PEP Conceptual Physics Class Notes · 2020. 12. 1. · PEP Conceptual Physics Class Notes Unit 4 –Matter and Energy Chapter 10 –The Atom. Atomic Structure •Section 10.1 •Early

PEP Conceptual PhysicsClass Notes

Unit 4 – Matter and EnergyChapter 10 – The Atom

Atomic Structure

• Section 10.1• Early Atomic Theory

• Nuclear Atomic Theory

• Subatomic Particles

• Fundamental Forces

• Atomic Number and Isotopes

• Atomic Mass

Early Atomic Theory• Atomic Theory – a theory which states that all

matter is composed of tiny particles called atoms

• John Dalton (1766-1844)• Matter is made of tiny, indivisible, indestructible atoms

• Elements are composed of one type of identical atom

• Compounds contain two or more different elements in the same relative numbers

• Atoms do not change identity in chemical reactions but are only rearranged

• Near the end of the 1800’s, the first two of these statements were challenged

Nuclear Atomic Theory• J.J. Thompson (1856-1940) discovered that the

electron is a separate particle• Like “plums” embedded in a positive “pudding”

• Ernest Rutherford (1871-1937) and several others discovered that the nucleus is a tiny, dense core• Fired helium ions at gold foil with some bouncing back

• Like an artillery shell shot at a tissue and coming back

• The proton was discovered soon afterward

• James Chadwick (1891-1974) discovered the neutron• Like Rutherford’s experiment but using beryllium

• This explained the “missing” mass of the atom

Subatomic Particles• Atoms consist of three fundamental particles

• Electron – a low-mass particle with a negative charge that occupies discrete energy levels in space around an atom’s nucleus

• Proton – a positively-charges particle found along with neutrons in the nucleus of an atom

• Neutron – an uncharged particle found in the nucleus of an atom and has about the same mass as a proton

• Some additional atomic facts• A proton is 1,837 times heavier than an electron

• An atom is about 10−10 𝑚 in diameter

• A nucleus is about 10−15 𝑚 in diameter

Fundamental Forces• There are four fundamental forces in nature

• Electromagnetic Force –created by electrostatic charges or magnetic fields and keeps electrons in orbit around the nucleus• Discovered by Charles-Augustin de Coulomb (1736-1806)

• 𝐹 = 𝑘𝑞1𝑞2

𝑟2(more in Chapter 14)

• Strong Nuclear Force – binds protons and neutrons in the nucleus of an atom together and overcomes the electrostatic repulsion between the positively charged protons• Discovered by Hideki Yukawa (1907-1981)

Fundamental Forces• Weak Nuclear Force – active when neutrons decay

into protons and electrons during beta decay• Discovered by Enrico Fermi (1901-1954)

• More about beta decay in section 10.3

• Gravitational Force – an unsolved mystery for how gravity works inside an atom• Discovered by Sir Isaac Newton (1643-1727)

• Measured by Henry Cavendish (1731-1819)

• 𝐹 = 𝐺𝑚1𝑚2

𝑟2

Atomic Number and Isotopes• Atomic Number –number of protons in an atom

• “Atoms of the same element always have the same number of protons” (page 249)

• Isotope – a form of the same atom with the same number of protons but have a different number of neutrons and a different mass number

• Mass Number – the total number of protons and neutrons in the nucleus of an atom• “Mass number = number of protons + number of neutrons”

(page 249)

• If there are too many neutrons in an isotope, it will be radioactive

Atomic Mass• Atomic Mass Unit (amu) – the standard unit of

atomic mass• 1/12 of the mass of a carbon-12 atom

• 1 𝑎𝑚𝑢 = 1.66 × 10−27 𝑘𝑔

• Atomic Mass – weighted average of the mixture of isotopes of a given element• 6% of all lithium atoms are lithium-6 (6 amu)

• 94% of all lithium atoms are lithium-7 (7 amu)

• The weighted atomic mass of lithium is 6.94 amu

Quantum Theory and the Atom• Section 10.2

• The Spectrum

• The Bohr Atom

• Quantum Model

• Exclusion Principle

• Uncertainty Principle

• Probability

The Spectrum• Spectrum – the characteristic pattern of colors

emitted by a pure substance

• Spectrometer – a device that breaks light into its component colors

• Spectral Line – each individual line of color that appears in a spectrometer

• Objects absorb or reflect light to give them color

• Light is a form of electromagnetic energy• Red light has lower energy than blue or violet light

• Yellow and green are between red and blue in energy

The Bohr Atom• Quantum Theory – the theory that describes the

behavior of matter and energy on an atomic scale• Energy levels in atoms are “quantized” to specific levels

• Niels Bohr (1885-1962) proposed that energy levels of electrons in an atom form its spectral lines• Look at Figure 10.12 on page 252

• An electron starts in a low “ground” state energy level

• Energy “excites” the electron to a higher energy level

• The electron “relaxes” to its ground state and emits light

• Each element has characteristic spectral lines• Look at Figure 10.11 on page 251

• Look at the hydrogen spectrum on page 252

Quantum Model• Quantum State – the specific values of energy and

momentum which are allowed for an electron as defined by quantum theory• Quantum theory is one area where classical physics and

Newton’s laws no longer work well

• Erwin Schrödinger (1887-1961) proposed the idea that electrons act as if they are fuzzy waves in a cloud surrounding the nucleus• Look at Figure 10.13, page 253

• The first energy level has only two quantum states

• The second energy level has eight quantum states

Exclusion Principle• Wolfgang Pauli (1900-1958) proposed the theory

that was later named after him• “Two electrons can never be in the same quantum state

in the same atom at the same time.” (page 253)

• An electron cannot occupy a lower energy level if that level is already occupied by other electrons

• Planck’s constant is important for quantum theory• When a particle’s size times its momentum gets near

Planck′s constant, classical mechanics begins to fail

• It also relates light’s energy to its color (or frequency)

• ℎ = 6.626 × 10−34 𝐽 ∙ 𝑠

Uncertainty Principle• Uncertainty Principle –it is impossible to precisely

know a particle’s position, momentum, energy, and time in a quantum system at the same time• Proposed by Werner Heisenberg (1901-1976)

• This especially applies to electrons in an atom

• Photon – the smallest quantity of light energy

• When a photon strikes an object, it transfers some of its energy and momentum to the object• For large objects like cars, there is no observable effect

• For small objects like electrons, the effect is noticeable due to the uncertainty principle

Uncertainty Principle• The uncertainty principle predicts strange effects

• Anything not forbidden can (and will) happen

• Matter and antimatter can form and disappear quickly in a small space to violate the law of conservation of energy

Probability• Probability – the science of describing the chance

of an event or events to occur• It describes the behavior of large numbers of events or

small particles in a system

• Example: rolling a six-sided die

• Example: tossing a two-sided coin

• A quantum of matter is described by wave function• It represents a solution to the quantum wave equation

• Example: the probability of finding an individual electron at a specific distance from the nucleus

• Look at Figure 10.16 on page 255

Nuclear Reactions• Section 10.3

• Nuclear Reactions

• Binding Energy

• Fusion Reactions

• Fission Reactions

• Radioactive Decay

• Periodic Table

• Half-Life

• Nuclear Power

Nuclear Reactions• Nuclear Reaction – a reaction that changes the

nucleus of an atom• It may change the element into another element

• It may change the element into another isotope

• Nuclear reactions differ from chemical reactions• Look at Figure 10.17 on page 256

• Chemical reactions involve only outer electrons, while nuclear reactions involve the nucleus

• Chemical reactions rearrange elements, while nuclear reactions can change elements

• Nuclear reactions involve much more energy than chemical reactions

Binding Energy• Strong nuclear force binds protons and neutrons

• An unbound proton and neutron have greater mass than a bound proton and neutron

• The difference in mass is released as energy according to Einstein’s famous formula 𝐸 = 𝑚𝑐2

• Look at the graph on page 257• Atomic number is plotted on the horizontal axis

• Nuclear energy is plotted on the vertical axis• Units are in the hundreds of trillions of joules per kilogram

• Energy is released when nuclei reform at a lower point

• Energy is used when nuclei reform at a higher point

Nuclear Reactions• Nuclear reactions are written in a format similar to

chemical reaction• 𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠 → 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠

• When writing nuclear reactions, atomic number and atomic mass are important for each reactant and product• 𝐴𝑡𝑜𝑚𝑖𝑐 𝑁𝑢𝑚𝑏𝑒𝑟

𝑀𝑎𝑠𝑠 𝑁𝑢𝑚𝑏𝑒𝑟 𝐸𝑙𝑒𝑚𝑒𝑛𝑡 𝑆𝑦𝑚𝑏𝑜𝑙

• Examples: 11𝐻, 6

12𝐶, 92235𝑈, 0

1𝑛

Fusion Reactions• Fusion reactions result from combining two lighter

atomic nuclei into a heavier atomic nucleus• 612𝐶 + 6

12𝐶 → 1224𝑀𝑔 + 𝑒𝑛𝑒𝑟𝑔𝑦

• It starts on the left side of the energy graph and proceeds down and to the right

• Look at Figure 10.20 on page 258

• Fusion is triggered when high temperatures force the lighter nuclei close enough to overcome the Coulomb repulsion

• Energy released computed from the energy graph• 104 𝑇𝐽/𝑘𝑔 − 48 𝑇𝐽/𝑘𝑔 = 56 𝑇𝐽/𝑘𝑔

Fission Reactions• Fission results from splitting a heavy, unstable

nucleus into two lighter nuclei• 01𝑛 + 92

235𝑈 → 4299𝑀𝑜 + 50

135𝑆𝑛 + 201𝑛 + 𝑒𝑛𝑒𝑟𝑔𝑦

• It starts on the right side of the energy graph and proceeds down and to the left

• Look at Figure 10.21 on page 259

• Fission is triggered when a free neutron strikes a nucleus and makes it unstable

• Energy released computed from the energy graph• 123 𝑇𝐽/𝑘𝑔 − 25 𝑇𝐽/𝑘𝑔 = 98 𝑇𝐽/𝑘𝑔

Fission Reactions• Chain Reaction – occurs when the neutrons from

one fission reaction trigger additional reactions with increasing frequency and release of energy

• Radioactivity – unstable atoms that spontaneously change into other atoms by emission of particles or energy from its nucleus• The products of fission reactions are radioactive

• That is why they are hazardous and hard to dispose of

Radioactive Decay• Radioactive Decay – the spontaneous change of a

nucleus through the release of radiation

• Alpha Decay – radioactive decay by the emission of an alpha particle (helium nucleus)• 92238𝑈 → 90

234𝑇ℎ + 24𝐻𝑒 (Figure 10.22 on page 260)

• Beta Decay – radioactive decay by the emission of a beta particle (electron)• 614𝐶 → 7

14𝑁 + 𝑒− (Figure 10.23 on page 261)

• Gamma Decay – radioactive decay by the emission of a high-energy photon (gamma ray)• Occurs alone or as part of other decay processes

Periodic Table• Periodic Table – organizes elements according to

how they chemically combine with other elements• Look at periodic table on page 261

• In order of increasing atomic number and mass• Lightest element (hydrogen) at the upper left

• Heaviest element (uuh – artificial) at the lower right

• Other characteristics:• Rows (periods) indicate highest unexcited energy level

• Columns (groups) indicate elements with the same number of valence electrons (for bonding)

Half-Life• Half-Life – the length of time it takes for half of any

sample of a radioactive isotope to change to other isotopes or elements

• Half-life is based on probability• You cannot know when an individual isotope will decay

• With a large sample, you can measure the time for one half to decay

• Half-life varies greatly with different isotopes• Carbon-14 5,700 years

• Americium-241 458 years

• Uranium-238 4.5 billion years

Carbon Dating• Carbon-14 has a half-life of 5,700 years

• It makes up a small percentage of all the naturally occurring carbon since it’s constantly being formed by solar cosmic rays in the upper atmosphere

• Living organisms breathe and have the same ratio of carbon-14 to carbon-12 as the atmosphere

• When the organism dies, the carbon-14 starts to decay into nitrogen-14

• By comparing how much carbon-14 remains to how much it should have had when it died, scientists can estimate how long the organism has been dead

Nuclear Power• Nuclear power is responsible for about 20% of the

electric power in the United States• Fission reactors heat water to produce steam to turn

electric turbine generators

• Drawbacks to nuclear fission are the radioactive waste which is hazardous to humans and difficult to store

• The sun and other stars produce energy by fusion• It requires a lot of initial energy in order to trigger fusion

• Scientists have not been able to create fusion in the lab

• Investigation of commercial viability of fusion continues

Other Commercial Uses• Nuclear Medicine

• Various nuclear isotopes are used to destroy disease cells, especially cancer cells

• Iodine-131 decays by beta emission and is used for the treatment of thyroid cancer

• Smoke Detectors• Americium-241 decays by alpha particle emission

• The alpha particle ionizes air around it, and an electric current is set in the detector

• Smoke interrupts the current and causes the alarm to sound