Foundations of Physics CPO Science Foundations of Physics Unit 9, Chapter 28

Chapter 28 Inside the Atom Unit 9: The Atom Chapter 28 Inside the Atom 28.1 The Nucleus and Structure of the Atom 28.2 Electrons and Quantum States 28.3 The Quantum Theory

Chapter 28 Objectives Describe the structure of an atom. Describe the four forces acting inside an atom. Use the periodic table to obtain information about the atomic number, mass number, atomic mass, and isotopes of different elements. Predict whether a certain nucleus is stable or unstable and explain why. Distinguish between and provide examples of chemical reactions and nuclear reactions. Describe how atomic spectral lines can be explained by energy levels and quantum states. Explain quantum theory as it relates to light and electrons. Describe the major developments in quantum theory and identify the scientists associated with each.

Chapter 28 Vocabulary Terms nucleus electron proton neutron atomic mass atomic mass unit electromagnetic force strong nuclear force weak force element atomic number mass number isotope radioactive nuclear reaction quantum spectral line spectrum quantum state energy level quantum numbers Pauli exclusion principle Planck’s constant wave function Probability orbital uncertainty principle photoelectric effect photon chemical reaction spectrometer quantum physics

28.1 The Nucleus and Structure of the Atom Key Question: What is inside an atom? *Students read Section 28.1 AFTER Investigation 28.1

28.1 The Nucleus and Structure of the Atom Atoms are made of three kinds of particles: electrons, protons, and neutrons.

28.1 The structure of the atom Because the mass of a proton is tiny by normal standards, scientists use atomic mass units (amu) instead of kg. (chart) One amu is 1.661 × 10-27 kg, slightly less than the mass of a proton. One electron has a mass of 0.0005 amu.

28.1 The structure of the atom A neutral atom has a total charge of zero. Because the number of electrons equals the number of protons in a complete atom they tend to stay neutral because electric forces are very strong.

28.1 The nucleus of the atom The neutrons and protons are grouped together in the nucleus, which is at the center of the atom. If the atom were the size of your classroom, the nucleus would be the size of a single grain of sand in the center of the room. Most of an atom’s mass is concentrated in the nucleus.

28.1 The structure of the atom Electrons are outside the nucleus in the electron cloud. Because electrons are so fast and light, physicists tend to speak of the "electron cloud" rather than talk about the exact location of each electron.

28.1 The nucleus of the atom The mass of a carbon nucleus is 12 amu. (6p+, 6no) The mass of the electrons is only 0.003 amu. So 99.97 % of the carbon atom’s mass is in the nucleus and only 0.03% is in the electron cloud.

28.1 The structure of the atom Electrons are bound to the nucleus by electromagnetic forces. The force is the attraction between protons (positive) and electrons (negative). The momentum of the electron causes it to move around the nucleus rather than falling straight in.

28.1 The structure of the atom The strong nuclear force attracts neutrons and protons to each other, otherwise the positively charged protons would repel each other.

28.1 The structure of the atom The weak force is weaker than both the electric force and the strong nuclear force. If you leave a solitary neutron outside the nucleus, the weak force eventually causes it to break up into a proton and an electron. The force of gravity inside the atom is much weaker even than the weak force. Every process we know in the universe can be explained in terms of these fundamental forces.

28.1 Review atoms and elements The variety of matter we find in nature (here on Earth) is made from 92 different types of atoms called elements. The atomic number of each element is the number of protons in its nucleus. The periodic table arranges the elements in increasing atomic number.

28.1 Calculate nuclear particles How many protons are in the nucleus of an atom of vanadium (V)? 1) You are asked for the number of protons. 2) You are given that the element is vanadium. 3) The number of protons is the atomic number. 4) Vanadium is atomic number 23 so there are 23 protons in the nucleus of a vanadium atom.

28.1 The structure of the atom Different isotopes exist for atoms of each element. Different isotopes of the same element have different mass numbers. The mass number is the total number of particles (protons and neutrons) in the nucleus. Some isotopes occur naturally. Other isotopes may be created in a laboratory for research.

28.1 The structure of the atom If an isotope has too many (or too few) neutrons, the nucleus eventually breaks up and we say the atom is radioactive. In a stable isotope the nucleus stays together.

28.1 Average atomic mass The average atomic mass give the proportion of each isotope by mass. For example, the periodic table lists an atomic mass of 6.94 for lithium. On average, 94% of lithium atoms are Li7 and 6% are Li6.

28.1 Calculate nuclear particles 49 22 How many neutrons are in the nucleus of an atom of titanium-49? 1) You are asked for the number of neutrons. 2) You are given that the isotope is titanium-49. 3) The number of neutrons is the mass number minus the atomic number. 4) Titanium is atomic number 22. If 22 of the 49 particles in the 2249Ti nucleus are protons, then there must be 27 neutrons (49 - 22).

28.1 Reactions inside and between atoms Most atoms in nature are found combined with other atoms into molecules. A molecule is a group of atoms that are chemically bonded together.

28.1 Reactions between atoms A chemical reaction rearranges the same atoms into different molecules. Chemical reactions rearrange atoms into new molecules but do not change atoms into other kinds of atoms.

28.1 Reactions inside atoms A nuclear reaction is any process that changes the nucleus of an atom. A nuclear reaction can change atoms of one element into atoms of a different element.

28.2 Electrons and Quantum Theory Key Question: How do atoms create and interact with light? *Students read Section 28.2 AFTER Investigation 28.2

28.2 Electrons and Quantum Theory Quantum physics is the branch of science that deals with extremely small systems such as an atom. A brilliant scientist, Neils Bohr is often called the father of quantum physics. Niels Bohr was the first person to put the clues together correctly and in 1913 proposed a theory that described the electrons in an atom.

28.2 Electrons and Quantum Theory An unusual feature of light was one clue that lead to the discovery of quantum physics. When substances were made into gases and electricity was passed through the gas, light was given off in the form of lines of color. Since the energy of light depends on the color, the lines in a spectrum meant that substances could only emit light of certain energies.

28.2 Electrons and Quantum Theory Each individual color is called a spectral line because each color appears as a line in a spectrometer. A spectrometer is a device that spreads light into its different wavelengths, or colors.

28.2 Balmer's formula The first serious clue to an explanation of the atom was discovered in 1885 by Johann Balmer, a Swiss high school teacher. He showed that the wavelengths of the light given off by hydrogen atoms could be predicted by a mathematical formula (Balmer’s formula).

n is an integer greater than two 28.2 Balmer's formula 1 = 91.16 1 - 1 l 22 n2 [ ] Wavelength (nm) n is an integer greater than two

28.2 Quantum states Bohr proposed that electrons in the atom were limited to certain quantum states. The quantum states in an atom have certain allowed values of energy, momentum, position, and spin. The number (n) in the Balmer formula is one of four quantum numbers that describe which quantum state an electron is in.

28.2 Quantum states Every quantum state in the atom is identified by a unique combination of the four quantum numbers. Every electron in an atom can be completely described by the values of its four quantum numbers: n, l, m, and s. From the four quantum numbers it is possible to calculate everything about the electron, including its energy, angular momentum, average position, and spin.

28.2 Quantum numbers The first quantum number (n) can be any integer bigger than zero. The second quantum number (l) must be a positive integer from zero to n-1. For example, if n = 1, the only possibility is l = 0. If n = 2, then l can be 0 or 1.

28.2 Quantum numbers The third quantum number (m) is an integer that can go from - l to + l. For example, if l = 3, m can have any of seven values between -3 and +3 (m = -3, -2, -1, 0, 1, 2, 3). The fourth quantum number (s) can only be either +1/2 or -1/2.

28.2 Energy levels An electron in a hydrogen atom dropping from the third level to the second level gives off an amount of energy exactly equal to the red line in the hydrogen spectrum.

28.2 Quantum states The quantum states in an atom are grouped into energy levels. Bohr explained that spectral lines are produced by electrons moving between different energy levels.

28.2 Pauli exclusion principle According to the quantum theory, two electrons in an atom can never be in the same quantum state at the same time. This rule is known as the Pauli exclusion principle after Wolfgang Pauli, the physicist who discovered it. Once all the quantum states in the first level are occupied by electrons, the next electron has to go into a higher energy level.

28.2 Periodicity and energy levels

28.2 The "shape" of quantum states In chemistry, the quantum states for electrons in an atom are called orbitals. The name comes from an older idea that electrons moved in orbits around the nucleus, Each “orbital” shape shows the most likely locations for a pair of electrons with matching quantum numbers n, l, and m.

28.2 Orbital shapes for n= 1, 2, 3

28.3 The Quantum Theory Key Question: How can a system be quantized? *Students read Section 28.3 AFTER Investigation 28.3

28.3 The Quantum Theory The quantum theory started between 1899 and 1905 when classical physics disagreed with results of new experiments. Max Planck and Albert Einstein were working on two phenomena that couldn't be explained by classical physics.

28.3 The Quantum Theory Einstein was thinking about the photoelectric effect. When light falls on the surface of a metal, sometimes electrons are emitted from the surface. If the light is made brighter, the metal absorbs more energy.

28.3 The Quantum Theory Classical physics predicts that electrons coming off the metal should have more kinetic energy when the light is made brighter. But that is NOT what happens.

28.3 Quantum theory of light In 1899 Max Planck proposed that light existed in small bundles of energy called photons. The smallest amount of light you could have is a single photon.

28.3 Quantum theory of light Bright light consists of billions of photons per second while dim light has very few photons per second. According to Planck, the energy of a single photon is related to its frequency. Higher frequency means higher photon energy. Like atoms, photons are such small quantities of energy that light appears as a continuous flow of energy under normal circumstances.

28.3 Planck's constant Planck’s idea was very different from the wave theory of light. frequency (Hz) Energy (J) E = h f Planck's constant (6.626 x 10-34 J.sec)

28.3 Quantum theory of light In 1905, Einstein proposed that an atom can absorb only one photon at a time. An electron needs a minimum amount of energy to break free from an atom. If the energy of the photon is too low there is not enough energy to free an electron and no photoelectric effect is observed. Making brighter light does not help.

28.3 Quantum theory of light In the quantum theory, all matter and energy have both wavelike and particle-like properties. To a physicist, if something is quantized, it can only exist in whole units, not fractions of units.

28.3 Quantum theory of light An electron acts like a particle when it is both free to move and far from other electrons. However, if an electron is confined in a small space (an atom), it behaves like a wave.

28.3 Planck's constant l = h mv The wavelength of a particle (λ) depends on its mass (m) and speed (v), according to the DeBroglie formula. Planck's constant (6.626 x 10-34 J.sec) wavelength (m) l = h mv mass (kg) speed (m/sec)

28.3 The Uncertaintly principle Quantum theory puts limits on how precisely we can know the value of quantities such as position, momentum, energy, and time. The uncertainty principle places a limit on how precisely these four parameters can be measured. The uncertainty principle arises because the quantum world is so small.

28.3 The Uncertainty principle The uncertainty principle works on pairs of variables because measuring one always disturbs the other in an unpredictable way. The uncertainty principle in position (Dx), multiplied by the uncertainty principle in momentum (Dp) can never be less than h/2p. D x D p > h 2P change in postition Planck's constant (6.626 x 10-34 J.sec) change in momentum

28.3 Quantum theory and probability Calculations in quantum physics do not result in knowing what will happen, but instead give the probability of what is likely to happen. While you can never accurately predict the outcome of one toss of the penny, you can make accurate predictions about a collection of many tosses. Quantum theory uses probability to predict the behavior of large numbers of particles.

28.3 Quantum theory and probability In quantum physics, each quantum of matter or energy is described by its wave function. The wave function mathematically describes how the probability for finding a quantum of matter or energy is spread out in space.

Application: The Laser