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Nuclear Physics

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**The Atom All matter is composed of atoms.**

An atom is composed of three subatomic particles: electrons (-), protons (+), and neutrons (0) The nucleus of the atom contains the protons and the neutrons (also called nucleons.) The electrons surround (orbit) the nucleus. Electrons and protons have equal but opposite charges.

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The Atom Protons and neutrons have nearly the same mass and are 2000 times more massive than an electron. Electron discovered by J.J. Thomson in 1897 Proton discovered by Ernest Rutherford in 1918 Neutron discovered by James Chadwick in 1932

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**Rutherford's Alpha-Scattering Experiment**

J.J. Thomson’s “plum pudding” model predicted the alpha particles would pass through the evenly distributed positive charges in the gold atoms. a particle = helium nucleus

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**The Atom Diameter of nucleus = about 10-14 m**

Electron orbit diameter = about m Atomic Mass is concentrated in the nucleus (>99.97%) Therefore the volume (or size) of an atom is determined by the orbiting electrons.

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**Nucleus Nucleus composed of neutrons and protons**

Protons are made of two “up” quarks and one “down” quark. Neutrons are made of one “up” quark and two “down” quarks. u + 2/3 u + 2/3 Proton Charge: 2/3 + 2/3 -1/3 = +1 d 1/3 u + 2/3 d 1/3 Neutron Charge: 2/3 - 1/3 -1/3 = 0 d 1/3

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Definitions Atomic Number (Z) – the # of protons in the nucleus (“defines” the element – the # of protons is always the same for a given element) Atomic Number also designates the number of electrons in an element. If an element either gains or loses electrons, the resulting particle is called an ion. For example, if a sodium atom (Na) loses an electron it becomes a sodium ion (Na+)

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**More Atomic Designations**

Atomic Number (Z) – the # of protons Mass Number (A) – protons + neutrons, or the total number of nucleons Isotope – when the number of neutrons vary in the nucleus of a given element (always same number of protons) Only 112 elements are known, but the total number of isotopes is about 2000. mass number

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Isotopes Some elements have several isotopes (like carbon – 12C, 13C, 14C) Isotopes of a single element have the ‘same’ chemical properties (due to same number of electrons), but they have different masses (due to varying number of neutrons.) Due to their various masses isotopes behave slightly different during reactions.

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Carbon Isotopes Neutron number = mass number – atomic number N = A - Z Symbol Protons (Z) Neutrons (N) Mass # (A) 12C 6 12 13C 7 13 14C 8 14

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**Three Isotopes of Hydrogen**

In naturally occurring Hydrogen - 1 atom in 6000 is deuterium and 1 in 10,000,000 is tritium. Heavy water = D2O

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**Example - Determining the Composition of an Atom**

Determine the number of protons, electrons, and neutrons in the fluorine atom 19F Atomic Number (Z) = 9 so protons = 9 and electrons = 9 Mass Number (A) = 19 A = N + Z {N = Neutron Number} so N = A – Z = 19 – 9 = 10 neutrons = 10 9

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**Review of Atom Protons & Neutrons – in nucleus**

Electrons – orbit around nucleus Mass Number (A) = protons + neutrons Atomic Number (Z) = # of protons Neutron Number (N) = # of neutrons Isotope – an element with different # of neutrons (same # of protons)

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Atomic Mass The weighted average mass of an atom of the element in a naturally occurring sample The Atomic Mass is measured in unified atomic mass units (u) – basically the weight of a proton or neutron. The 12C atom is used as the standard, and is assigned the Atomic Mass of exactly 12 u. The weighted average mass of all carbon is slightly higher than 12 (12.011) because some is 13C and 14C.

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**Schematic Drawing of a Mass Spectrometer**

Copyright © Houghton Mifflin Company The ion with the greatest mass is deflected the least, the ion with the least mass is deflected the most.

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**Calculating an Element’s Atomic Mass**

Naturally occurring chlorine is a mixture consisting of 75.77% 35Cl (atomic mass = u) and 24.23% 37Cl (atomic mass = u). Calculate the atomic mass for the element chlorine. Calculate the contribution of each Cl isotope. x u = u (35Cl) x u = u (37Cl) Atomic Mass for Cl = u = Total

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Strong Nuclear Force Two fundamental forces of nature – gravitational and electromagnetic. The electromagnetic force between a proton (+) and an electron (-) is 1039 greater than the gravitational forces between the two particles. Strong nuclear force between nucleons m1 m1 e- p+ r re p+ p+ p+ n n n

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Strong Nuclear Force According to Coulomb’s Law like charges repel each other. Therefore the repulsive forces in a nucleus are huge and the nucleus should fly apart. There must exist a third fundamental force that somehow holds the nucleus together. That 3rd force is the strong nuclear force. It is much stronger than the electromagnetic force. But strong only at short range! (< m) As nucleus gets larger, the strong nuclear force is much weaker and is overcome by the electromagnetic force. The nucleus decays or disintegrates.

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Radioactivity Radioactivity (radioactive decay) – the spontaneous process of nuclei undergoing a change by emitting particles or rays Nuclide – a specific type of nucleus 238U or 14C Radionuclides (radioactive isotopes or radioisotopes) – nuclides whose nuclei undergo spontaneous decay (disintegration) Substances that give off such radiation are said to be radioactive

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**Radioactive Decay Parent nucleus – the original nucleus before decay**

Daughter nucleus (or daughter product) – the resulting nucleus after decay Radioactive nuclei can decay (disintegrate) in three common ways Alpha decay Beta decay Gamma decay

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**Radioactive Decay (disintegration)**

Alpha decay – disintegration of a nucleus into a nucleus of another element, with the emission of an alpha particle (α) - a helium nucleus (4He) A B + 4He Beta decay – a neutron is transformed into a proton, with the emission of a beta particle (β) – an electron ( 0e) A B + 0e Gamma decay – occurs when a nucleus emits a gamma ray (γ) and becomes a less energetic form of the same nucleus 2 2 -1 -1 A* B + γ The * means nucleus is in excited state.

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**Three Components of Radiation**

Alpha(a), Beta(b), Gamma(g)

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**Nuclear Decay Equations - Examples**

Alpha decay = 232Th 228Ra + 4He 90 88 2 A = 228+4=232 Z = 88+2 = 90 Beta decay = 14C 14N + 0e 6 7 -1 A = = 14 Z = = 6 Gamma decay = 204Pb* 204Pb + g 82 A = = 204 Z = = 82 In a nuclear decay equation, the sums of the mass numbers (A) and the sums of the atomic numbers (Z) will be the equivalent on each side

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**The Products of Alpha Decay – Example**

238 U undergoes alpha decay. Write the equation for the process 92 238 U ? 92 238 = A so A = = Z so Z = 90 238 U AX + 4He 92 2 Z 238 U 234X + 4He 92 2 90 Must determine the mass number (A), the atomic number (Z), and the chemical symbol for the daughter product 238 U 234Th + 4He 92 2 90

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**Five Forms of Nuclear Radiation**

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**Decay Series of Uranium-238 to Lead-206**

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**Identifying Radionuclides (unstable)**

Pattern emerges: Most stable nuclides have an even number of both protons and neutrons (even-even nuclides) Most unstable nuclides have an odd number of both protons and neutrons (odd-odd nuclides) A nuclide will be radioactive if: - Its atomic number (Z) is greater than 83 n < p (except for 1H and 3He) 1 2 It is an odd-odd nuclide (except for 2H, 6Li, 10B, 14N) 1 3 5 7

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**Example - Identifying Radionuclides**

Identify the radionuclide in each pair, and state your reasoning. 208Pb and 222Rn 82 86 Z above 83 19Ne and 20Ne 10 fewer n than p odd-odd 63Cu and 64Cu 29

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**Half-Life of a Radinuclide**

Half-Life – the time it takes for half of the nuclei of a given sample to decay In other words – after one half-life has expired, only one-half of the original amount of radionuclide remains undecayed After 2 half-lives only one-quarter (½ of ½) of the original amount of the radionuclide remains undecayed

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**Decay of Thorium-234 Decay of Thorium-234 over Two Half-Lives**

Thorium-234 has a Half-Life of 24 days

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**Decay Curve for Any Radionuclide**

Curve can be applied for any radionuclide. Number Number of Half Lives of Nuclei No 1 ½ No 2 ¼ No 3 1/8 No

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**Half-Life Carbon-14 dating can be used for 10s of thousands of years.**

Uranium-238 dating can be used for 100s of millions of years

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**Example - Finding the Number of Half-Lives**

What fraction and mass of a 40 mg sample of iodine-131 (half-live = 8d) will remain in 24d? Step 1 – find the number of half-lives that have passed in 24 days: 24 days = 3 half-lives 8d/half-life Step 2 – Start with the given amount No = 40mg, and half it 3 times (3 half-lives) Once No/2 = 20 mg (after 8 days) Twice No/4 = 10 mg (after 16 days) Thrice No/8 = 5 mg (after 24 days)

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**Example - Finding the Elapsed Time**

How long would it take a sample of 14C to decay to one-fourth its original activity? (half-live of 14C is 5730 years) Solution: No No/2 No/4 So 14C would need to decay for two half-lives in order to be reduced to ¼ its original activity. (2 half-lives)(5730 y / half-life) = 11,460 years

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**Determining the Half-Live**

In order to determine the half-life of a particular radionuclide, we must monitor the activity of a known amount in the laboratory Activity – the rate of emission of the decay particles (usually in counts per minute, cpm) When (time) the initial activity rate has fallen to one-half – we have reached One Half-Life Measured with a Geiger Counter Geiger developed this in 1913 helping Rutherford

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Nuclear Reaction We know that radioactive nuclei can spontaneously change into nuclei of other elements, a process called transmutation. Particle (proton or neutron) can also be added to a nucleus to change it into another element. This process is called a nuclear reaction a + A B + b a is particle that bombards nucleus A to form nucleus B and an emitted particle b

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**Gold from Mercury! 1H + 200Hg 197Au + 4He 1 80 79 2**

Particle accelerators can create gold (Au) by bombarding Mercury with Hydrogen. But very expensive! $1,000,000 per ounce! Elements with atomic numbers greater than 92 have been created this way. 1H + 200Hg 197Au + 4He 1 80 79 2

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**Example - Equation for a Nuclear Reaction**

Complete the equation for the proton bombardment of lithium-7. 1H + 7Li ???? + 1n 1 3 Note, the sum of the mass #’s on left = 8. The mass # on the right must also = 8, therefore the missing particle must have a mass # = 7. The sum of the atomic #’s on left = 4 Therefore the sum of the atomic #’s on right must also equal 4.

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**Example - Equation for a Nuclear Reaction**

1H + 7Li ???? + 1n 1 3 The missing particle must have an atomic number = 4 Therefore the missing particle has a mass number of 7 and an atomic number of 4. This element is 7Be (beryllium.) Completed equation 4 1H + 7Li 7Be + 1n 1 3 4

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Smoke Detector A weak radioactive source ionizes the air and sets up a small current. If smoke particles enter, the current is reduced, causing an alarm.

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**Units Used for Mass and Energy**

Mass in atomic mass units Energy in mega electron volts (MeV) 1 MeV = 1.60 x J 1 u has energy of 931 MeV 1 u = 1.66 x kg ≈ mass of proton 1 eV = qe (1 V) = 1.6 x C V (1 J = C V) E = mc2 = (1.66 x kg)(3.0x108m/s)2 = 1.49 x J / (1.60 x J / MeV) 931 MeV / u

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**Types of Radioactive decay**

Alpha: Emits a helium nucleus (heavy, charged particle) Beta: Emits an electron (light, charged particle) Gamma: Emits very high energy EM wave (uncharged) The figure below shows penetration of these three types of radiation. Only Gamma radiation harmful to humans externally.

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**Penetration of Radiation**

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Radiometric Dating Radiometric dating – the determination of age by the measurement of the rate of decay of radionuclides in rocks or dead organic material Recall that an atomic nuclei is said to be radioactive when it will naturally decay. The product of decay is generally called the daughter nuclei or daughter product. Daughter products may themselves be stable or radioactive (unstable.)

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**Radiometric Dating – Half-life**

Half-life – the length of time taken for half of the radionuclide in a sample to decay This rate of decay has been found to always be constant. Unaffected by temperature, pressure, and chemical environment The older the rock the less parent and the more daughter product is present. Different radioactive parents may have drastically different half-lives.

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**Half-Life and Radiometric Dating**

As the parent nuclide decays the proportion of the parent decreases and the proportion of the daughter increases.

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**Rock “Clocks” – Condition #1**

Radioactive decay can serve as a “clock” for dating rocks, if the following conditions are met Over the lifetime of the rock, no daughter or parent has been added or subtracted. This condition requires that there has been no contamination of the rock. If either parent or daughter nuclides are added or subtracted by metamorphism or fluid movement, the date obtained is not valid. 1

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**Rock “Clocks” – Condition #2**

The age of the rock is reasonably close to the half-life of the parent radionuclide. If too many half-lives transpire it may become impossible to measure the amount of the remaining parent nuclide. If only a small portion of one half-life transpires then it may be impossible to measure the amount daughter product present. In either case, a valid date cannot be obtained. 2

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**Rock “Clocks” - Condition #3**

No daughter product was present when the rock initially formed. If daughter product was present when the rock formed, later analysis of the rock will result in an inaccurate parent to daughter ratio. Sometimes it may be possible to determine the amount of daughter nuclide initially present. In order to use radiometric dating techniques at all, the rocks must actually contain the appropriate radionuclides. 3

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**Condition #3 – Sometimes a Problem**

In the case of uranium-lead dating, there are many different isotopes of lead. For example, we know that primordial lead consists of 1.4% lead-204, 24.1% lead-206, 22.1% lead-207, and 52.4% lead-208. We also know that lead-204 is never created from radioactive decay. Therefore if any lead-204 is present we know that the other three lead isotopes are also present and we know their ratios.

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**Primordial and Radiogenic Lead**

Since lead-204 is present, we know how much of the other isotopes are primordial and how much are radiogenic.

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**Major Radionuclides Used for Radiometric Dating**

Note that since the half-lives vary the range of ages also varies. Not all rocks can be radiometrically dated, only those with the appropriate mineral present.

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**Radionuclides Used for Radiometric Dating**

Note that since the half-lives vary the range of ages also varies. Not all rocks can be radiometrically dated, only those with the appropriate mineral present.

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**Example - Using Radiometric Dating**

The ratio of U-235 to its daughter, Pb-207, is 1 to 3 in a certain rock. That is, only 25% of the original U-235 remains. (The half-life of U-235 is 704 x 106 years.) How old is the rock? To decay from 100% to 25% takes 2 half-lives. 100% 50% 25% (2) x (704 x 106 years) = 1408 x 106 years or 1.41 billion years = age of the rock

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**Carbon Dating Developed in 1950 by American, Willard Libby**

Carbon-14 (14C) dating is the only radiometric dating technique that can be used to date once-living organisms. 14C is a radionuclide with a half-life of 5730 years. The age of an ancient organic remain is measured by comparing the amount of 14C in the ancient sample compared to the amount of 14C in modern organic matter.

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**Carbon Dating 14C is a natural product formed in the atmosphere.**

About one in a trillion C atoms in plants is 14C. 14C is incorporated into all living organisms. Living matter has an activity of about 15.3 counts/minute/gram C. At death the 14C present begins to decay.

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**Carbon Dating – Modern Methods**

In the newest carbon dating techniques, the amounts of both 14C and 12C are measured. The ratio of these two isotopes in the ancient sample is compared to the ratio in living matter. Using this method only very small samples are needed and specimens as old as 75,000 years can be accurately dated. Beyond 75,000 years, the amount of 14C still not decaying is too small to measure.

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**Carbon Dating - Limitations**

Carbon dating techniques assumes that the amount of 14C in the atmosphere (and therefore in living organisms) has been constant for the past 75,000 years. We now know that the amount of 14C in the atmosphere has varied by (+) or (-) 5%. These variations in 14C levels have been due to changes in solar activity and changes in the Earth’s magnetic field.

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**Carbon Dating - Limitations**

These slight variations in 14C abundance have been corrected by careful analyses of California’s 5,000 year-old bristlecone pines. An extremely accurate calibration curve has been developed for 14C dates back to about 5000 B.C. Carbon dating is widely used in archaeology, and has been used to date bones and other organic remains, charcoal from fires, beams in pyramids, the Dead Sea Scrolls, and the Shroud of Turin.

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**Equations N = A – Z AX N = number of neutrons Alpha Decay: A B + 4He**

Beta Decay: A B + 0e Gamma Decay: A* B + γ Half Life = Time / (time/half-life) E = mc2 Z 2 -1

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