t. Norah Ali Al-moneef king Saud university Chapter (30) Nuclear Physics 30.1 Radioactivity 30.2 half-life 30.9 Radioactive decay t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university 30.1 Radioactivity Atomic Structure Contain the symbol of the element, the mass number and the atomic number. Mass number Superscript → X Subscript → Atomic number A – Z = number of neutrons Number of neutrons = Mass Number – Atomic Number t. Norah Ali Al-moneef king Saud university

Subatomic Particles in Some Atoms 16 31 65 O P Zn 8 15 30 8 p+ 8 n0 8 e- 15 p+ 30 p+ 16 n0 35 n 15 e- 30 e- Find each of these: number of protons number of neutrons number of electrons Atomic number Mass Number Br 80 35 t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university If an element has an atomic number of 34 and a mass number of 78, what is the: number of protons number of neutrons number of electrons complete symbol If an element has 78 electrons and 117 neutrons what is the Atomic number Mass number number of protons complete symbol If an element has 91 protons and 140 neutrons what is the Atomic number Mass number number of electrons complete symbol t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Isotopes Atoms of the same element can have different numbers of neutrons. having different masses, due to varying numbers of neutrons. Thus, different mass numbers. These are called isotopes. Chemically identical Isotopes: elements with the same number of protons, but a different number of neutrons. 12 6 C 13 14 There are many types of uranium: U 235 92 U 238 92 t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Most of the isotopes which occur naturally are stable. A few naturally occurring isotopes and all of the man-made isotopes are unstable. Unstable isotopes can become stable by releasing different types of particles. This process is called radioactive decay and the elements which undergo this process are called radioisotopes/radio nuclides. t. Norah Ali Al-moneef king Saud university

What do we mean by Radioactivity? Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. There are numerous types of radioactive decay. The general idea: An unstable nucleus releases energy to become more stable It is a natural process in our universe It is spontaneous – we cannot predict when an atom will undergo decayThey do not need encouraging or triggering in any way. A new substance may form t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Alpha, Beta, and Gamma Historically, the products of radioactivity were called alpha, beta, and gamma when it was found that they could be analyzed into three distinct species by either a magnetic field or an electric field: t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Radioactive Decay Three types of radiation Radioactive decay results in the emission of either: an alpha particle (a), Consists of 2 protons and 2 neutrons and is identical to a helium-4 nucleus (+2 charge) a beta particle (b), electrons(- charge) positrons (+ charge) or a gamma ray(g). t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Nuclear Stability What happens to an unstable nucleus? Band of Stability Depends on the neutron to proton ratio. They will undergo decay The type of decay depends on the reason for the instability Number of Neutrons, (N) Number of Protons (Z) t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Alpha Decay Alpha-particle production Alpha particle – helium nucleus Net effect is loss of 4 in mass number and loss of 2 in atomic number. Ra 226 88 Rn 222 86 + He 4 2 Rn 222 86 He 4 2 + Po 218 84 t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Beta Decay 1 - (- decay) Beta particles are just electrons from the nucleus, the term "beta particle”. In -decay processes a neutron is converted into a proton by electron emission (--decay), or a proton is converted in a neutron by positron emission (+-decay): a nuclear neutron changes into a nuclear proton n P + - (e- ) X A Z Y Z + 1 + e -1 - release of anti-neutrino (no charge, no mass) t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Beta-particle production Beta particle – electron Examples Net effect is to change a neutron to a proton. Po 218 84 Rn 85 + b -1 Th 234 90 Pa 91 + b -1 Tl 210 81 Pb 82 + b -1 t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university 2 - POSITRON (ß+) EMISSION (+ decay) Occurs when the nucleus of the atom has too many protons (i.e., is proton-rich). It is also known as positive beta decay. Results in a positive electron emitted from the nucleus of the proton rich atom. This positive electron is known as a positron. An additional particle, a neutrino, is also emitted from the nucleus. Neutrinos are very small particles with no electric charge. They have little or no mass and participate in weak interactions. Positrons have same mass as electrons Positrons have charge +1 Positrons are less ionizing than alphas Positrons are more penetrating than alpha decay but less than gamma The best shielding is lead with thickness of 1 inch or more t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university 2) + decay occurs with ratio nuclides that are “neutron poor” (i.e., low N/Z ratio) a nuclear proton changes into a nuclear neutron p n + + (e+ ) X A Z Y Z - 1 + e +1 + + release of neutrino t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Nuclear Shell Model Discrete energy levels for protons and neutrons and discrete energies for radiation when energy levels change or following radioactive decay t. Norah Ali Al-moneef king Saud university

Why N  Z for light nuclei protons neutrons energy protons neutrons energy If the electrostatic repulsion of protons can be neglected (this is the case of light nuclei: recall that the positive electrostatic energy Z2), the nucleus tends to keep approximately equal numbers of protons and neutrons. energy energy Even in this case, the nucleus can still lower its total energy: the rest energy of neutron is slightly more than the rest energy of a proton and an electron. protons neutrons protons neutrons t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university 3) Electron capture In an Electron capture a parent nucleus may capture one of its orbital electrons and emit a neutrino. This is a process which competes with positron emission and has the same effect on the atomic number. Most commonly, it is a K-shell electron which is captured, and this is referred to as K-capture. X + A Z Y Z - 1 + e -1 t. Norah Ali Al-moneef king Saud university

Converting protons and neutrons There are certain combinations of protons and neutrons that are more stable than others If the number of protons :neutrons is not correct the nucleus is unstable. The solution is to release certain types of radioactivity. Note: proton (11p), neutron (10n) 10n  11p + 0–1e (– emission) 11p  10n + 01e (+ emission) 11p + 0–1e  10n (EC – electron capture) t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Gamma Decay Gamma rays are very high-energy photons. They are emitted when a nucleus decays from an excited state to a lower state, just as photons are emitted by electrons returning to a lower state. Written as follows A Z X*  X  Gamma rays are not charged particles like a and b particles. Gamma rays have the same property as X-rays, but are generated different: – X-ray through energetic electron interactions Net effect is no change in mass number or atomic number. t. Norah Ali Al-moneef king Saud university

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t. Norah Ali Al-moneef king Saud university Types of Ionizing Radiation Alpha Particles Stopped by a sheet of paper Radiation Source Beta Particles Stopped by a layer of clothing or less than an inch of a substance (e.g. plastic) Gamma Rays Stopped by inches to feet of concrete or less than an inch of lead t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university 31-2 Half-Life For example, suppose we had 20,000 atoms of a radioactive substance. If the half-life is 1 hour, how many atoms of that substance would be left after: 10,000 (50%) 5,000 (25%) 2,500 (12.5%) 1 hour (one lifetime) ? 2 hours (two lifetimes) ? 3 hours (three lifetimes) ? Time #atoms remaining % of atoms remaining t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Half-Life Number of atoms decaying per unit time is proportional to the number of unstable atoms Constant of proportionality is the decay constant () ∆N/ ∆ t =-  N the minus sign indicates that N is decreasing. The number of decays are represented by ∆N The short time interval that ∆N occurs is represented by ∆t N is the number of nuclei present λ is the decay constant = -  t Nt N0 ln Nt = N0e-t where: Nt = number of radioactive atoms at time t N0 = initial number of radioactive atoms e = base of natural logarithm = 2.71828… t = time t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Radioactive Decay The number of atoms in a sample that decay depends on the total number of atoms in the sample!! This fact yields a rate of decay called an exponential decay The Decay Constant, λ • The rate of decay is called the decay constant. It determines the half-life of a radioactive element. • The decay constant is unique for each radioactive element. there is a definite time in which the number decreases by half, regardless of what the beginning number is N(T=half life) = No/2 t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Half lives are calculated according to the equation: N = N0(½)n N = number of radioactive atoms at time t N0 = initial number of radioactive atoms n= the number of half lives that have passed since you have begun counting example Carbon-14, a radioactive isotope of carbon, has a half life of 5730 years. If a 20 gram sample of carbon-14 is allowed to decay for 10,000 years, how much remains at the end of this period? N = N0(½)n N0 = 20 grams n = 10,000 yrs/5730 yrs/half life = 1.75 N = 20 grams(½)1.75 = 5.95 grams t. Norah Ali Al-moneef king Saud university

How to calculate half-life? The decay constant and half-life has the relationship : half –life = ln(2) / λ = o.693 / λ The fraction of a radionuclide remaining after a certain time period is an exponential function of the decay constant and the time: NN0=e−λt t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university example 64 grams of Serenium-87, is left 4 grams after 20 days by radioactive decay. How long is its half life? Half lives are calculated according to the equation: N = N0(½)n 4 = 64 x(½)n 4 / 64 = (½)n :4 half lives Half life = 20/ 4 = 5 dayes t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university The half life of radium Ra is 1.6x103 yr. If the sample contains 3.00x1016 nuclei find the decay constant t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Example: Tritium has a half life of 12.3 years. How many years will it take for 88.0 grams to decay to 5.50 grams t=49.25 years t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Problems 1-You have 400 mg of a radioisotope with a half-life of 5 minutes. How much will be left after 30 minutes? Answer 6.25mg 2-How many half-lives have passed if 255 g of Co-60 remain from a sample of 8160 g? Answer 5 half-lives 3-Suppose you have a sample containing 400 nuclei of a radioisotope. If only 25 nuclei remain after one hour, what is the half-life of the isotope? Answer 15 minutes 4-If a radioactive element has diminished by 7/8 of its original amount in 30 seconds, what is its half-life? answer 10 seconds 5- The half life of radium Ra is 1.6x103 yr. If the sample contains 3.00x1016 nuclei. Find the number of nuclei after 4.8x103 yr. t. Norah Ali Al-moneef king Saud university

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t. Norah Ali Al-moneef king Saud university Physical Half-Life Useful parameter related to the decay constant; defined as the time required for the number of radioactive atoms in a sample to decrease by one half  = ln 2/T1/2 = 0.693/T1/2 Physical half-life and decay constant are inversely related and unique for each radionuclide = t1/2 0.693  The half-life of such a process is: Effective Half-Life E.g., for an isotope with a 6-hr half life attached to various carrier molecules with different biological half-lives. TP TB TE 6 hr 1 hr 0.86 hr 6 hr 6 hr 3 hr 6 hr 60 hr 5.5 hr 6 hr 600 hr 5.9 hr t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university activity The activity of a radioactive substance is defined as the number of radioactive nuclei that disintegrate per second. A = |N/  t| A = N= No e t Ao = No A(t) = Ao e t At = activity at time t A0= activity at time t =0 Nt / N0= e-t N/ N0= (½)n N = N0(½)n A = Ao(1/2)t/T1/2 t = nT1/2 A = Ao(1/2)n Units of Radioactivity(activity) The becquerel (Bq) or The curie (Ci) 1 Ci = 3.7x10 10 Bq t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Example The half life of radium 1.6x103 yr if the sample contains 3.0x1016nuclei . Find the activity in curies (1Ci 3.7x1010decays/s t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Example The half life of radium ( Ra) is 1.6x103yr .if the sample contain 3.00x1016nuclei . Find the number of nuclei after 4.8x103yr t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university example What is the half-life of N2O5 if it decomposes with a rate constant of 5.7 x 10-4 s-1? 13.3 t½ ln2 λ = 0.693 5.7 x 10-4 s-1 = 1200 s = 20 minutes How do you know decomposition is first order? units of λ (s-1) t. Norah Ali Al-moneef king Saud university

example If I have a sample of 2259 atoms U-238 left, how old is the sample if there were originally 2560 atoms U-238? Nt = # of atoms (or mass) at time t N0 = # atoms (or mass) at time t = 0 t = length of time indicated (not half-life) λ = decay constant lnNt = lnN0 - λt t1/2 = half life of substance ln2259 = ln2560 – λt λ = 1.53659 x 10-10 Problem: I need λ t1/2 = 0.693 λ ln2259 = ln2560 – (1.54 x 10-10)t -0.1250850 = – (1.54 x 10-10)t 4.51 x 109 years = 0.693 λ t = 8.122 x 108 years t. Norah Ali Al-moneef king Saud university 38

t. Norah Ali Al-moneef king Saud university example A watch made in 1521 AD contained 24.5 mg radium-226. In 1967, the amount of radium-226 is 20.2 mg. What is the half- life of radium-226? t1/2 = 0.693 4.327 x 10-4 lnNt = lnN0 - λt t1/2 = 1600 years ln20.2 = ln24.5 – λ(446) λ = 4.327 x 10-4 t1/2 = 0.693 λ t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university example 14C 14N + 0 +  6 7 -1 t½ = 5730 years If a sample of wood has only 32% of the original amount of carbon-14 left, how old is the sample? t1/2 = 0.693 λ lnNt = lnN0 - λ t 5730 years = 0.693 λ ln32 = ln100 – λt λ = 1.21 x 10-4 ln32 = ln100 – (1.21 x 10-4)t -1.13943 = – (1.21 x 10-4)t t = 9400 years t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university example The half life of I-123 is 13 hr. How much of a 64.0 g sample of I- 123 is left after 31 hours? t1/2 = 0.693 λ lnNt = lnN0 - λ t lnNt = ln64.0 – (5.33076 x 10-2)(31) 13 = 0.693 λ lnNt = 4.158883 – 1.652536 λ = 5.33076 x 10-2 lnNt = 2.506347 e e Nt = e 2.506347 Nt = 12.3 grams t. Norah Ali Al-moneef king Saud university 41

Fundamental Decay Equation Nt = N0e-t or At = A0e-t where: Nt = number of radioactive atoms at time t At = activity at time t N0 = initial number of radioactive atoms A0 = initial activity e = base of natural logarithm = 2.71828… λ= decay constant = ln 2/Tp1/2 = 0.693/Tp1/2 t = time Fundamental Decay Equation The activity of a radioactive substance is defined as the number of radioactive nuclei that disintegrate per second. A = |N/  t| A = N= No et Ao = No A(t) = Ao e t t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university BASIC TYPES OF RADIOACTIVE DECAY Alpha () decay Occurs when atomic nuclei have too many protons and neutrons (i.e., Are heavy) Consist of 2 protons and 2 neutrons Mass of an alpha particle is ~8000 me Charge = +2 Are highly ionizing Have low penetrating abilities (only cm in air and mm in water) Easily shielded; common types of shielding are paper, cardboard, air, clothing; will not penetrate skin Changes both the mass and identity of the nucleus of the parent radionuclide This means that the decay results in the formation of a new element as the daughter product t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university NEGATIVE BETA (ß-) DECAY Occurs when atoms have too many neutrons (i.e., Are “neutron-rich”) and decay by emitting a negative beta particle (ß-) During negative beta decay, excess neutrons are converted into protons, electrons, and antineutrinos. The protons remain in the nucleus but the new electrons are emitted as negative beta particles (ß-) or negatrons. Less ionizing than alphas due to decreased mass of negatrons Changes the identity of the nucleus but not the mass The z number is increased due to conversion of neutrons into protons More penetrating than alpha particles; ~ 12 meters in air They can penetrate skin–best shielding is wood, plastics, thick cardboard t. Norah Ali Al-moneef king Saud university 17

t. Norah Ali Al-moneef king Saud university GAMMMA () -ray Is a form of pure electromagnetic radiation emitted from nuclei that have excess energy. It is sometimes called gamma photon radiation. Are photons emitted from unstable nuclei to rid themselves of excess energy. Gamma photons are subatomic packets of pure energy. They are higher in energy and more penetrating than the photons that make up visible light. GAMMMA RAYS AND X RAYS Have the same properties except for their origin Gammas come from within the nuclei of atoms X-rays come from outside the nuclei Both are electromagnetic energy in the form of emitte photons t. Norah Ali Al-moneef king Saud university 27 25

t. Norah Ali Al-moneef king Saud university Penetration of Matter Though the most massive and most energetic of radioactive emissions, the alpha particle is the shortest in range because of its strong interaction with matter. The electromagnetic gamma ray is extremely penetrating, even penetrating considerable thicknesses of concrete. The electron of beta radioactivity strongly interacts with matter and has a short range. t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university  decay - three types 1) - decay - converts one neutron into a proton and electron - no change in mass number, but different element - release of anti-neutrino (no charge, no mass) 2) + decay - converts one proton into a neutron and electron - no change in mass number, but different element - release of neutrino 3) Electron capture t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university g decay - conversion of strong to coulombic E - no change of A or Z (element) - release of photon - usually occurs in conjunction with other decay t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university Nuclear Physics General Rules: 1) a emitted to reduce mass, only emitted if mass number is above 209 2) b- emitted to change neutron into proton, happens when there are too many neutrons 3) b+ emitted (or electron captured) to change proton into neutron, happens when there are too few neutrons 4) g emitted to conserve energy in reaction, may accompany a or b. t. Norah Ali Al-moneef king Saud university

t. Norah Ali Al-moneef king Saud university 238U 206Pb + 8 4 + 6 0 92 -1 82 2 t½ = 4.51 x 109 years 5. How long will it take for 100 atoms U-238 to become 25 atoms U-238 and 75 atoms other stuff? (ignore sf) atoms (number) 100 50 25 Time (years) 4.51 x 109 9.02 x 109 But what if I asked for something inexact, like 10.2 days? Or the amount of time for 30.8 grams to decay into Polonium? t. Norah Ali Al-moneef king Saud university