Mastering Physics Solutions Chapter 32 Nuclear Physics and Nuclear Radiation

Mastering Physics Solutions Chapter 32 Nuclear Physics and Nuclear Radiation

Mastering Physics Solutions

Chapter 32 Nuclear Physics and Nuclear Radiation Q.1CQ
Nucleus A and nucleus B have different numbers of protons and different numbers of neutrons. Explain how it is still possible for these nuclei to have equal radii.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.1P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.2CQ
When α particles are emitted in a nuclear decay, they have well-defined energies. In contrast, ß particles are found to be emitted with a range of energies. Explain this difference.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.2P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.3CQ
Is it possible for a form of heavy hydrogen to decay by emitting an α particle? Explain.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.3P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.4CQ
Which is more likely to expose film kept in a cardboard box, α particles or ß particles? Explain.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.4P
A certain chlorine nucleus has a radius of approximately 4.0 × 10−15 m. How many neutrons are in this nucleus?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.5CQ
It is not possible for a stable nucleusto contain more than one proton without also having at least one neutron. Explain why neutrons are necessary in a stable, multiparticle nucleus.
Solution:
No. It is not possible for a stable nucleus to have more than one proton and no neutrons.
If the nucleus has only protons, the nucleus would be unstable and blow apart because of the electrostatic repulsion between the protons.
If neutrons are present, they separate the protons, reducing the mutual repulsion between them. Also, the presence of neutrons adds a strong attractive nuclear force, enabling the nuclei to hold it together.

Chapter 32 Nuclear Physics and Nuclear Radiation Q.5P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.6CQ
Different isotopes of a given element have different masses, but they have the same chemical properties. Explain why chemical properties are unaffected by a change of isotope.
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Isotopes are elements with same atomic number but different mass numbers.That means the isotopes of an element have same number of protons and electrons but different number of neutrons. The electrons are responsible for chemical reactions.

Chapter 32 Nuclear Physics and Nuclear Radiation Q.6P
IP (a) What initial kinetic energy must an alpha particle bave if it is to approach a stationary gold nucleus to within a distance of 22.5 fm?
(b) If the initial speed of the alpha particle is reduced by a factor of 2,bywhat factor is the distance of closest approach changed? Explain.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.7CQ
(a) Give three examples of objects for winch carbon-14 dating would give useful results.
(b) Give three examples of objects for which carbon-14 dating would not be useful.
Solution:
(a) Carbon-14 dating is useful to date specimen’s upto about 45,000 years old.
It is useful for dating organic materials like human and animal remains like
bones, ivory tusks, burnt bones, also cloth, pottery, paper, hide etc.
(b) Carbon dating is not very useful for dating inorganic materials like rocks and organic materials like fossils which are a million years old, inorganic carbon in shell, etc.

Chapter 32 Nuclear Physics and Nuclear Radiation Q.7P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.8CQ
Explain why the large, stable nuclei in Figure 32-1 are found to lie above the N = Z line, ratherthan below the une.
Solution:
The nucleus that does not undergo radioactive decay is defined as the stable nuclei.
The elements above the N = Z line will have more neutrons than protons. These neutrons spread out the positive charge of the protons making the nuclei stable.
The nucleii below the N = Z line have more number of protons than the number of neutrons. These protons repel each other blowing the nucleus apart.
Therefore the elements above the N = Z line are said to be stable nuclei.

Chapter 32 Nuclear Physics and Nuclear Radiation Q.8P
Suppose a marble with a radius of 1.5 cm has the density of a nucLeus, as given in Example 32–2.
(a) What is the mass of this marble?
(b) How many of these marbles would be required to have a mass equal to the mass of Earth?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.9CQ
Suppose each of the following items is about 10,000 years old: a feather, a tooth, an obsidian arrowhead, a deer hide moccasin. Which of these items cannot be dated with carbon-14? Explain.
Solution:
Carbon dating is applicable only to matter which was once living (which has biological origin) and presumed to be in equilibrium with the atmosphere.
A feather, a tooth, a deer hide moccasin are all of biological origin. But obsidian is not of biological origin and so it cannot dated with carbon-14.

Chapter 32 Nuclear Physics and Nuclear Radiation Q.9P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.10CQ
Can carbon-14 dating give the age of fossil dinosaur skeletons? Explain.
Solution:
No. Carbon-14 dating is useful to date specimen’s upto about 45,000 years old. But dinosaurs are thousands of times too old to be dated by this technique.

Chapter 32 Nuclear Physics and Nuclear Radiation Q.10P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.11CQ
Two different samples contain the same radioactive isotope. Is it possible for these samples to have different activities? Explain.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.11P
IP Suppose a uraninm-236 nucleus undergoes fission by splitting into two smaller nuclei of equal size.
(a) Is the radius of each of the smaller nuclei one-half, more than one-half, or less than one-half the radius of the uranium-236 nucleus? Explain.
(b) Calculate the radius of the uranium-236 nucleus.
(c) Calculate the radii of the two smaller nuclei.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.12CQ
Two samples contain different radioactive isotopes. Is it possible for these samples to have the same activity? Explain.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.12P
A hypothetical nucleus weighs 11b.
(a) How many nucleons are in this nucleus?
(b) What is the radius of this nucleus?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.13CQ
Two different types of radiation deliver the same amount of energy to a sample of tissue. Does it follow that each of these types of radiation has the same RBE? Explain.
Solution:
No,
RBE is the acronym for relative biological effective ness. RBE is related to the extent of biological effect caused by a radiation RBE is not related to the amount of energy it gives. So the RBE of two different types of radiation giving same amount of energy are not equal.

Chapter 32 Nuclear Physics and Nuclear Radiation Q.13P
CE Predict/Explain Consider a nucleus that undergoes α decay.
(a) Is the radius of the resulting daughter nucleus greater than, less than, or equal to the radius of the original nucleus?
(b) Choose the test explanation from among the following:
I. The decay adds an alpha particle to the nucleus, causing its radius to increase.
II. When the nucleus undergoes decay it ejects two neutrons and two protons. This decreases the number of nucleons in the nucleus, and therefore its radius will decrease.
III. An α decay leaves the number of nucleons unchanged. As a result, the radius of the nucleus stays the same.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.14P
CE Predict/Explain Consider a nucleus that undergoes ß decay.
(a) Is the radius of the resulting daughter nucleus greater than, less than, or the same as that of the original nucleus?
(b) Choose the best explanation from among the following:
I. Capturing a ß particle will cause the radius of a nucleus to increase. Therefore, the daughter nucleus has the greater radius.
II. The original nucleus emits a ß particle, and anytime a particle is emitted from a nucleus the result is a smaller radius. Therefore, the radius of the daughter nucleus is less than the radius of the original nucleus,
III. When a nucleus emits a β particle a neutron is convened proton, but the number of nucleons is unchanged. As a result, the radius of the daughter nucleus is the same as that of the original nucleus.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.15P
CE Which of the three decay processes (α, ß or γ)results in a new element? Explain.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.16P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.17P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.18P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.19P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.20P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.21P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.22P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.23P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.24P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.25P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.26P
CE The half-life of carbon-14 is 5730 y.
(a) Is it possible for a particular nucleus in a sample of carbon-14 to decay after only 1 s has passed? Explain.
(b) Is it possible for a particular nucleus to decay after 10,000 y? Explain.
Solution:
Yes. The half-life of carbon-14 nucleus is 5,730 y. The half-life of the carbon-14 nucleus represents the average time required for half of a large number of nuclei to decay. A given nucleus in a sample of carbon-14 can decay after only 1 s, because it has a random nature of radioactive decay.
Yes. A given nucleus in a sample of carbon-14 can decay after 10,000 y has passed, because it has a random nature of radioactive decay.

Chapter 32 Nuclear Physics and Nuclear Radiation Q.27P
CE Suppose we were to discover that the ratio of carbon-14 to carbon-12 in the atmosphere was significantly smaller 10,000 yearsago than it is today. How would this affect the ages we have assigned to objects on the basis of carbon-14 dating? In particular, would the true age of an object be greater than or less than the age we had previously assigned to it? Explain.
Solution:
We use carbon 14 dating method to find the ages. If the ratio C – 14 to C – 12 is small 10,000 years ago, then initial amount of carbon – 14 might have been smaller. Then less time is needed for the decay state to reduce to its present value. The age of an object measured in this case will be less than the true age of the object.

Chapter 32 Nuclear Physics and Nuclear Radiation Q.28P
CE A radioactive sample is placed in a closed container. Two days later only one-quarter of the sample is still radioactive. What is the half-life of this sample?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.29P
Radon gas has a half-life of 3.82 d. What is the decay constant for radon?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.30P
A radioactive substance has a decay constant equal to 8.9 × 10−3 s−1. What is the half-life of this substance?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.31P
The number of radioactive nuclei in a particular sample decreases over a period of 18 d to one-sixteenth the original number. What is the half-life of these nuclei?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.32P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.33P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.34P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.35P
An archeologist on a dig finds a fragment of an ancient basket woven from grass. Later, it is determined that the carbon-14 content of the grass in the basket is 9.25% that of an equal carbon sample from present-day grass. What is the age of the basket?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.36P
The bones of a saber-toothed tiger are found to have an activity per gram of carbon that is 15.0% of what would be found in a similar live animal. How old are these bones?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.37P
Charcoal from an ancient fire pit is found to have a carbon-14 content that is only 17.5% that of an equivalent sample of carbon from a living tree. What is the age of the fire pit?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.38P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.39P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.40P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.41P
The atomic mass of gold-197 is 196.96654 u. How much energy is required to completely separate the nucleons in a gold-197 nucleus?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.42P
The atomic mass of lithrum-7 is 7.016003 u. How much energy is required to completely separate the nucleons in a lithium-7 nucleus?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.43P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.44P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.45P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.46P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.47P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.48P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.49P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.50P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.51P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.52P
Assuming a release of 173 MeV per fission reaction, calculate how many reactions must occur per second to produce a power output of 150 MW.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.53P
Consider a fusion reaction in which two deuterium nuclei fuse to form a tritium nucleus and a proton. Mow much energy is released in this reaction?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.54P
Consider a fusion reaction in which a proton fuses with a neutron to form a deuterium nucleus. How much energy is released in this reaction?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.55P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.56P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.57P
The Evaporating Sun The Sun radiates energy at the prodigious rate of 3.90 × 1026 W.
(a) At what rate, in kilograms per second, does the Sun convert mass into energy?
(b) Assuming that the Sun has radiated at this same rate for its entire lifetime of 4.50 × 109 y, and that the current mass of the Sun is 2.00 × 1030 kg, what percentage of its original mass has been converted to energy?.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.58P
BIO Radiation Damage A sample of tissue absorbs a 55-rad dose of α particles (RBE = 20).
How many rad of protons (RBB = 10) cause the same amount of damage to the tissue?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.59P
BIO X-ray Damage How many rad of 200-keV X-rays cause the same amount of biological damage as 50 rad of heavy ions?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.60P
IP BIO
(a) Find the energy absorbed by a 78-kg person who is exposed to 52 mrem of α particles with an “RBE of 15.
(b) If the RBE of the α particles is increased, does the energy absorbed increase, decrease, or stay the same? Explain.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.61P
BIO A patient undergoing radiation therapy for cancer receives a 225-rad dose of radiation.
(a) Assuming the cancerous growth has a mass of 0.17 kg, calculate how much energy it absorbs.
(b) Assuming the growth to have the specific heat of water, determine its increase in temperature.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.62P
BIO Alpha particles with an RBE of 13 deliver a 32-mrad whole-body radiation dose to a 72-kg patient.
(a) What dosage, in rem, does the patient receive?
(b) How much energy is absorbed by the patient?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.63P

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.64GP
CE An α particle (charge + 2e)and a ß particle (charge − e) deflect in opposite directions when they pass through a mag netic field. Which particle defLects by a greater amount, give: that both particles have the same speed? Explain.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.65GP
CE Radioactive samples A and B have equal half-lives. The initial activity of sample A is twice that of sample B. What is the ratio of the activity of sample A to that of sample B after two half-lives have elapsed?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.66GP
CE The initial activity of sample A is twice that of sample B After two half-lives of sample A have elapsed, the two samples have the same activity. What is the ratio of the half-life of B to the half-life of A?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.67GP

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.68GP

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.69GP

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.70GP
Suppose it is desired to give a cancerous tumor a dose of 3800 rem. How many rads are needed if the tumor is exposed to alpha radiation?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.71GP
A patient is exposed to 260 rad of gamma rays. What is the dose the patient receives in rem?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.72GP

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.73GP
Moon Rocks In one of the rocks brought back from the Moon, it is found that 80.5% of the initial potassium-40 in the rock has decayed to argon-40.
(a) If the half-life for this decay is 1.20 × 109 years, how old is the rock?
(b) How much longer will it take before only 10.0% of the original potassium-40 is still present in the rock?
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.74GP

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.75GP

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.76GP
An α particle fired head-on at a stationary nickel nucleus approaches to a radius of 15 fm
before being turned around.
(a) What is the maximum Coulomb force exerted on the α particle?
(b) What is the electric potential energy of the α particle at its point of closest approach?
(c) Find the initial kinetic energy of the α particle.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.77GP

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.78GP
IP Initially, a sample of radioactive nuclei of type A contains four times as many nuclei as a sample of radioactive nuclei of type B. Two days later (2.00 d) the two samples contain the same number of nuclei.
(a) Which type of nucleus has the longer half-life? Explain.
(b) Determine the half-life of type B nuclei if the half-life of type A nuclei is known to be 0.500 d.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.79GP
Stable nuclei have mass numbers that range from a minimum of 1 to a maximum of 209.
(a) Find the corresponding range in nuclear radii.
(b) Assuming all nuclei to be spherical, determine the ratio of the surface area of the largest stable nucleus to the surface area of the smallest nucleus.
(c) Repeat part (b), only this time find the ratio of the volumes.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.80GP
Radius of a Neutron Star Neutron stars are so named because they are composed of neutrons and have a density the same as that of a nucleus. Referring to Example 32–2 for the nuclear density, find the radius of a neutron star whose mass is 0.50 that of the Sun.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.81GP
A specimen taken from the wrappings of a mummy contains 7.82 g of carbon and has an activity of 1.38 Bq. How old is the mummy? (Refer to pages 1132 and 1133 for relevant information regarding the isotopes of carbon.)
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.82GP

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.83GP
IP Energy is released when three α particles fuse to form carbon-12.
(a) Is the mass of carbon-12 greater than, less than, or the same as the mass of three α particles? Explain.
(b) Calculate the energy given off in this fusion reaction.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.84GP
Find the dose of y rays that must be absorbed by a block of ice at 0 °C to convert it to water at 0 °C.-Givc the dosage inrad.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.85GP
IP
(a) What dosage (in rad) must a 1.0-kg sample of water absorb to increase its temperature by 1.0 C°?
(b) Tf the mass of the water sample is increased, does the dosage found in part (a) increase, decrease, or stay the same? Explain.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.86GP
BIO Chest X-rays A typical chest X-ray uses X-rays with an RBE of 0.85. If the radiation dosage is 35 mrem, find the energy absorbed by a 72-kg patient, assuming one-quarter of the patient’s body is exposed to the X-rays.
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.87GP

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.88GP

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.89GP

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Chapter 32 Nuclear Physics and Nuclear Radiation Q.90PP
What is the decay constant, A, for iodine-131?
A. 9.98 ×10−7 s−1
B. 1.44 × ×10−6 s−1
C. 2.39 ×10−5 s−1
D. 5.99 ×10−5 s−1
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.91PP
If a sample of iodine-131 contains 4.5 × 1016 nuclei, what is the activity of the sample?
Express your answer in curies.
A. 0.27 Ci
B. 1.2 Ci.
C. 1.7 Ci
D. 4.5 Ci
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Chapter 32 Nuclear Physics and Nuclear Radiation Q.92PP
If the half-life of iodine-131 were only half of its actual value, would the activity of the sample in Problem be increased or decreased?
Problem
If a sample of iodine-131 contains 4.5 × 1016 nuclei, what is the activity of the sample? Express your answer in curies.
A. 0.27 Ci
B. 1.2 Ci.
C. 1.7 Ci
D. 4.5 Ci
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