Solved: There are four stable isotopes of iron with mass

When nuclei undergo nuclear transformations, rays of characteristic frequencies are observed. How does this fact, along with other information in the chapter on nuclear stability, suggest that a quantum mechanical model may apply to the nucleus?

There is a trend in the United States toward using coal-fired power plants to generate electricity rather than building new nuclear fission power plants. Is the use of coal-fired power plants without risk? Make a list of the risks to society from the use of each type of power plant.

Which type of radioactive decay has the net effect of changing a neutron into a proton? Which type of decay has the net effect of turning a proton into a neutron?

What is annihilation in terms of nuclear processes?

What are transuranium elements and how are they synthesized?

Scientists have estimated that the earths crust was formed 4.3 billion years ago. The radioactive nuclide 176Lu, which decays to 176Hf, was used to estimate this age. The half-life of 176Lu is 37 billion years. How are ratios of 176Lu to 176Hf utilized to date very old rocks?

Why are the observed energy changes for nuclear processes so much larger than the energy changes for chemical and physical processes?

Natural uranium is mostly nonfissionable 238U; it contains only about 0.7% of fissionable 235U. For uranium to be useful as a nuclear fuel, the relative amount of 235U must be increased to about 3%. This is accomplished through a gas diffusion process. In the diffusion process, natural uranium reacts with fluorine to form a mixture of 238UF6(g) and 235UF6(g). The fluoride mixture is then enriched through a multistage diffusion process to produce a 3% 235U nuclear fuel. The diffusion process utilizes Grahams law of effusion (see Chapter 5, Section 5.7). Explain how Grahams law of effusion allows natural uranium to be enriched by the gaseous diffusion process.

Strontium-90 and radon-222 both pose serious health risks. 90Sr decays by _-particle production and has a relatively long half-life (28.8 yr). Radon-222 decays by alpha-particle production and has a relatively short half-life (3.82 days). Explain why each decay process poses health risks.

A recent study concluded that any amount of radiation exposure can cause biological damage. Explain the differences between the two models of radiation damage, the linear model and the threshold model.

Write balanced equations for each of the processes described below. a. Chromium-51, which targets the spleen and is used as a tracer in studies of red blood cells, decays by electron capture. g b. Iodine-131, used to treat hyperactive thyroid glands, decays by producing a particle.

Write balanced equations for each of the processes described below. a. Phosphorus-32, which accumulates in the liver, decays by -particle production. b. Uranium-235, which is used in atomic bombs, decays initially by -particle production.

Write an equation describing the radioactive decay of each of the following nuclides. (The particle produced is shown in parentheses, except for electron capture, where an electron is a reactant.) a. 68Ga (electron capture) c. 212Fr (_) b. 62Cu (positron) d. 129Sb (_)

In each of the following nuclear reactions, supply the missing particle. a. 73Ga S 73Ge _ ? c. 205Bi S 205Pb _ ? b. 192Pt S 188Os _ ? d. 241Cm _ ? S 241Am

The radioactive isotope 247Bk decays by a series of -particle and -particle productions, taking 247Bk through many transformations to end up as 207Pb. In the complete decay series, how many _ particles and particles are produced?

One type of commercial smoke detector contains a minute amount of radioactive americium-241 (241Am), which decays by -particle production. The _ particles ionize molecules in the air, allowing it to conduct an electric current. When smoke particles enter, the conductivity of the air is changed and the alarm buzzes. a. Write the equation for the decay of 241 95Am by _-particle production. b. The complete decay of 241Am involves successively _, _, _, _, _, _, _, _, _, _, _, and _ production. What is the final stable nucleus produced in this decay series? c. Identify the 11 intermediate nuclides.

There are four stable isotopes of iron with mass numbers 54, 56, 57, and 58. There are also two radioactive isotopes: iron-53 and iron- 59. Predict modes of decay for these two isotopes. (See Table 18.2.)

The only stable isotope of fluorine is fluorine-19. Predict possible modes of decay for fluorine-21, fluorine-18, and fluorine-17.

In 1994 it was proposed (and eventually accepted) that element 106 be named seaborgium, Sg, in honor of Glenn T. Seaborg, discoverer of the transuranium elements. a. 263Sg was produced by the bombardment of 249Cf with a beam of 18O nuclei. Complete and balance an equation for this reaction. b. 263Sg decays by _ emission. What is the other product resulting from the _ decay of 263Sg?

Many elements have been synthesized by bombarding relatively heavy atoms with high-energy particles in particle accelerators. Complete the following nuclear reactions, which have been used to synthesize elements. a. ________ _ 4 2He S 243 97Bk _ 1 0n b. 238 92U _ 12 6C S ________ _ 6 1 0n c. 249 98Cf _ ________ S 260 105Db _ 4 10 n d. 249 98Cf _ 10 5B S 257 103Lr _ ________

The rate constant for a certain radioactive nuclide is 1.0 _ What is the half-life of this nuclide?

Americium-241 is widely used in smoke detectors. The radiation released by this element ionizes particles that are then detected by a charged-particle collector. The half-life of 241Am is 432.2 years, and it decays by emitting alpha particles. How many alpha particles are emitted each second by a 5.00-g sample of 241Am?

Krypton consists of several radioactive isotopes, some of which are listed in the following table. Which of these isotopes is most stable and which isotope is hottest? How long does it take for 87.5% of each isotope to decay?

Radioactive copper-64 decays with a half-life of 12.8 days. a. What is the value of k in b. A sample contains 28.0 mg 64Cu. How many decay events will be produced in the first second? Assume the atomic mass of 64Cu is 64.0. c. A chemist obtains a fresh sample of 64Cu and measures its radioactivity. She then determines that to do an experiment, the radioactivity cannot fall below 25% of the initial measured value. How long does she have to do the experiment?

Phosphorus-32 is a commonly used radioactive nuclide in biochemical research, particularly in studies of nucleic acids. The half-life of phosphorus-32 is 14.3 days. What mass of phosphorus- 32 is left from an original sample of 175 mg of Na3 32PO4 after 35.0 days? Assume the atomic mass of 32P is 32.0.

The curie (Ci) is a commonly used unit for measuring nuclear radioactivity: 1 curie of radiation is equal to decay events per second (the number of decay events from 1 g of radium in 1 s). a. What mass of Na2 38SO4 has an activity of 10.0 mCi? Sulfur- 38 has an atomic mass of 38.0 and a half-life of 2.87 h. b. How long does it take for 99.99% of a sample of sulfur-38 to decay?

The first atomic explosion was detonated in the desert north of Alamogordo, New Mexico, on July 16, 1945. What fraction of the strontium-90 ( years) originally produced by that explosion still remains as of July 16, 2006?

Iodine-131 is used in the diagnosis and treatment of thyroid disease and has a half-life of 8.1 days. If a patient with thyroid disease consumes a sample of Na131I containing 10 of 131I, how long will it take for the amount of 131I to decrease to of the original amount?

The Br-82 nucleus has a half-life of min. If you wanted 1.0 g of Br-82 and the delivery time was 3.0 days, what mass of NaBr should you order (assuming all of the Br in the NaBr was Br-82)?

Fresh rainwater or surface water contains enough tritium ( ) to show 5.5 decay events per minute per 100. g of water. Tritium has a half-life of 12.3 years. You are asked to check a vintage wine that is claimed to have been produced in 1946. How many decay events per minute should you expect to observe in 100. g of that wine?

A living plant contains approximately the same fraction of carbon- 14 as in atmospheric carbon dioxide. Assuming that the observed rate of decay of carbon-14 from a living plant is 13.6 counts per minute per gram of carbon, how many counts per minute per gram of carbon will be measured from a 15,000-year-old sample? Will radiocarbon dating work well for small samples of 10 mg or less? (For14C, years.)

Assume a constant ratio of 13.6 counts per minute per gram of living matter. A sample of a petrified tree was found to give 1.2 counts per minute per gram. How old is the tree?

A rock contains 0.688 mg of 206Pb for every 1.000 mg of 238U present. Assuming that no lead was originally present, that all the 206Pb formed over the years has remained in the rock, and that the number of nuclides in intermediate stages of decay between 238U and 206Pb is negligible, calculate the age of the rock. (For 238U, years.)

The mass ratios of 40Ar to 40K also can be used to date geologic materials. Potassium-40 decays by two processes: 4 1 09 K _ _ 0 1e 88n 4 1 0 8Ar (10.7%) t1_2 _ 1.27 _ 109 years 4 1 09 K 88n 4 2 0 0Ca _ _ 0 1e (89.3%) a. Why are 40Ar_40K ratios used to date materials rather than 40Ca_40K ratios? b. What assumptions must be made using this technique? c. A sedimentary rock has an 40Ar_40K ratio of 0.95. Calculate the age of the rock. d. How will the measured age of a rock compare to the actual age if some 40Ar escaped from the sample?

The sun radiates J of energy into space every second. What is the rate at which mass is lost from the sun?

The earth receives kJ/s of solar energy. What mass of solar material is converted to energy over a 24-h period to provide the daily amount of solar energy to the earth? What mass of coal would have to be burned to provide the same amount of energy? (Coal releases 32 kJ of energy per gram when burned.)

Many transuranium elements, such as plutonium-232, have very short half-lives. (For 232Pu, the half-life is 36 minutes.) However, some, like protactinium-231 have relatively long half-lives. Use the masses given in the following table to calculate the change in energy when 1 mol of 232Pu nuclei and 1 mol of 231Pa nuclei are each formed from their respective number of protons and neutrons. (Since the masses of 232Pu and 231Pa are atomic masses, they each include the mass of the electrons present. The mass of the nucleus will be the atomic mass minus the mass of the electrons.)

The most stable nucleus in terms of binding energy per nucleon is 56Fe. If the atomic mass of 56Fe is 55.9349 amu, calculate the binding energy per nucleon for 56Fe.

Calculate the binding energy in J/nucleon for carbon-12 (atomic mass 12.0000) and uranium-235 (atomic mass 235.0439). The atomic mass of 11 H is 1.00782 amu and the mass of a neutron is 1.00866 amu. The most stable nucleus known is 56Fe (see Exercise 38). Would the binding energy per nucleon for 56Fe be larger or smaller than that of 12C or 235U? Explain.

Calculate the binding energy per nucleon for 21 H and 3 1H. The atomic masses are 2 1H, 2.01410, and 3 1H, 3.01605.

The mass defect for a Li-6 nucleus is g/mol. Calculate the atomic mass of Li-6.

The binding energy per nucleon for Mg-27 is J/nucleon. Calculate the atomic mass of Mg-27.

Calculate the amount of energy released per gram of hydrogen nuclei reacted for the following reaction. The atomic masses are 1 1H, 1.00782 amu, 2 1H, 2.01410 amu, and an electron, amu. (Hint: Think carefully about how to account for the electron mass.)

The easiest fusion reaction to initiate is Calculate the energy released per 42 He nucleus produced and per mole of 42 He produced. The atomic masses are 21 H, 2.01410; 31 H, 3.01605; and 42 He, 4.00260. The masses of the electron and neutron are and 1.00866 amu, respectively.

The typical response of a GeigerMller tube is shown below. Explain the shape of this curve.

When using a GeigerMller counter to measure radioactivity, it is necessary to maintain the same geometrical orientation between the sample and the GeigerMller tube to compare different measurements. Why?

Photosynthesis in plants can be represented by the following overall reaction: Algae grown in water containing some 18O (in H2 18O) evolve oxygen gas with the same isotopic composition as the oxygen in the water. When algae growing in water containing only 16O were furnished carbon dioxide containing 18O, no 18O was found to be evolved from the oxygen gas produced. What conclusions about photosynthesis can be drawn from these experiments?

Consider the following reaction to produce methyl acetate: Methyl acetate When this reaction is carried out with CH3OH containing oxygen- 18, the water produced does not contain oxygen-18. Explain.

U-235 undergoes many different fission reactions. For one such reaction, when U-235 is struck with a neutron, Ce-144 and Sr-90 are produced along with some neutrons and electrons. How many neutrons and _-particles are produced in this fission reaction?

Breeder reactors are used to convert the nonfissionable nuclide to a fissionable product. Neutron capture of the is followed by two successive beta decays. What is the final fissionable product?

Which do you think would be the greater health hazard: the release of a radioactive nuclide of Sr or a radioactive nuclide of Xe into the environment? Assume the amount of radioactivity is the same in each case. Explain your answer on the basis of the chemical properties of Sr and Xe. Why are the chemical properties of a radioactive substance important in assessing its potential health hazards?

Consider the following information: i. The layer of dead skin on our bodies is sufficient to protect us from most _-particle radiation. ii. Plutonium is an _-particle producer. iii. The chemistry of Pu4_ is similar to that of Fe3_. iv. Pu oxidizes readily to Pu4_. Why is plutonium one of the most toxic substances known?

Predict whether each of the following nuclides is stable or unstable (radioactive). If the nuclide is unstable, predict the type of radioactivity you would expect it to exhibit. a. 45 19K b. 56 26Fe c. 20 11Na d. 194 81Tl

At a flea market, youve found a very interesting painting done in the style of Rembrandts dark period (16421672). You suspect that you really do not have a genuine Rembrandt, but you take it to the local university for testing. Living wood shows a carbon-14 activity of 15.3 counts per minute per gram. Your painting showed a carbon-14 activity of 15.1 counts per minute per gram. Could it be a genuine Rembrandt?

Define third-life in a similar way to half-life and determine the third-life for a nuclide that has a half-life of 31.4 years.

A proposed system for storing nuclear wastes involves storing the radioactive material in caves or deep mine shafts. One of the most toxic nuclides that must be disposed of is plutonium-239, which is produced in breeder reactors and has a half-life of 24,100 years. A suitable storage place must be geologically stable long enough for the activity of plutonium-239 to decrease to 0.1% of its original value. How long is this for plutonium-239?

During World War II, tritium (3H) was a component of fluorescent watch dials and hands. Assume you have such a watch that was made in January 1944. If 17% or more of the original tritium was needed to read the dial in dark places, until what year could you read the time at night? (For 3H, yr.)

A positron and an electron can annihilate each other on colliding, producing energy as photons: Assuming that both rays have the same energy, calculate the wavelength of the electromagnetic radiation produced.

A small atomic bomb releases energy equivalent to the detonation of 20,000 tons of TNT; a ton of TNT releases J of energy when exploded. Using J/mol as the energy released by fission of 235U, approximately what mass of 235U undergoes fission in this atomic bomb?

During the research that led to production of the two atomic bombs used against Japan in World War II, different mechanisms for obtaining a supercritical mass of fissionable material were investigated. In one type of bomb, a gun shot one piece of fissionable material into a cavity containing another piece of fissionable material. In the second type of bomb, the fissionable material was surrounded with a high explosive that, when detonated, compressed the fissionable material into a smaller volume. Discuss what is meant by critical mass, and explain why the ability to achieve a critical mass is essential to sustaining a nuclear reaction.

Using the kinetic molecular theory (Section 5.6), calculate the root mean square velocity and the average kinetic energy of nuclei at a temperature of K. (See Exercise 44 for the appropriate mass values.)

A 0.20-mL sample of a solution containing that produces cps is injected into the bloodstream of an animal. After allowing circulatory equilibrium to be established, a 0.20-mL sample of blood is found to have an activity of 20. cps. Calculate the blood volume of the animal.

A 0.10-cm3 sample of a solution containing a radioactive nuclide ( counts per minute per milliliter) is injected into a rat. Several minutes later 1.0 cm3 of blood is removed. The blood shows 48 counts per minute of radioactivity. Calculate the volume of blood in the rat. What assumptions must be made in performing this calculation?

Zirconium is one of the few metals that retains its structural integrity upon exposure to radiation. The fuel rods in most nuclear reactors therefore are often made of zirconium. Answer the following questions about the redox properties of zirconium based on the half-reaction a. Is zirconium metal capable of reducing water to form hydrogen gas at standard conditions? b. Write a balanced equation for the reduction of water by zirconium. c. Calculate e, _G, and K for the reduction of water by zirconium metal. d. The reduction of water by zirconium occurred during the accidents at Three Mile Island in 1979. The hydrogen produced was successfully vented and no chemical explosion occurred. If 1.00 _ 103 kg of Zr reacts, what mass of H2 is produced? What volume of H2 at 1.0 atm and 1000.C is produced? e. At Chernobyl in 1986, hydrogen was produced by the reaction of superheated steam with the graphite reactor core: It was not possible to prevent a chemical explosion at Chernobyl. In light of this, do you think it was a correct decision to vent the hydrogen and other radioactive gases into the atmosphere at Three Mile Island? Explain.

In addition to the process described in the text, a second process called the carbonnitrogen cycle occurs in the sun: Overall reaction: a. What is the catalyst in this process? b. What nucleons are intermediates? c. How much energy is released per mole of hydrogen nuclei in the overall reaction? (The atomic masses of 11 H and 4 2He are 1.00782 and 4.00260, respectively.)

The most significant source of natural radiation is radon-222. 222Rn, a decay product of 238U, is continuously generated in the earths crust, allowing gaseous Rn to seep into the basements of buildings. Because 222Rn is an -particle producer with a relatively short half-life of 3.82 days, it can cause biological damage when inhaled. a. How many particles and particles are produced when 238U decays to 222Rn? What nuclei are produced when 222Rn decays? b. Radon is a noble gas so one would expect it to pass through the body quickly. Why is there a concern over inhaling 222Rn? c. Another problem associated with 222Rn is that the decay of 222Rn produces a more potent -particle producer ( 3.11min) that is a solid. What is the identity of the solid? Give the balanced equation of this species decaying by -particle production. Why is the solid a more potent a-particle producer? d. The U.S. Environmental Protection Agency (EPA) recommends that 222Rn levels not exceed 4 pCi per liter of air ( decay events per second; 1 pCi _ ). Convert 4.0 pCi per liter of air into concentrations units of 222Rn atoms per liter of air and moles of 222Rn per liter of air.

To determine the Ksp value of Hg2I2, a chemist obtained a solid sample of Hg2I2 in which some of the iodine is present as radioactive 131I. The count rate of the Hg2I2 sample is counts per minute per mole of I. An excess amount of Hg2I2(s) is placed into some water, and the solid is allowed to come to equilibrium with its respective ions. A 150.0-mL sample of the saturated solution is withdrawn and the radioactivity measured at 33 counts per minute. From this information, calculate the Ksp value for Hg2I2.

Estimate the temperature needed to achieve the fusion of deuterium to make an alpha particle. The energy required can be estimated from Coulombs law [use the form (Q1Q2 r), using C for a proton, and m for the helium nucleus; the unit for the proportionality constant in Coloumbs law is ]

A recently reported synthesis of the transuranium element bohrium (Bh) involved the bombardment of berkelium-249 with neon-22 to produce bohrium-267. Write a nuclear reaction for this synthesis. The half-life of bohrium-267 is 15.0 seconds. If 199 atoms of bohrium-267 could be synthesized, how much time would elapse before only 11 atoms of bohrium-267 remain? What is the expected electron configuration of elemental bohrium?

Radioactive cobalt-60 is used to study defects in vitamin B12 absorption because cobalt is the metallic atom at the center of the vitamin B12 molecule. The nuclear synthesis of this cobalt isotope involves a three-step process. The overall reaction is iron-58 reacting with two neutrons to produce cobalt-60 along with the emission of another particle. What particle is emitted in this nuclear synthesis? What is the binding energy in J per nucleon for the cobalt-60 nucleus (atomic masses: ). What is the de Broglie wavelength of the emitted particle if it has a velocity equal to 0.90c where c is the speed of light?