Page 1 of 17 Physics Week 16(Sem. ) Name The Nuclear Chapter Summary Nuclear Structure Atoms consist of electrons in orbit about a central nucleus. The electron orbits are quantum mechanical in nature. The nucleus consists of protons and neutrons, collectively referred to as nucleons. The neutron was discovered in 193 by James Chadwick. It was found to have no electrical charge and a mass slightly larger than that of a proton (almost the same). The number of protons in the nucleus of an atom is different in different elements, it is given by the atomic number (Z). In an electrically neutral atom, the number of protons are equal to the number of electrons. The number of neutrons in the nucleus is N. The total number of neutrons and protons in the nucleus is called the atomic mass number (A), this is because the total mass is approximately equal to the neutrons and protons together. Therefore, the atomic mass number is the number of protons and neutrons added together (A=N+Z). For a proton the symbol is typically, the neutron is denoted, and the electron is. Isotopes are elements that contain the same number of protons and different numbers of neutrons in the nuclei. Carbon for example has two stable isotopes; the most common atom of carbon has 6 protons, 6 neutrons and 6 electrons (98.9%). The other common stable isotope of carbon has 6 protons, 7 neutrons, and 6 electrons (1.1%). The atomic masses in the periodic table are an average of the most common stable isotopes of the elements. The protons and neutrons are clustered in the nucleus in a nearly spherical arrangement. Experiment shows that the radius of the nucleus (r) depends on atomic number (A) and can be calculated in meters by 1. 10 / Using this equation and the equation for density, it can be found that the density of differing atoms is approximately the same. Therefore, the differences in material densities arise mainly because of the difference in how closely the atoms are packed to themselves, not the nuclear density. Strong Nuclear Force & Stability of Nucleus Two positively charged objects or particles would typically have strong repulsive forces. However, the nucleus can stay intact with many positive charges residing within a small region together. There must be some attractive force that overcomes the electrical repulsion to allow for a stable nucleus. The gravitational force is too weak (mass is small), so there must be some other force. This force is called the strong nuclear force and is one of the three fundamental forces (also gravitational and electroweak forces). Much is known about the strong nuclear force. The strong nuclear force is almost independent of electrical charge. At a set distance of separation, the nuclear force of attraction between two protons, two neutrons or between one proton and one neutron. The range of effectiveness of the force is very short, it is very strong at distances on the order of 10 15 m and essentially zero at larger distances. The strong nuclear force only acts over very short distances, it is this that makes it so important in nuclear stability. For the nucleus to be stable, the electrostatic repulsion between protons, must be balanced by the strong nuclear force. Figure 31. shows the line for N=Z and the belt of stability. For all elements (few exceptions), the belt of stability range is mostly around A (twice the total of protons). For the most part all elements with 83 protons and more at unstable nuclei.
Mass Defect Page of 17 Because of the strong nuclear force, the nucleus is help together. Therefore, energy is required to separate a stable nucleus into its constituent protons and neutrons. The more stable the nucleus is the more energy needed to break it apart. The required energy to do this is called the binding energy. It follows Einstein s famous equation Where E is the binding energy (J), m is the mass in kg, c is the speed of light (m/s). See example. Knowing the mass of the hydrogen atom (containing only a proton) is 1.0073 amu and has a mass of 1.676x10 7 kg, thus 1 amu=1.6605x10 7 kg. Using this and then solving the equation above for the energy equivalent of 1 amu, you would obtain 1.6605 10 7.9979 10 Therefore the energy equivalent to 1 amu mass defect is 1.494x10 10 J. Or in electron volts (1eV=1.60x10 19 J) thus the energy equivalent of 1 amu is 931.5 MeV. See example 3. If the binding energy for different atoms were to be analyzed it would be important to do it on a per nucleon basis. As can be seen in the graph of binding energy per nucleon versus nucleon number (A), the maximum binding energy per nucleon is approximately 8.7 MeV. Helium (A=4) has a binding energy per nucleon very close to the maximum at about 7MeV/nucleon. Also, it is important to note the binding energies per nucleon peak at about Fe and As and then gradually decrease continually. After Bi (bismuth) the nucleus gets so massive that there is insufficient binding energy to hold the nucleus together leading to unstable and hence radioactive nuclei. Radioactivity When an unstable or radioactive nucleus disintegrates spontaneously, certain kinds of particles and/or highenergy photons are released. These are released particles/photons are called rays. There are three commonly released rays; alpha rays (α), beta rays (β), and gamma rays (γ). They were given these names in order of their penetrating power (following the Greek alphabet), thus alpha particles penetrate the least and gamma the most. The process that produces the rays has to follow the laws of physics (cons. Laws). To all of the previously learned conservation laws (linear momentum, mass/energy, electrical charge, angular momentum) another conservation law applies, this is conservation of nucleon number. This last conservation law was determined after studying disintegrated nuclei where it was found the number of nucleons after was equal to the original number of nucleons. A simple experiment can be setup to observe the three types of naturally occurring radioactivity. A magnetic field could be setup which will deflect only the charged particles resulting in a separation of the charged particles from the uncharged particles.
Analyzing the previous image the alpha particles are deflected toward the top of the page, the beta particles were deflected toward the bottom of the page, and the gamma rays were unaffected. Therefore, alpha and beta rays were discovered to be charged particles. Meanwhile, gamma rays were found to be uncharged rays. Alpha Decay Alpha decay is the result of an unstable nucleus emitting an alpha particle. The alpha particle has a positive charge of +e and a nucleon number of A=4. This is the nucleus of a Helium atom, which was previously found to be very stable compared to other nuclei. An example of an alpha decay disintegration would be: This is the alpha decay that results from a Uranium nucleus. The original nucleus is commonly referred to as the parent nucleus (P). The remaining nucleus after the disintegration is referred to as the daughter nucleus (D). When the parent and daughter nuclei are different, this process converts one element into another and is called transmutation. Note that the above alpha decay is consistent with conservation of charge and nucleon number (top and bottom numbers). When a nucleus releases an alpha particle the nucleus also releases heat, this is in part the source of heat for Earth. See Example 4. It is important to note that the released energy appears as kinetic energy of the recoiling Thorium nucleus and alpha particle (not including some carried away as a gamma ray). Alpha decay is used commonly in smoke detectors. Beta Decay Beta particles have an opposite charge compared to alpha particles, they are negative. Experiment shows that these particles are electrons. Consider the following beta decay: Beta decay, similarly to alpha decay, results in the transmutation of one element into another. The above equation obeys the conservation of nucleon number and charge. It has been found that the emission of the electron is the result of a neutron decaying into a proton and an electron. The number of nucleons remained unchanged, while the number of protons increased by one (neutron into proton). The charge was conserved since a neutral particle decayed into a positive and negative particle. This type of beta decay is called β decay. There is also β+ decay, the particle emitted in this case is called a positron (or a positive charge, with the mass of an electron). The nucleon number remains unchanged while the nucleus decreases by one proton. This positron is the result of a proton transforming into a neutron. Gamma Decay Page 3 of 17 The nucleus, like orbiting electrons, exist only in discrete energy states or levels. When the nucleus changes from a higher energy state (denoted by *) to a lower energy state, a photon is emitted. The process is similar to the photon emission that leads to the bright line emission spectrum. With nuclear energy levels, however, the photon has a much higher energy and is called specifically the gamma ray (γ). The process for gamma decay can be seen below: Gamma decay does not cause a transmutation of one element into another. See Example 7 for Gamma decay. Gamma knife surgery is a very promising surgical technique for the removal of masses/tumors in the brain. The intense concentration of gamma rays meet at the exact location of the problem and this intensity will destroying the target and leaving the healthy tissue unharmed (b/c it is the combination of small dose rays). This is noninvasive and reduces hospital stays by about
90%, allowing patients to return to work within a few days. The Neutrino When a beta particle is emitted from an unstable nucleus, energy is simultaneously released. Experiments show that the kinetic energy and mass defect during this process does not completely account for the total energy lost. Wolfgang Pauli proposed that part of the energy is carried away by another particle that is emitted with the beta particle, called the neutrino. The existence of the neutrino was confirmed in 1956, it is represented by the Greek symbol (ν nu). Therefore the beta decay of thorium (Th) should be: The bar over the neutrino is to indicate an antimatter neutrino or antineutrino. A normal neutrino (ν without a bar over it) is emitted when Beta positive decay occurs. Currently, there are some thoughts that the neutrino may actually have some mass but this has not been proven. If the mass is zero then it travels at the speed of light. Also, the neutrino has no electrical charge and interacts too weakly with matter to be detected easily. The emission of neutrinos and beta particles involves a force called the weak nuclear force (much weaker than the strong force). It is known, now, that the weak nuclear force and the electromagnetic force are two different manifestations of a single, more fundamental force called the electroweak force. The electroweak force, gravitational force, and the strong nuclear force and the three fundamental forces in nature. Radioactivity Knowing which nucleus in a group of nuclei will disintegrate at a given time cannot be known; random disintegrations will occur randomly. As time passes, the number (N) of parent nuclei decreases. The N will smoothly decrease and approach zero as time passes on. The half life (T 1/ ) of a radioactive isotope is the time required for one half of the nuclei present to disintegrate. For example, radium ( Page ) 4 has of 17 a half life of 1600 years so it takes this amount of time for one half of the given quantity of this isotope to disintegrate. In another 1600 years the half of the original that remains will be reduced to ¼ of the original sample size. The value of the half life depends on the radioactivity of the nucleus. Values range from milliseconds to thousands of years. The activity of a radioisotope is the number of disintegrations per second that occur. The activity can be obtained by dividing the change in the number of nuclei (ΔN) by the time interval during which the change takes place (Δt). The equation below can be used to determine the decay constant (λ): Δ Δ λ Where N is the number of radioactive nuclei remaining. The SI unit of radioactivity is the Becquerel (Bq), one Bq is equal to 1 disintegration per second. It can also be measured in the curie (Ci) where 1 Ci=3.70x10 10 Bq. The amount of radium put into a watch to make it glow in the dark has an activity of about 4x10 4 Bq, while the activity used in radiation therapy is about a billion times greater. If the activity of a nucleus is known then the half life can be calculated, or visa versa. Therefore the resulting equation is: / 0.693 λ Where T 1/ is the half life and λ is the activity of an elements nucleus. See example 9. Radioactive Dating If an object contains radioactive nuclei when it is formed, then the decay of these nuclei marks the passage of time like a clock (half of the nuclei decay for each half life that passes). If the half life is known, a measurement of the ratio of the nuclei present today can be compared to the nuclei present today and give the age of the sample. The most accurate way of determining the number of radioactive nuclei present today would be to use a mass spectrometer. See example 10 for the dating of a living organism.
Radioactive Decay Series Page 5 of 17 When an unstable parent nucleus decays, the resulting daughter nucleus is sometimes also unstable. If so, the daughter nucleus then decays and produces another daughter nucleus. The sequential decay of one nucleus after another is called a radioactive decay series. The following equation is for uranium: As the graph representing the possible decay series of uranium indicates there are many possible branches for intermediate species. Ultimately, however, the series ends with lead ( ), which is stable. See the possible branches in the graph below:
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Name: Page 1 1683 of 17-1 - Page 1 Questions 1 through 4 refer to the following: The two equations below are nuclear equations: 7 4 30 Al + He ˆ P + X + energy 13 15 30 30 P ˆ Si + Y + energy 15 14 1) 7 The number of neutrons in the nucleus of Al is 13 A) 40 B) 7 C) 13 D) 14 ) In the second equation, particle Y is A) a neutron B) a positron C) an electron D) an alpha particle 3) In the first equation, particle X is A) a neutrino B) a positron C) a neutron D) an electron 30 4) Compared to the mass of the P, the sum of the masses of 15 30 Si + Y is 14 A) the same B) more C) less Questions 5 and 6 refer to the following: When nitrogen is bombarded with protons, the first reaction 14 1 15 that occurs is N + H ˆ O + X. The oxygen produced is 7 1 8 radioactive, with a half-life of 0.10 second, and decays in 15 15 the following manner: O ˆ N + Y. 8 7 5) In the first reaction, X represents A) an alpha particle C) a neutron B) a gamma photon D) a beta particle 6) In the second reaction, Y represents A) an electron C) a positron B) a proton D) a neutron Questions 7 and 8 refer to the following: The following represents a nuclear equation. 30 A 0 P ˆ Si + X 15 Z +1 7) What is the value of A in the equation? A) 8 C) 31 B) 30 D) 9 8) In the equation, X represents A) a gamma photon C) a positron B) a proton D) an electron 9) Which force between the protons in a helium atom will have the greatest magnitude? A) magnetic force C) nuclear force B) electrostatic force D) gravitational force 10) Approximately how much energy would be generated if the mass in a nucleus of a H atom were completely converted to energy? 1 [The mass of H is.0 atomic mass units.] 1 A) 9.3 x 10 MeV B) 1.9 x 10 3 MeV C) 1.5 x 10-10 J D) 3. x 10-19 J
11) Moderators are used to slow neutrons down in a nuclear reactor in order to A) achieve critical mass B) remove radioactive impurities in the core C) improve the probability of fission D) reduce nuclear reactions 1) The total number of neutrons in the nucleus of any atom is equal to the A) mass number of the atom B) mass number minus the atomic number C) atomic number minus the mass number D) atomic number of the atom Questions 13 through 15 refer to the following: The information below represents a nuclear reaction. 3 1 4 H + H ˆ He + energy 1 1 The masses of the nuclei are: 1 H = 1.00813 u (amu) 1 3 H = 3.01695 u (amu) 1 4 He = 4.00388 u (amu) 13) How much energy is released during the reaction? A) 0.01 MeV C) 19.7 MeV B) 30.0 x 10-19 MeV D).00 MeV 14) This reaction is an example of A) fission C) fusion B) alpha decay D) beta decay Page 13 1683 of 17-1 - Page 3 1 15) The symbols H and H represent 1 1 A) isotopes B) alpha particles C) electrons D) deuterium ions 16) Which equation represents nuclear fission? 6 4 A) Ra ˆ Rn + He 88 86 B) 9 4 1 1 Be + He ˆ C + n 4 6 0 C) 35 1 141 9 1 U + n ˆ Ba + Kr + 3 n + Q 9 0 56 36 0 D) 4 4 0 Na ˆ Mg + e 11 1-1 17) After the decay of a radioactive sample, helium gas was one of the products. This suggests that the nuclear disintegrations consisted of A) positron emissions C) alpha decays B) beta decays D) gamma emissions 18) Which equation is a step in the Uranium Disintegration Series? 34 30 4 A) Th ˆ Ra + He 90 88 34 34 0 B) Th ˆ Pa + e 90 91-1 34 6 0 C) Th ˆ Ac + e 90 89-1 34 6 4 D) Th ˆ Ra + He 90 88 19) 131 I initially decays by emission of beta particles. Beta 53 particles are A) electromagnetic waves C) electrons B) neutrons D) protons 0) The function of the moderator in a nuclear reactor is to A) produce extra neutrons B) speed up neutrons C) slow down neutrons D) absorb neutrons 14 1) Which is an isotope of X? 83 10 14 A) X C) X 8 8 14 B) X 84 10 D) X 83 38 ) In the Uranium Disintegration Series, when an atom of U 9 06 decays to Pb, the total number of beta particles emitted is 8 A) B) 14 C) 6 D) 8
3) Which isotope is used in defining the atomic mass unit? 1 A) C 6 16 B) O 8 1 C) H 1 38 D) U 9 44 4) Which is an isotope of Sc? 1 44 A) Ca 0 46 B) Sc 1 44 C) Ti 46 D) Ca 0 5) Which two symbols represent isotopes of the same element? 6 8 A) X and X 4 B) X and X 4 8 8 C) X and X 4 3 D) X and X 3 Questions 6 and 7 refer to the following: A pure sample of radon (Rn) gas is sealed inside a glass tube. The half-life of radon is 4 days. 6) The contents of the tube were analyzed after twenty days and another gas was found in addition to the radon. The new gas is most likely A) helium B) oxygen C) hydrogen D) nitrogen 7) If the pressure inside the tube were decreased to one-half, the half-life of the radon would be A) decreased to one-quarter B) unchanged C) decreased to one-half D) doubled 8) Which nucleus has the greatest nuclear charge? 4 7 8 A) Z B) Y C) X D) W 3 5 1 7 4 30 1 9) The equation Al + He ˆ P + n is an example of 13 15 0 A) beta decay C) natural transmutation B) alpha decay D) artificial transmutation 30) The splitting apart of a heavier nucleus to form lighter nuclei is called A) beta emission C) fusion B) positron emission D) fission 3) Given: Mass of a proton == 1.00777 amu Mass of a neutron == 1.008665 amu Mass of an electron == 0.0005486 amu 4 Mass of a He nucleus == 4.001509 amu 31) A certain radioactive isotope with a half-life of 5.0 minutes decays to a stable (nonradioactive) nucleus by emitting one alpha particle. The difference between the atomic number of the original nucleus and the atomic number of the new stable nucleus is A) 4 B) 3 C) 1 D) 4 What is the mass defect of a He nucleus? A) 0.0978 amu B) 1.985018 amu C) 1.985567 amu D) 0.030375 amu Questions 33 and 34 refer to the following: 38 An atom of U absorbs a neutron as indicated in the equation 9 38 1 U + n ˆ Y. 9 0 38 33) How many neutrons does U have in its nucleus? 9 A) 38 B) 37 C) 146 D) 147 Page 14 1683 of 17-1 - Page 3
34) The atomic number of the element Y is A) 91 B) 9 C) 89 D) 90 35) Which device is used to produce a stream of high-velocity charged particles? A) photographic plates B) cyclotron C) electroscope D) Geiger counter 36) Isotopes of the same element must have different A) mass numbers B) numbers of electrons C) atomic number D) numbers of protons 37) Which device is used to detect nuclear radiation? A) cyclotron C) cloud chamber B) linear accelerator D) synchrotron 8 38) The total number of nucleons in an atom of B is 5 A) 5 B) 13 C) 8 D) 3 39) When a nucleus captures an electron, the mass number of the nucleus A) increases B) decreases C) remains the same 40) A lithium nucleus contains three protons and four neutrons. What is its atomic mass number? A) 4 B) 3 C) 1 D) 7 41) Neutrons are used in some nuclear reactions as bombarding particles because they are A) uncharged and have negligible mass B) negatively charged and are attracted by the nucleus C) uncharged and are not repelled by the nucleus D) positively charged and are repelled by the nucleus 4) The diagram below represents an inverted test tube over a sample of a radioactive material. Helium has collected in the test tube. The presence of helium indicates that the sample is most probably undergoing the process of A) alpha decay C) beta decay B) gamma emission D) neutron decay 43) What kind of nuclear reaction is represented by the equation below? 14 4 17 1 N + He ˆ O + H 7 8 1 A) artificial transmutation B) nuclear fission C) alpha decay D) beta decay Page 15 1683 of 17-1 - Page 4 18 14 44) In the nuclear reaction Po ˆ Pb + X, the X represents 84 8 1 A) n 0 0 B) e +1 4 C) He 0 D) e -1
45) The fission process in a nuclear reactor is controlled by regulating the number of available A) positrons B) protons C) electrons D) neutrons 46) Which device is normally used to accelerate charged particles? A) electroscope B) Geiger counter C) cyclotron D) cloud chamber Page 1683 of 17-1 - Page 5 47) Which part of a nuclear reactor would most likely contain plutonium? A) control rod B) fuel rod 1 1 48) In the reaction Q + H ˆ H + n, Q represents the energy 1 1 0 needed to separate the neutrons from the deuterium nucleus. C) shielding D) moderator Given: Mass of deuterium H =.0141 amu 1 1 Mass of hydrogen H = 1.0078 amu 1 1 Mass of neutron n = 1.0087 amu 0 What is the value of Q? A) 4.0306 amu B).0165 amu C) 0.004 amu D) 0.0009 amu 49) 4 How many nucleons are in a He nucleus? A) 8 B) 6 C) 4 D) 50) Which device is used to accelerate a charged particle? A) a cloud chamber B) a cyclotron C) an electroscope D) a photographic plate 51) What is the energy equivalent of a mass of 1 kilogram? A) 9 x 10 7 J C) 9 x 10 16 J B) 9 x 10 10 J D) 9 x 10 13 J 5) Which graph best represents the relationship between energy and mass in the mass-energy equation? 38 53) An atom of U absorbs a neutron as indicated in the equation 9 38 1 U + n ˆ Y. 9 0 38 If the U atom decays before the neutron can be absorbed, 9 then according to the Uranium Disintegration Series, the 38 U atom will emit 9 A) a neutron B) an alpha particle C) a beta particle D) a positron A) B) C) D)
131 131 54) I initially decays by emission of beta particles. When I 53 53 decays by beta emission, it becomes 130 A) I 53 135 B) Xe 54 131 C) Xe 54 Page 17 1683 of 17-1 - Page 6 19 D) Sb 51 55) The function of a moderator in a nuclear reaction is to A) slow down neutrons B) absorb neutrons C) speed up neutrons D) produce more neutrons 56) If a certain radioactive isotope has a half-life of days, how much of a 64-kilogram sample of the isotope will remain after 10 days? A) 1 kg C) kg B) 4 kg D) 3 kg 57) Which equation represents a part of the Uranium Disintegration Series? 3 1 4 A) H + H ˆ He + energy 1 1 B) 30 14 4 Th ˆ Pb + x He 90 8 C) 35 1 90 140 1 U + n ˆ Sr + Xe + 6 n 9 0 38 54 0 D) 14 4 17 N + He ˆ O + y 7 8 58) How much energy is released when 1 x 10-3 kilogram of matter is converted to energy? A) 9 x 10 13 J C) 3 x 10 8 J B) 9 x 10 16 J D) 3 x 10 5 J 59) How many beta particles are given off when one atom of U-38 completely disintegrates to Pb-06? A) 8 C) 14 B) 6 D) 10 60) What is the force which holds the nucleons of an atom together? A) atomic force C) magnetic force B) nuclear force D) coulomb force 30 14 4 61) In the equation, Th ˆ Pb + x He, what is the number of 90 8 4 He particles represented by the coefficient x? A) 1 B) 3 C) 4 D) 4 4 6) In the reaction Na ˆ Mg + x, what does x represent? 11 1 A) an alpha particle B) a beta particle C) a positron D) a neutron 63) Which group of particles can all be accelerated by a cyclotron? A) neutrons, protons, and alpha particles B) electrons, neutrons, and protons C) alpha particles, electrons, and neutrons D) protons, alpha particles, and electrons 14 4 17 64) In the equation, N + He ˆ O + y, y represents 7 8 A) an alpha particle B) an electron C) a neutron D) a proton 65) What is the mass number of an atom with 9 protons, 11 neutrons, and 9 electrons? A) 9 B) 0 C) 18 D) 9