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physics
college physics 2nd

College Physics 2nd Edition OpenStax - Solutions

(a) What is the kinetic energy in MeV of a β ray that is traveling at 0.998c? This gives some idea of how energetic a β ray must be to travel at nearly the same speed as a γ ray.(b) What is the velocity of the y ray relative to the β ray?
β- decay of 3H (tritium), a manufactured isotope of hydrogen used in some digital watch displays, and manufactured primarily for use in hydrogen bombs.
What do the three types of beta decay have in common that is distinctly different from alpha decay?
β- decay of 40K, a naturally occurring rare isotope of potassium responsible for some of our exposure to background radiation.
In a 3 x 109 -year-old rock that originally contained some 238U, which has a half-life of 4.5 x 109 years, we expect to find some 238U remaining in it. Why are 226Ra, 222Rn, and 210Po also found in such a rock, even though they have much shorter half-lives (1600 years, 3.8 days, and 138 days,
Does the number of radioactive nuclei in a sample decrease to exactly half its original value in one half-life? Explain in terms of the statistical nature of radioactive decay.
Radioactivity depends on the nucleus and not the atom or its chemical state. Why, then, is one kilogram of uranium more radioactive than one kilogram of uranium hexafluoride?
Explain how a bound system can have less mass than its components. Why is this not observed classically, say for a building made of bricks?
Spontaneous radioactive decay occurs only when the decay products have less mass than the parent, and it tends to produce a daughter that is more stable than the parent. Explain how this is related to the fact that more tightly bound nuclei are more stable.
To obtain the most precise value of BE from the equation , we should take into account the binding energy of the electrons in the neutral atoms. Will doing this produce a larger or smaller value for BE? Why is this effect usually negligible? BE=[ZM (¹H)+Nmn]c² - m(^X)c²,
β- decay producing 90Y. The parent nuclide is a major waste product of reactors and has chemistry similar to calcium, so that it is concentrated in bones if ingested (90Y is also radioactive.)
α decay of 226Ra, another isotope in the decay series of 238U, first recognized as a new element by the Curies. Poses special problems because its daughter is a radioactive noble gas.
How does the finite range of the nuclear force relate to the fact that BE/A is greatest for A near 60?
β- decay producing 137Ba. The parent nuclide is a major waste product of reactors and has chemistry similar to potassium and sodium, resulting in its concentration in your cells if ingested.
Why is the number of neutrons greater than the number of protons in stable nuclei having A greater than about 40, and why is this effect more pronounced for the heaviest nuclei?
(a) Write the complete α decay equation for 249Cf.(b) Find the energy released in the decay.
(a) Write the complete β- decay equation for the neutron. (b) Find the energy released in the decay.
(a) Write the complete β- decay equation for 90Sr, a major waste product of nuclear reactors.(b) Find the energy released in the decay.
Calculate the energy released in the β+ decay of 22Na, the equation for which is given in the text. The masses of 22Na and 22Ne are 21.994434 and 21.991383 u, respectively.
(a) Calculate the energy released in the α decay of 238U.(b) What fraction of the mass of a single 238U is destroyed in the decay? The mass of 234Th is 234.043593 u.(c) Although the fractional mass loss is large for a single nucleus, it is difficult to observe for an entire macroscopic sample of
(a) Write the complete reaction equation for electron capture by 7Be. (b) Calculate the energy released.
(a) Write the complete reaction equation for electron capture by 15O. (b) Calculate the energy released.
An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount of 14C. Estimate the minimum age of the charcoal, noting that 210 = 1024.
A 60Co source is labeled 4.00 mCi, but its present activity is found to be 1.85 x 107 Bq. (a) What is the present activity in mCi?(b) How long ago did it actually have a 4.00-mCi activity?
Show that the activity of the 14C in 1.00 g of 12C found in living tissue is 0.250 Bq.
Mantles for gas lanterns contain thorium, because it forms an oxide that can survive being heated to incandescence for long periods of time. Natural thorium is almost 100% 232Th, with a half-life of 1.405 x 1010 y. If an average lantern mantle contains 300 mg of thorium, what is its activity?
Cow's milk produced near nuclear reactors can be tested for as little as 1.00 pCi of 131I per liter, to check for possible reactor leakage. What mass of 131I has this activity?
(a) Natural potassium contains 40K, which has a half-life of 1.277 x 109 y. What mass of 40K in a person would have a decay rate of 4140 Bq? (b) What is the fraction of 40K in natural potassium, given that the person has 140 g in his body? (These numbers are typical for a 70-kg adult.)
There is more than one isotope of natural uranium. If a researcher isolates 1.00 mg of the relatively scarce 235U and finds this mass to have an activity of 80.0 Bq, what is its half-life in years?
50V has one of the longest known radioactive half-lives. In a difficult experiment, a researcher found that the activity of 1.00 kg of 50V is 1.75 Bq. What is the half-life in years?
You can sometimes find deep red crystal vases in antique stores, called uranium glass because their color was produced by doping the glass with uranium. Look up the natural isotopes of uranium and their half-lives, and calculate the activity of such a vase assuming it has 2.00 g of uranium in it.
A tree falls in a forest. How many years must pass before the 14C activity in 1.00 g of the tree's carbon drops to 1.00 decay per hour?
What fraction of the 40K that was on Earth when it formed 4.5 x 109 years ago is left today?
A 5000-Ci 60Co source used for cancer therapy is considered too weak to be useful when its activity falls to 3500 Ci. How long after its manufacture does this happen?
World War II aircraft had instruments with glowing radium-painted dials (see Figure 31.2). The activity of one such instrument was 1.0 x 105 Bq when new.(a) What mass of 226Ra was present?(b) After some years, the phosphors on the dials deteriorated chemically, but the radium did not escape. What
Natural uranium is 0.7200% 235U and 99.27% 238U. What were the percentages of 235U and 238U in natural uranium when Earth formed 4.5 x 109 years ago?
(a) The 210Po source used in a physics laboratory is labeled as having an activity of 1.0 μCi on the date it was prepared. A student measures the radioactivity of this source with a Geiger counter and observes 1500 counts per minute. She notices that the source was prepared 120 days before her
Armor-piercing shells with depleted uranium cores are fired by aircraft at tanks. (The high density of the uranium makes them effective.) The uranium is called depleted because it has had its 235U removed for reactor use and is nearly pure 238U. Depleted uranium has been erroneously called
The ceramic glaze on a red-orange Fiestaware plate is U2O3 and contains 50.0 grams of 238U, but very little 235U.(a) What is the activity of the plate?(b) Calculate the total energy that will be released by the 238U decay.(c) If energy is worth 12.0 cents per kW · h, what is the monetary value of
Large amounts of depleted uranium (238U) are available as a by-product of uranium processing for reactor fuel and weapons. Uranium is very dense and makes good counter weights for aircraft. Suppose you have a 4000-kg block of 238U.(a) Find its activity.(b) How many calories per day are generated by
The Galileo space probe was launched on its long journey past several planets in 1989, with an ultimate goal of Jupiter. Its power source is 11.0 kg of 238Pu, a by-product of nuclear weapons plutonium production. Electrical energy is generated thermoelectrically from the heat produced when the
Consider the generation of electricity by a radioactive isotope in a space probe, such as described in the previous exercise. Construct a problem in which you calculate the mass of a radioactive isotope you need in order to supply power for a long space flight. Among the things to consider are the
A nuclear physicist finds 1.0 μg of 236U in a piece of uranium ore and assumes it is primordial since its half-life is 2.3 x 107 y.(a) Calculate the amount of 236U that would had to have been on Earth when it formed 4.5 x 109 y ago for 1.0 μg to be left today.(b) What is unreasonable about this
(a) Repeat Exercise 31.57 but include the 0.0055% natural abundance of 234U with its 2.45 x 105 y half-life.(b) What is unreasonable about this result?(c) What assumption is responsible?(d) Where does the 234U come from if it is not primordial?Data from Exercise 31.57Natural uranium is 0.7200%
56Fe is among the most tightly bound of all nuclides. It is more than 90% of natural iron. Note that 56Fe has even numbers of both protons and neutrons. Calculate BE/A, the binding energy per nucleon, for 56Fe and compare it with the approximate value obtained from the graph in Figure 31.24.Data
The manufacturer of a smoke alarm decides that the smallest current of a radiation he can detect is 1.00 μA.(a) Find the activity in curies of an α emitter that produces a 1.00 μA current of α particles.(b) What is unreasonable about this result?(c) What assumption is responsible?
(a) Calculate BE/A for 235U, the rarer of the two most common uranium isotopes.(b) Calculate BE/A for 238 U. (Most of uranium is 238U.) Note that 238U has even numbers of both protons and neutrons. Is the BE/A of 238U significantly different from that of 235U ?
(a) Calculate BE/A for 12C. Stable and relatively tightly bound, this nuclide is most of natural carbon.(b) Calculate BE/A for 14C. Is the difference in BE/A between 12C and 14C significant? One is stable and common, and the other is unstable and rare.
Derive an approximate relationship between the energy of a decay and half-life using the following data. It may be useful to graph the log of t1/2 against Eα to find some straight-line relationship. Nuclide 216 Ra 194 Po 240 Cm 226 Ra 232 Th Ex (MeV) 9.5 7.0 6.4 4.91 4.1 11/2 0.18 ps 0.7 s 27
The fact that BE/A is greatest for A near 60 implies that the range of the nuclear force is about the diameter of such nuclides.(a) Calculate the diameter of an A = 60 nucleus.(b) Compare BE/A for 58Ni and 90Sr. The first is one of the most tightly bound nuclides, while the second is larger and
(a) Write the decay equation for the a decay of 235U.(b) What energy is released in this decay? The mass of the daughter nuclide is 231.036298 u.(c) Assuming the residual nucleus is formed in its ground state, how much energy goes to the α particle?
The relatively scarce naturally occurring calcium isotope 48Ca has a half-life of about 2 x 1016 y.(a) A small sample of this isotope is labeled as having an activity of 1.0 Ci. What is the mass of the 48Ca in the sample?(b) What is unreasonable about this result?(c) What assumption is responsible?
A physicist scatters γ rays from a substance and sees evidence of a nucleus 7.5 x 10-13 min radius.(a) Find the atomic mass of such a nucleus.(b) What is unreasonable about this result?(c) What is unreasonable about the assumption?
A frazzled theoretical physicist reckons that all conservation laws are obeyed in the decay of a proton into a neutron, positron, and neutrino (as in β+ decay of a nucleus) and sends a paper to a journal to announce the reaction as a possible end of the universe due to the spontaneous decay of
Consider the decay of radioactive substances in the Earth’s interior. The energy emitted is converted to thermal energy that reaches the earth’s surface and is radiated away into cold dark space. Construct a problem in which you estimate the activity in a cubic meter of earth rock? And then
(a) What is the density of 235U in u/fm3?(b) If 235 U splits into 141Ba and 92Kr + 3 neutrons, how does the density of 235U compare with the density of each element it splits into?
The angle between the axes of two polarizing filters is 45.0°. By how much does the second filter reduce the intensity of the light coming through the first?
If you have completely polarized light of intensity 150 W/m2, what will its intensity be after passing through a polarizing filter with its axis at an 89.0° angle to the light's polarization direction?
What angle would the axis of a polarizing filter need to make with the direction of polarized light of intensity 1.00 kW/m2 to reduce the intensity to 10.0 W/m2?
At the end of Example 27.8, it was stated that the intensity of polarized light is reduced to 90.0% of its original value by passing through a polarizing filter with its axis at an angle of 18.4° to the direction of polarization. Verify this statement.Data from Example 27.8What angle is needed
Show that if you have three polarizing filters, with the second at an angle of 45° to the first and the third at an angle of 90.0° to the first, the intensity of light passed by the first will be reduced to 25.0% of its value. (This is in contrast to having only the first and third, which reduces
Prove that, if I is the intensity of light transmitted by two polarizing filters with axes at an angle and I' is the intensity when the axes are at an angle 90.0° - θ, then I + I′ = I0, the original intensity. ( Use the trigonometric identities cos (90.0° - θ)= sin θ and cos2 θ + sin2 θ =
At what angle will light reflected from diamond be completely polarized?
A scuba diver sees light reflected from the water’s surface. At what angle will this light be completely polarized?
At what angle is light inside crown glass completely polarized when reflected from water, as in a fish tank?
Light reflected at 55.6° from a window is completely polarized. What is the window's index of refraction and the likely substance of which it is made?
(a) Light reflected at 62.5° from a gemstone in a ring is completely polarized. Can the gem be a diamond?(b) At what angle would the light be completely polarized if the gem was in water?
If θb is Brewster's angle for light reflected from the top of an interface between two substances, and θ′b is Brewster's angle for light reflected from below, prove that θb + θ′b = 90.0°.
If a polarizing filter reduces the intensity of polarized light to 50.0% of its original value, by how much are the electric and magnetic fields reduced?
Suppose you put on two pairs of Polaroid sunglasses with their axes at an angle of 15.0°. How much longer will it take the light to deposit a given amount of energy in your eye compared with a single pair of sunglasses? Assume the lenses are clear except for their polarizing characteristics.
(a) On a day when the intensity of sunlight is 1.00 kW/m2, a circular lens 0.200 m in diameter focuses light onto water in a black aluminum beaker. Two polarizing sheets of plastic are placed in front of the lens with their axes at an angle of 20.0°. Assuming the sunlight is unpolarized and the
A semiconductor laser emits light at 400.0 nm. The light is passed through a grating where 1,000 lines are etched covering a space of 10.00 mm. The light is directed directly at the grating.(a) What is the angle the light beam diffracts for first order diffraction? (b) What is the angle the light
Which of Einstein’s postulates of special relativity includes a concept that does not fit with the ideas of classical physics? Explain.
(a) What is γ if v = 0.250c? (b) If v = 0.500c?
Explain how special relativity differs from general relativity.
Is Earth an inertial frame of reference? Is the Sun? Justify your response.
Suppose an astronaut, such as the twin discussed in Simultaneity and Time Dilation, travels so fast that γ = 30.00.(a) She travels from the Earth to the nearest star system, Alpha Centauri, 4.300 light years (ly) away as measured by an Earth-bound observer. How far apart are the Earth and Alpha
(a) What is γ if v = 0.100c? (b) If v = 0.900c?
1. What is γ if v = 0.650c? 2. A particle travels at 1.90 x 108 m/s and lives 2.10 x 10-8 s when at rest relative to an observer. How long does the particle live as viewed in the laboratory?
A particle is traveling through the Earth’s atmosphere at a speed of 0.750c. To an Earth-bound observer, the distance it travels is 2.50 km. How far does the particle travel in the particle’s frame of reference?
When you are flying in a commercial jet, it may appear to you that the airplane is stationary and the Earth is moving beneath you. Is this point of view valid? Discuss briefly.
Particles called -mesons are produced by accelerator beams. If these particles travel at 2.70 x 108 m/s and live 2.60 x 10-8 s when at rest relative to an observer, how long do they live as viewed in the laboratory?
Suppose a spaceship heading directly towards the Earth at half the speed of light sends a signal to us on a laserproduced beam of light. Given that the light leaves the ship at speed as observed from the ship, calculate the speed at which it approaches the Earth.StrategyBecause the light and the
Suppose a space probe moves away from the Earth at a speed 0.350c. It sends a radio wave message back to the Earth at a frequency of 1.50 GHz. At what frequency is the message received on the Earth?
Does motion affect the rate of a clock as measured by an observer moving with it? Does motion affect how an observer moving relative to a clock measures its rate?
Suppose the spaceship in the previous example is approaching the Earth at half the speed of light and shoots a canister at a speed of 0.750c.(a) At what velocity will an Earth-bound observer see the canister if it is shot directly towards the Earth?(b) If it is shot directly away from the Earth?
Suppose a particle called a kaon is created by cosmic radiation striking the atmosphere. It moves by you at 0.980c, and it lives 1.24 x 10-8 s when at rest relative to an observer. How long does it live as you observe it?
What is the momentum of an electron traveling at a speed 0.985c? The rest mass of the electron is 9.11 x 10-31 kg.
To whom does the elapsed time for a process seem to be longer, an observer moving relative to the process or an observer moving with the process? Which observer measures proper time?
A neutral -meson is a particle that can be created by accelerator beams. If one such particle lives 1.40 x 10-16 s as measured in the laboratory, and 0.840 x 10-16 s when at rest relative to an observer, what is its velocity relative to the laboratory?
Suppose a galaxy is moving away from the Earth at a speed 0.825c. It emits radio waves with a wavelength of 0.525 m. What wavelength would we detect on the Earth?StrategyBecause the galaxy is moving at a relativistic speed, we must determine the Doppler shift of the radio waves using the
A photon decays into an electron-positron pair. What is the kinetic energy of the electron if its speed is 0.992c?
How could you travel far into the future without aging significantly? Could this method also allow you to travel into the past?
Calculate the rest energy of a 1.00-g mass.StrategyOne gram is a small mass—less than half the mass of a penny. We can multiply this mass, in SI units, by the speed of light squared to find the equivalent rest energy.
To whom does an object seem greater in length, an observer moving with the object or an observer moving relative to the object? Which observer measures the object’s proper length?
If relativistic effects are to be less than 1%, then γ must be less than 1.01. At what relative velocity is γ = 1.01?
A car battery is rated to be able to move 600 ampere-hours (A·h) of charge at 12.0 V.(a) Calculate the increase in rest mass of such a battery when it is taken from being fully depleted to being fully charged. (b) What percent increase is this, given the battery's mass is 20.0 kg?StrategyIn part
An electron has a velocity v = 0.990c.(a) Calculate the kinetic energy in MeV of the electron.(b) Compare this with the classical value for kinetic energy at this velocity. (The mass of an electron is 9.11 x 10-31 kg.)StrategyThe expression for relativistic kinetic energy is always correct, but for
Relativistic effects such as time dilation and length contraction are present for cars and airplanes. Why do these effects seem strange to us?
If relativistic effects are to be less than 3%, then γ must be less than 1.03. At what relative velocity is γ = 1.03?

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