28.976 amu 0.0470 = 1.36 amu 30Si: 29.974 amu 0.0309 = 0.926 amu 28.09 amu Example 5.3Calculation of Atomic Mass Silicon is the second most abundant element in Earth’s crust. Calculate the atomic mass of silicon given the following data for its three natural isotopes:

25. Practice Exercise Calculate the atomic mass of copper given the following data: Concept Exercise A bag of marbles has 75 large marbles with a mass of 2.00 g each, and 25 small marbles with a mass of 1.00 g each. Calculate (a) the simple average mass, and (b) the weighted average mass of the marble collection. Exercise 5.3 Calculation of Atomic Mass

26. 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. Chapter 5

27. Solution In the periodic table we observe Example 5.4Nuclear Composition from the Periodic Table Refer to the periodic table on the inside cover of this textbook and determine the atomic number and atomic mass for iron. The atomic number of iron is 26, and the atomic mass is 55.85 amu. From the periodic table information, we should note that it is not possible to determine the number of isotopes for iron or their mass numbers.

28. Concept Exercise Practice Exercise Which of the following is never a whole number value: atomic number, atomic mass, or mass number? Refer to the periodic table on the inside cover of this text and determine the atomic number and mass number for the given radioactive isotope of radon gas. Exercise 5.4 Nuclear Composition from the Periodic Table

29. Wave Nature of Light • Light travels through space as a wave, similar to an ocean wave. • Wavelength is the distance light travels in one cycle. • Frequency is the number of wave cycles completed each second. • Light travels at a constant speed: 3.00 × 108 m/s (given the symbol c). Chapter 5

30. Wavelength Versus Frequency • The longer the wavelength of light, the lower the frequency. • The shorter the wavelength of light, the higher the frequency. Chapter 5

31. 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. Chapter 5

32. Visible 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. Chapter 5

33. Solution Referring to Figure 5.9, we notice that the wavelength of yellow light is about 600 nm and that of blue light is about 500 nm. Thus, (a) yellow light has a longer wavelength than blue light.(b) blue light has a higher frequency because it has a shorter wavelength. (c) blue light has a higher energy because it has a higher frequency. Example 5.5Properties of Light Considering blue light and yellow light, which has the (a) longer wavelength? (b) higher frequency? (c) higher energy?

34. Practice Exercise Concept Exercise Considering infrared light and ultraviolet light, which has the (a) longer wavelength? (b) higher frequency? (c) higher energy? The energy of light (increases/decreases) as the wavelength increases. The energy of light (increases/decreases) as the frequency increases. Exercise 5.5 Properties of Light

35. The Quantum Concept • 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. Chapter 5

36. 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. Chapter 5

37. Example 5.6Quantum Concept • State whether each of the following scientific instruments gives a continuous or a quantized measurement of mass: • triple-beam balance • (b) digital electronic balance Solution • Refer to Figure 2.3 if you have not used these balances in the laboratory. • On a triple-beam balance a small metal rider is moved along a beam. Since the metal rider can be moved to any position on the beam, a triple-beam balance gives a continuous mass measurement. • (b) On a digital electronic balance the display indicates the mass of an object to a particular decimal place, for example, 5.015 g. Since the last digit in the display must be a whole number, a digital balance gives a quantized mass measurement. Figure 2.3 Balances for Measuring Mass (a) A platform balance having an uncertainty of ±0.1 g. (b) A beam balance having an uncertainty of ±0.01 g. (c) A digital electronic balance having an uncertainty of ±0.001 g.

38. Exercise 5.6 Quantum Concept Practice Exercise State whether each of the following musical instruments produces continuous or quantized musical notes: (a) acoustic guitar (b) electronic keyboard Concept Exercise Complete the following quantum analogy: a water wave is to a drop of water, as a light wave is to a _______. Figure 2.3 Balances for Measuring Mass (a) A platform balance having an uncertainty of ±0.1 g. (b) A beam balance having an uncertainty of ±0.01 g. (c) A digital electronic balance having an uncertainty of ±0.001 g.

39. Emission Line Spectra • 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: 434 nm, 486 nm, and 656 nm. Chapter 5

40. 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. Chapter 5

41. “Atomic Fingerprints” • The emission line spectrum of each element is unique. • We can use the line spectrum to identify elements using their “atomic fingerprint.” Chapter 5

42. Solution When an electron drops from a higher to a lower energy level, light is emitted. For each electron that drops, a single photon of light energy is emitted. The energy lost by the electron that drops equals the energy of the photon that is emitted. Several photons of light having the same energy are observed as a spectral line. Example 5.7Emission Spectra and Energy Levels Explain the relationship between an observed emission line in a spectrum and electron energy levels.

43. Practice Exercise Concept Exercise Indicate the number and color of the photons emitted for each of the following electron transitions in hydrogen atoms: (a) 1 e– dropping from energy level 3 to 2 (b) 10 e– dropping from energy level 3 to 2 (c) 100 e– dropping from energy level 4 to 2 (d) 500 e– dropping from energy level 5 to 2 • Which of the following statements are true according to the Bohr model of the atom? • (a) Electrons are attracted to the atomic nucleus. • (b) Electrons have fixed energy as they circle the nucleus. • Electrons lose energy as they drop to an orbit closer to the nucleus. Exercise 5.7 Emission Spectra and Energy Levels

44. 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. Chapter 5

45. 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 level. Chapter 5

46. 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. Chapter 5

47. 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. Chapter 5

48. Electrons per Energy Level Chapter 5

49. Solution The third energy level is split into three sublevels: 3s, 3p, and 3d. The maximum number of electrons that can occupy each sublevel is as follows: s sublevel = 2 e– p sublevel = 6 e– d sublevel = 10 e– The maximum number of electrons in the third energy level is found by adding the three sublevels together: 3s + 3p + 3d = total electrons 2 e– + 6 e– + 10 e– = 18 e– The third energy level can hold a maximum of 18 electrons. Of course, in elements where the third energy level of an atom is not filled, there are fewer than 18 electrons. Example 5.8Energy Levels, Sublevels, & Electrons What is the maximum number of electrons that can occupy the third energy level?

50. Practice Exercise Concept Exercise What is the maximum number of electrons that can occupy the fourth energy level? Answers: 4s, 4p, 4d, 4f; 32 e– (2 e– + 6 e– + 10 e– + 14 e–) What is the theoretical number of sublevels in the tenth energy level? Exercise 5.8Energy Levels, Sublevels, and Electrons