Identify the unknown nuclides and particles X and X9 in

In nuclear magnetic resonance, suppose we increase the value of the constant magnetic field. As a result, the frequency of the photons that are absorbed in a particular transition changes. How is the frequency of the photons absorbed related to the magnetic field? (a) The frequency is proportional to the square of the magnetic field. (b) The frequency is directly proportional to the magnetic field. (c) The frequency is independent of the magnetic field. (d) The frequency is inversely proportional to the magnetic field. (e) The frequency is proportional to the reciprocal of the square of the magnetic field.

When the 95 36Kr nucleus undergoes beta decay by emitting an electron and an antineutrino, does the daughter nucleus (Rb) contain (a) 58 neutrons and 37 protons, (b) 58 protons and 37 neutrons, (c) 54 neutrons and 41 protons, or (d) 55 neutrons and 40 protons?

When 32 15P decays to 32 16S, which of the following particles is emitted? (a) a proton (b) an alpha particle (c) an electron (d) a gamma ray (e) an antineutrino

The half-life of radium-224 is about 3.6 days. What approximate fraction of a sample remains undecayed after two weeks? (a) 1 2 (b) 1 4 (c) 1 8 (d) 1 16 (e) 1 32

Two samples of the same radioactive nuclide are prepared. Sample G has twice the initial activity of sample H. (i) How does the half-life of G compare with the half-life of H? (a) It is two times larger. (b) It is the same. (c) It is half as large. (ii) After each has passed through five half-lives, how do their activities compare? (a) G has more than twice the activity of H. (b) G has twice the activity of H. (c) G and H have the same activity. (d) G has lower activity than H.

If a radioactive nuclide A Z X decays by emitting a gamma ray, what happens? (a) The resulting nuclide has a different Z value. (b) The resulting nuclide has the same A and Z values. (c) The resulting nuclide has a different A value. (d) Both A and Z decrease by one. (e) None of those statements is correct.

Does a nucleus designated as 40 18X contain (a) 20 neutrons and 20 protons, (b) 22 protons and 18 neutrons, (c) 18 protons and 22 neutrons, (d) 18 protons and 40 neutrons, or (e) 40 protons and 18 neutrons?

When 144 60Nd decays to 140 58Ce, identify the particle that is released. (a) a proton (b) an alpha particle (c) an electron (d) a neutron (e) a neutrino

What is the Q value for the reaction 9Be 1 a S 12C 1 n? (a) 8.4 MeV (b) 7.3 MeV (c) 6.2 MeV (d) 5.7 MeV (e) 4.2 MeV

(i) To predict the behavior of a nucleus in a fission reaction, which model would be more appropriate, (a) the liquid-drop model or (b) the shell model? (ii) Which model would be more successful in predicting the magnetic moment of a given nucleus? Choose from the same answers as in part (i). (iii) Which could better explain the gamma-ray spectrum of an excited nucleus? Choose from the same answers as in part (i).

A free neutron has a half-life of 614 s. It undergoes beta decay by emitting an electron. Can a free proton undergo a similar decay? (a) yes, the same decay (b) yes, but by emitting a positron (c) yes, but with a very different half-life (d) no

Which of the following quantities represents the reaction energy of a nuclear reaction? (a) (final mass 2 initial mass)/c 2 (b) (initial mass 2 final mass)/c 2 (c) (final mass 2 initial mass)c 2 (d) (initial mass 2 final mass)c 2 (e) none of those quantities

In the decay 234 90Th S A ZRa 1 4 2He, identify the mass number and the atomic number of the Ra nucleus: (a) A 5 230, Z 5 92 (b) A 5 238, Z 5 88 (c) A 5 230, Z 5 88 (d) A 5 234, Z 5 88 (e) A 5 238, Z 5 86

Can a nucleus emit alpha particles that have different energies? Explain

In Rutherfords experiment, assume an alpha particle is headed directly toward the nucleus of an atom. Why doesnt the alpha particle make physical contact with the nucleus?

Suppose it could be shown that the cosmic-ray intensity at the Earths surface was much greater 10 000 years ago. How would this difference affect what we accept as valid carbon-dated values of the age of ancient samples of once-living matter? Explain your answer.

Compare and contrast the properties of a photon and a neutrino.

The peak of the graph of nuclear binding energy per nucleon occurs near 56Fe, which is why iron is prominent in the spectrum of the Sun and stars. Show that 56Fe has a higher binding energy per nucleon than its neighbors 55Mn and 59Co.

Nuclei having the same mass numbers are called isobars. The isotope 139 57La is stable. A radioactive isobar, 139 59Pr, is located below the line of stable nuclei as shown in Figure P44.19 and decays by e1 emission. Another radioactive isobar of 139 57La, 139 55Cs, decays by e2 emission and is located above the line of stable nuclei in Figure P44.19. (a)Which of these three isobars has the highest neutron-to-proton ratio? (b) Which has the greatest binding energy per nucleon? (c) Which do you expect to be heavier, 139 59Pr or 139 55Cs?

The energy required to construct a uniformly charged sphere of total charge Q and radius R is U 5 3keQ 2/5R, where ke is the Coulomb constant (see Problem 77). Assume a 40Ca nucleus contains 20 protons uniformly distributed in a spherical volume. (a) How much energy is required to counter their electrical repulsion according to the above equation? (b) Calculate the binding energy of 40Ca. (c) Explain what you can conclude from comparing the result of part (b) with that of part (a).

Calculate the minimum energy required to remove a neutron from the 43 20Ca nucleus.

Using the graph in Figure 44.5, estimate how much energy is released when a nucleus of mass number 200 fissions into two nuclei each of mass number 100.

(a) Use the semiempirical binding-energy formula (Eq. 44.3) to compute the binding energy for 56 26Fe. (b) What percentage is contributed to the binding energy by each of the four terms?

(a) In the liquid-drop model of nuclear structure, why does the surface-effect term 2C2A2/3 have a negative sign? (b) What If? The binding energy of the nucleus increases as the volume-to-surface area ratio increases. Calculate this ratio for both spherical and cubical shapes and explain which is more plausible for nuclei.

What time interval is required for the activity of a sample of the radioactive isotope 72 33As to decrease by 90.0% from its original value? The half-life of 72 33As is 26 h.

A freshly prepared sample of a certain radioactive isotope has an activity of 10.0 mCi. After 4.00 h, its activity is 8.00 mCi. Find (a) the decay constant and (b) the half-life. (c) How many atoms of the isotope were contained in the freshly prepared sample? (d) What is the samples activity 30.0 h after it is prepared?

A sample of radioactive material contains 1.00 3 1015 atoms and has an activity of 6.00 3 1011 Bq. What is its half-life?

From the equation expressing the law of radioactive decay, derive the following useful expressions for the decay constant and the half-life, in terms of the time interval Dt during which the decay rate decreases from R0 to R: l 5 1 Dt ln a R0 R b T1/2 5 1ln 22 Dt ln 1R 0/R2

The radioactive isotope 198Au has a half-life of 64.8 h. A sample containing this isotope has an initial activity (t 5 0) of 40.0 mCi. Calculate the number of nuclei that decay in the time interval between t1 5 10.0 h and t 2 5 12.0 h.

A radioactive nucleus has half-life T1/2. A sample containing these nuclei has initial activity R0 at t 5 0. Calculate the number of nuclei that decay during the interval between the later times t1 and t 2.

The half-life of 131I is 8.04 days. (a) Calculate the decay constant for this nuclide. (b) Find the number of 131I nuclei necessary to produce a sample with an activity of 6.40 mCi. (c) A sample of 131I with this initial activity decays for 40.2 d. What is the activity at the end of that period?

Tritium has a half-life of 12.33 years. What fraction of the nuclei in a tritium sample will remain (a) after 5.00 yr? (b) After 10.0 yr? (c) After 123.3 yr? (d) According to Equation 44.6, an infinite amount of time is required for the entire sample to decay. Discuss whether that is realistic.

Consider a radioactive sample. Determine the ratio of the number of nuclei decaying during the first half of its half-life to the number of nuclei decaying during the second half of its half-life.

(a) The daughter nucleus formed in radioactive decay is often radioactive. Let N10 represent the number of parent nuclei at time t 5 0, N1(t) the number of parent nuclei at time t, and l1 the decay constant of the parent. Suppose the number of daughter nuclei at time t 5 0 is zero. Let N2(t) be the number of daughter nuclei at time t and let l2 be the decay constant of the daughter. Show that N2(t) satisfies the differential equation dN2 dt 5 l1N1 2 l2N2 (b) Verify by substitution that this differential equation has the solution N2 1t2 5 N10l1 l1 2 l2 1e 2l2t 2 e 2l1t 2 This equation is the law of successive radioactive decays. (c) 218Po decays into 214Pb with a half-life of 3.10 min, and 214Pb decays into 214Bi with a half-life of 26.8 min. On the same axes, plot graphs of N1(t) for 218Po and N2(t) for 214Pb. Let N10 5 1 000 nuclei and choose values of t from 0 to 36 min in 2-min intervals. (d) The curve for 214Pb obtained in part (c) at first rises to a maximum and then starts to decay. At what instant tm is the number of 214Pb nuclei a maximum? (e) By applying the condition for a maximum dN2/dt 5 0, derive a symbolic equation for tm in terms of l1 and l2. (f) Explain whether the value obtained in part (c) agrees with this equation.

Determine which decays can occur spontaneously. (a) 40 20Ca S e1 1 40 19K (b) 98 44Ru S 4 2He 1 94 42Mo (c) 144 60Nd S 4 2He 1 140 58Ce

A 3H nucleus beta decays into 3He by creating an electron and an antineutrino according to the reaction 3 1H S 3 2He 1 e2 1 n Determine the total energy released in this decay

The 14C isotope undergoes beta decay according to the process given by Equation 44.21. Find the Q value for this process.

Identify the unknown nuclide or particle (X). (a) X S 65 28Ni 1 g (b) 215 84Po S X 1 a (c) X S 55 26Fe 1 e1 1 n

Find the energy released in the alpha decay 238 92U S 234 90Th 1 4 2He

A sample consists of 1.00 3 106 radioactive nuclei with a half-life of 10.0 h. No other nuclei are present at time t 5 0. The stable daughter nuclei accumulate in the sample as time goes on. (a) Derive an equation giving the number of daughter nuclei Nd as a function of time. (b) Sketch or describe a graph of the number of daughter nuclei as a function of time. (c) What are the maximum and minimum numbers of daughter nuclei, and when do they occur? (d) What are the maximum and minimum rates of change in the number of daughter nuclei, and when do they occur?

The nucleus 15 8O decays by electron capture. The nuclear reaction is written 15 8O 1 e2 S 15 7N 1 n (a) Write the process going on for a single particle within the nucleus. (b) Disregarding the daughters recoil, determine the energy of the neutrino

A living specimen in equilibrium with the atmosphere contains one atom of 14C (half-life 5 5 730 yr) for every 7.70 3 1011 stable carbon atoms. An archeological sample of wood (cellulose, C12H22O11) contains 21.0 mg of carbon. When the sample is placed inside a shielded beta counter with 88.0% counting efficiency, 837 counts are accumulated in one week. We wish to find the age of the sample. (a) Find the number of carbon atoms in the sample. (b) Find the number of carbon-14 atoms in the sample. (c) Find the decay constant for carbon-14 in inverse seconds. (d) Find the initial number of decays per week just after the specimen died. (e) Find the corrected number of decays per week from the current sample. (f) From the answers to parts (d) and (e), find the time interval in years since the specimen died

Uranium is naturally present in rock and soil. At one step in its series of radioactive decays, 238U produces the chemically inert gas radon-222, with a half-life of 3.82 days. The radon seeps out of the ground to mix into the atmosphere, typically making open air radioactive with activity 0.3 pCi/L. In homes, 222Rn can be a serious pollutant, accumulating to reach much higher activities in enclosed spaces, sometimes reaching 4.00 pCi/L. If the radon radioactivity exceeds 4.00 pCi/L, the U.S. Environmental Protection Agency suggests taking action to reduce it such as by reducing infiltration of air from the ground. (a) Convert the activity 4.00 pCi/L to units of becquerels per cubic meter. (b) How many 222Rn atoms are in 1 m3 of air displaying this activity? (c) What fraction of the mass of the air does the radon constitute?

The most common isotope of radon is 222Rn, which has half-life 3.82 days. (a) What fraction of the nuclei that were on the Earth one week ago are now undecayed? (b) Of those that existed one year ago? (c) In view of these results, explain why radon remains a problem, contributing significantly to our background radiation exposure.

Enter the correct nuclide symbol in each open tan rectangle in Figure P44.45, which shows the sequences of decays in the natural radioactive series starting with the long-lived isotope uranium-235 and ending with the stable nucleus lead-207.

A rock sample contains traces of 238U, 235U, 232Th, 208Pb, 207Pb, and 206Pb. Analysis shows that the ratio of the amount of 238U to 206Pb is 1.164. (a) Assuming the rock originally contained no lead, determine the age of the rock. (b) What should be the ratios of 235U to 207Pb and of 232Th to 208Pb so that they would yield the same age for the rock? Ignore the minute amounts of the intermediate decay products in the decay chains. Note: This form of multiple dating gives reliable geological dates.

A beam of 6.61-MeV protons is incident on a target of 27 13Al. Those that collide produce the reaction p 1 27 13Al S 27 14Si 1 n Ignoring any recoil of the product nucleus, determine the kinetic energy of the emerging neutrons.

(a) One method of producing neutrons for experimental use is bombardment of light nuclei with alpha particles. In the method used by James Chadwick in 1932, alpha particles emitted by polonium are incident on beryllium nuclei: 4 2He 1 9 4Be S 12 6C 1 1 0n What is the Q value of this reaction? (b) Neutrons are also often produced by small-particle accelerators. In one design, deuterons accelerated in a Van de Graaff generator bombard other deuterium nuclei and cause the reaction 2 1H 1 2 1H S 3 2He 1 1 0n Calculate the Q value of the reaction. (c) Is the reaction in part (b) exothermic or endothermic?

Identify the unknown nuclides and particles X and X9 in the nuclear reactions (a) X 1 4 2He S 24 12Mg 1 1 0n, (b) 235 92U 1 1 0n S 90 38Sr 1 X 1 2(1 0n), and (c) 2(1 1H) S 2 1H 1 X 1 X9.

Natural gold has only one isotope, 197 79Au. If natural gold is irradiated by a flux of slow neutrons, electrons are emitted. (a) Write the reaction equation. (b) Calculate the maximum energy of the emitted electrons.

The following reactions are observed: 9 4Be 1 n S 10 4Be 1 g Q 5 6.812 MeV 9 4Be 1 g S 8 4Be 1 n Q 5 21.665 MeV Calculate the masses of 8Be and 10Be in unified mass units to four decimal places from these data.

Construct a diagram like that of Figure 44.19 for the cases when I equals (a) 5 2 and (b) 4.

The radio frequency at which a nucleus having a magnetic moment of magnitude m displays resonance absorption between spin states is called the Larmor frequency and is given by f 5 DE h 5 2mB h Calculate the Larmor frequency for (a) free neutrons in a magnetic field of 1.00 T, (b) free protons in a magnetic field of 1.00 T, and (c) free protons in the Earths magnetic field at a location where the magnitude of the field is 50.0 mT.

A wooden artifact is found in an ancient tomb. Its carbon-14 (14 6C) activity is measured to be 60.0% of that in a fresh sample of wood from the same region. Assuming the same amount of 14C was initially present in the artifact as is now contained in the fresh sample, determine the age of the artifact.

A 200.0-mCi sample of a radioactive isotope is purchased by a medical supply house. If the sample has a half-life of 14.0 days, how long will it be before its activity is reduced to 20.0 mCi?

Why is the following situation impossible? A 10B nucleus is struck by an incoming alpha particle. As a result, a proton and a 12C nucleus leave the site after the reaction.

(a) Find the radius of the 12 6C nucleus. (b) Find the force of repulsion between a proton at the surface of a 12 6C nucleus and the remaining five protons. (c) How much work (in MeV) has to be done to overcome this electric repulsion in transporting the last proton from a large distance up to the surface of the nucleus? (d) Repeat parts (a), (b), and (c) for 238 92U.

(a) Why is the beta decay p S n 1 e1 1 n forbidden for a free proton? (b) What If? Why is the same reaction possible if the proton is bound in a nucleus? For example, the following reaction occurs: 13 7N S 13 6C 1 e1 1 n (c) How much energy is released in the reaction given in part (b)?

Review. Consider the Bohr model of the hydrogen atom, with the electron in the ground state. The magnetic field at the nucleus produced by the orbiting electron has a value of 12.5 T. (See Problem 6 in Chapter 30.) The proton can have its magnetic moment aligned in either of two directions perpendicular to the plane of the electrons orbit. The interaction of the protons magnetic moment with the electrons magnetic field causes a difference in energy between the states with the two different orientations of the protons magnetic moment. Find that energy difference in electron volts.

Show that the 238U isotope cannot spontaneously emit a proton by analyzing the hypothetical process 238 92U S 237 91Pa 1 1 1H Note: The 237Pa isotope has a mass of 237.051 144 u

Review. (a) Is the mass of a hydrogen atom in its ground state larger or smaller than the sum of the masses of a proton and an electron? (b) What is the mass difference? (c) How large is the difference as a percentage of the total mass? (d) Is it large enough to affect the value of the atomic mass listed to six decimal places in Table 44.2?

Why is the following situation impossible? In an effort to study positronium, a scientist places 57Co and 14C in proximity. The 57Co nuclei decay by e1 emission, and the 14C nuclei decay by e2 emission. Some of the positrons and electrons from these decays combine to form sufficient amounts of positronium for the scientist to gather data.

A by-product of some fission reactors is the isotope 239 94Pu, an alpha emitter having a half-life of 24 120 yr: 239 94Pu S 235 92U 1 a Consider a sample of 1.00 kg of pure 239 94Pu at t 5 0. Calculate (a) the number of 239 94Pu nuclei present at t 5 0 and (b) the initial activity in the sample. (c) What If? For what time interval does the sample have to be stored if a safe activity level is 0.100 Bq?

After the sudden release of radioactivity from the Chernobyl nuclear reactor accident in 1986, the radioactivity of milk in Poland rose to 2 000 Bq/L due to iodine-131 present in the grass eaten by dairy cattle. Radioactive iodine, with half-life 8.04 days, is particularly hazardous because the thyroid gland concentrates iodine. The Chernobyl accident caused a measurable increase in thyroid cancers among children in Poland and many other Eastern European countries. (a) For comparison, find the activity of milk due to potassium. Assume 1.00 liter of milk contains 2.00 g of potassium, of which 0.011 7% is the isotope 40K with half-life 1.28 3 109 yr. (b) After what elapsed time would the activity due to iodine fall below that due to potassium?

A theory of nuclear astrophysics proposes that all the elements heavier than iron are formed in supernova explosions ending the lives of massive stars. Assume equal amounts of 235U and 238U were created at the time of the explosion and the present 235U/238U ratio on the Earth is 0.007 25. The half-lives of 235U and 238U are 0.704 3 109 yr and 4.47 3 109 yr, respectively. How long ago did the star(s) explode that released the elements that formed the Earth?

The activity of a radioactive sample was measured over 12 h, with the net count rates shown in the accompanying table. (a) Plot the logarithm of the counting rate as a function of time. (b) Determine the decay constant and half-life of the radioactive nuclei in the sample. (c) What counting rate would you expect for the sample at t 5 0? (d) Assuming the efficiency of the counting instrument is 10.0%, calculate the number of radioactive atoms in the sample at t 5 0. Time (h) Counting Rate (counts/min) 1.00 3 100 2.00 2 450 4.00 1 480 6.00 910 8.00 545 10.0 330 12.0 200

When, after a reaction or disturbance of any kind, a nucleus is left in an excited state, it can return to its normal (ground) state by emission of a gamma-ray photon (or several photons). This process is illustrated by Equation 44.25. The emitting nucleus must recoil to conserve both energy and momentum. (a) Show that the recoil energy of the nucleus is Er 5 1DE2 2 2Mc 2 where DE is the difference in energy between the excited and ground states of a nucleus of mass M. (b) Calculate the recoil energy of the 57Fe nucleus when it decays by gamma emission from the 14.4-keV excited state. For this calculation, take the mass to be 57 u. Suggestion: Assume hf ,, Mc 2.

In a piece of rock from the Moon, the 87Rb content is assayed to be 1.82 3 1010 atoms per gram of material and the 87Sr content is found to be 1.07 3 109 atoms per gram. The relevant decay relating these nuclides is 87Rb S 87Sr 1 e2 1 n. The half-life of the decay is 4.75 3 1010 yr. (a) Calculate the age of the rock. (b) What If? Could the material in the rock actually be much older? What assumption is implicit in using the radioactive dating method?

Free neutrons have a characteristic half-life of 10.4 min. What fraction of a group of free neutrons with kinetic energy 0.040 0 eV decays before traveling a distance of 10.0 km?

On July 4, 1054, a brilliant light appeared in the constellation Taurus the Bull. The supernova, which could be seen in daylight for some days, was recorded by Arab and Chinese astronomers. As it faded, it remained visible for years, dimming for a time with the 77.1-day halflife of the radioactive cobalt-56 that had been created in the explosion. (a) The remains of the star now form the Crab nebula (see the photograph opening Chapter 34). In it, the cobalt-56 has now decreased to what fraction of its original activity? (b) Suppose that an American, of the people called the Anasazi, made a charcoal drawing of the supernova. The carbon-14 in the charcoal has now decayed to what fraction of its original activity?

When a nucleus decays, it can leave the daughter nucleus in an excited state. The 93 43Tc nucleus (molar mass 92.910 2 g/mol) in the ground state decays by electron capture and e1 emission to energy levels of the daughter (molar mass 92.906 8 g/mol in the ground state) at 2.44 MeV, 2.03 MeV, 1.48 MeV, and 1.35 MeV. (a) Identify the daughter nuclide. (b) To which of the listed levels of the daughter are electron capture and e1 decay of 93 43Tc allowed?

The radioactive isotope 137Ba has a relatively short halflife and can be easily extracted from a solution containing its parent 137Cs. This barium isotope is commonly used in an undergraduate laboratory exercise for demonstrating the radioactive decay law. Undergraduate students using modest experimental equipment took the data presented in Figure P44.72. Determine the half-life for the decay of 137Ba using their data.

As part of his discovery of the neutron in 1932, James Chadwick determined the mass of the newly identified particle by firing a beam of fast neutrons, all having the same speed, at two different targets and measuring the maximum recoil speeds of the target nuclei. The maximum speeds arise when an elastic head-on collision occurs between a neutron and a stationary target nucleus. (a) Represent the masses and final speeds of the two target nuclei as m1, v1, m2, and v2 and assume Newtonian mechanics applies. Show that the neutron mass can be calculated from the equation mn 5 m1v1 2 m2v2 v2 2 v1 (b) Chadwick directed a beam of neutrons (produced from a nuclear reaction) on paraffin, which contains hydrogen. The maximum speed of the protons ejected was found to be 3.30 3 107 m/s. Because the velocity of the neutrons could not be determined directly, a second experiment was performed using neutrons from the same source and nitrogen nuclei as the target. The maximum recoil speed of the nitrogen nuclei was found to be 4.70 3 106 m/s. The masses of a proton and a nitrogen nucleus were taken as 1.00 u and 14.0 u, respectively. What was Chadwicks value for the neutron mass?

When the nuclear reaction represented by Equation 44.28 is endothermic, the reaction energy Q is negative. For the reaction to proceed, the incoming particle must have a minimum energy called the threshold energy, Eth. Some fraction of the energy of the incident particle is transferred to the compound nucleus to conserve momentum. Therefore, Eth must be greater than Q. (a) Show that Eth 5 2Q a1 1 Ma MX b (b) Calculate the threshold energy of the incident alpha particle in the reaction 4 2He 1 14 7N S 17 8O 1 1 1H

In an experiment on the transport of nutrients in a plants root structure, two radioactive nuclides X and Y are used. Initially, 2.50 times more nuclei of type X are present than of type Y. At a time 3.00 d later, there are 4.20 times more nuclei of type X than of type Y. Isotope Y has a half-life of 1.60 d. What is the half-life of isotope X?

In an experiment on the transport of nutrients in a plants root structure, two radioactive nuclides X and Y are used. Initially, the ratio of the number of nuclei of type X present to that of type Y is r1. After a time interval Dt, the ratio of the number of nuclei of type X present to that of type Y is r2. Isotope Y has a half-life of TY. What is the half-life of isotope X?

Review. Consider a model of the nucleus in which the positive charge (Ze) is uniformly distributed throughout a sphere of radius R. By integrating the energy density 1 2P0E2 over all space, show that the electric potential energy may be written. U 5 3Z 2 e 2 20pP0R 5 3keZ 2 e 2 5R Problem 72 in Chapter 25 derived the same result by a different method.

After determining that the Sun has existed for hundreds of millions of years, but before the discovery of nuclear physics, scientists could not explain why the Sun has continued to burn for such a long time interval. For example, if it were a coal fire, it would have burned up in about 3 000 yr. Assume the Sun, whose mass is equal to 1.99 3 1030 kg, originally consisted entirely of hydrogen and its total power output is 3.85 3 1026 W. (a) Assuming the energy-generating mechanism of the Sun is the fusion of hydrogen into helium via the net reaction 4(1 1H) 1 2(e2) S 4 2He 1 2n 1 g calculate the energy (in joules) given off by this reaction. (b) Take the mass of one hydrogen atom to be equal to 1.67 3 10227 kg. Determine how many hydrogen atoms constitute the Sun. (c) If the total power output remains constant, after what time interval will all the hydrogen be converted into helium, making the Sun die? (d) How does your answer to part (c) compare with current estimates of the expected life of the Sun, which are 4 billion to 7 billion years?