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cambridge international as & a level physics coursebook

Cambridge International AS And A Level Physics Coursebook 3rd Edition David Sang, Graham Jones, Gurinder Chadha, Richard Woodside - Solutions

An X-ray beam of initial intensity 50 W m−2 is incident on soft tissue of attenuation coefficient 1.2 cm−1. Calculate its intensity after it has passed through a 5.0 cm thickness of tissue.
Calculate the minimum wavelength (in air) of X-rays produced when the accelerating potential across the source is 20 kV.
An X-ray beam transfers 400 J of energy through an area of 5.0 cm2 each second. Calculate its intensity in W m−2.
a. Explain what is meant by ionising radiation and explain why it can be harmful to humans.b. Which of the following scans use ionising radiation?. X-ray shadow imaging. Ultrasound A-scan. Ultrasound B-scan. PET scan. CT scan
Use the equation I = I0 e−μx to show that the half-thickness x½ is related to the attenuation coefficient μ by: x½ = In 2/μ
Which statement about PET scanning is correct?A. A positron is emitted by the radiotracer that interacts with an electron in the detector producing two γ-rays that move apart at 180° to each other.B. A positron is emitted by the radiotracer that interacts with an electron in the detector
Determine the minimum wavelength of X-rays emitted from an X-ray tube operated at a voltage of 120 kV.
X-rays are produced by firing electrons at a metal anode target. Which statement is correct?A. The frequencies of the characteristic spectrum lines are determined by the potential used to accelerate the electrons.B. The frequencies of the characteristic spectrum lines are determined by the metal
a. Summarise the energy changes that take place in an X-ray tube.b. An X-ray tube is operated with a potential difference of 80 kV between the cathode and the tungsten anode. Calculate the kinetic energy (in electronvolts and joules) of an electron arriving at the anode. Estimate the impact speed
A sample contains an isotope of half-life t 1/2 .a. Show that the fraction f of nuclei in the sample that remain undecayed after a time t is given by the equation:f = (1/2)n where n = 1/t 1/2b. Calculate the fraction f after each of the following times:i. t 1/2ii. 2t 1/2iii. 2.5t 1/2iv. 8.3t
The isotope 167N decays with a half-life of 7.4 s.a. Calculate the decay constant for this nuclide.b. A sample of N initially contains 5000 nuclei. Calculate how many will remain after a time of:i. 14.8 sii. 20.0 s.
The decay constant of a particular isotope is 3.0 × 10−4 s−1. Calculate how long it will take for the activity of a sample of this substance to decrease to one-eighth of its initial value.
Figure 29.13 shows the decay of an isotope of caesium, 13455 Cs. Use the graph to determine the half-life of this nuclide in years, and hence find the decay constant in year−1. 400- 300- 200- 100- 0+ 4 6. 8 Time / years Activity/Bq 2-
The value of λ for protactinium-234 is 9.6 × 10−3 s−1. Table 29.5 shows the number of undecayed nuclei N in a sample.Copy and complete Table 29.5. Draw a graph of N against t, and use it to find the half-life t 1/2 of protactinium-234. t/s 20 40 60 80 100 120 140 N 400 330
A sample of an isotope for which λ = 0.10 s−1 contains 5.0 × 109 undecayed nuclei at the start of an experiment. Determine:a. The number of undecayed nuclei after 50 sb. Its activity after 50 s.
The isotope nitrogen-13 has a half-life of 10 min. A sample initially contains 8.0 × 1010 undecayed nuclei.a. Write down an equation to show how the number undecayed N depends on time t.b. Calculate how many undecayed nuclei will remain after 10 min, and after 20 min.c. Determine how many nuclei
A nuclear reactor is fuelled by fission of uranium. The output from the reactor is 200 MW. The following equation describes a typical fission reaction:23592U + 10 n → 23692U → 8735Br + 14657La + 310na. State and explain into what form the majority of the energy released in the
A radioactive sample is known to emit α-, β- and γ-radiations. Suggest four reasons why the count rate measured by a Geiger counter placed next to this sample would be lower than the activity of the sample.
The isotope of polonium, 21881Po , decays by the emission of an α-particle with a half-life of 183 s.a. In an accident at a reprocessing plant some of this isotope, in the form of dust, is released into the atmosphere.Explain why a spillage in the form of a dust is far more dangerous to health
A small sample of radium gives a received count rate of 20 counts per minute in a detector. It is known that the counter detects only 10% of the decays from the sample. The sample contains 1.5 × 109 undecayed nuclei. Calculate the decay constant of this form of radium.
a. Explain what is meant by nuclear fusion and explain why it only occurs at very high temperatures.b. The main reactions that fuel the Sun are the fusion of hydrogen nuclides to form helium nuclides. However, other reactions do occur. In one such reaction, known as the triple alpha process, three
This question is about the nucleus of uranium-235 (23592 U), which has a mass of 3.89 × 10−25 kg.a. State the number of protons and neutrons in this nucleus.b. The radius r of a nucleus is given by the equation:r = 1.41 x 10-15 A1/3Where A is the nucleon number of the nucleus.Calculate the
A sample of carbon-15 initially contains 500,000 undecayed nuclei. The decay constant for this isotope of carbon is 0.30 s−1. Calculate the initial activity of the sample.
The table shows the received count rate when a sample of the isotope vanadium-52 decays.a. i. Sketch a graph of the count rate against the time.ii. Comment on the scatter of the points.b. From the graph, determine the half-life of the isotope.c. Describe the changes to the graph that you would
Use the information given in the fusion section, to determine the binding energy (in MeV) per nucleon of each particle in the following fusion reaction:21H + 11p → 32 He
The proportions of different isotopes in rocks can be used to date the rocks. The half-life of uranium-238 is 4.9 × 109 years. A sample has 99.2% of the proportion of this isotope compared with newly formed rock.a. Calculate the decay constant in y−1 for this isotope of uranium.b. Calculate
Use the binding energy graph (Figure 29.6) to suggest why fission is unlikely to occur with ‘light nuclei’ (A < 20) and why fusion is unlikely to occur for heavier nuclei (A > 40). 16 12 fission fusion 40 80 120 160 200 240 Nucleon number, A -13 Binding energy per nucleon / 10- J per
The graph of count rate against time for a sample containing indium-116 is shown.a. Use the graph to determine the half-life of the isotope.b. Calculate the decay constant. 160 120 80 40 10 20 30 40 50 60 70 Time /s Figure 29.14 Count rate / s
The mass of a 84 Be nucleus is 1.33 × 10−26 kg. For the nucleus of 84 Be, determine:a. The mass defect in kgb. The binding energy of the nucleus in MeVc. The binding energy (in MeV) per nucleon for the nucleus.
The initial activity a sample of 1 mole of radon-220 is 8.02 × 1021 s−1. Calculate:a. The decay constant for this isotopeb. The half-life of the isotope.
a. Explain why hydrogen 11 H (proton) cannot appear on the graph shown in Figure 29.4.b. Use Figure 29.4 to estimate the binding energy of the nuclide 147 N. 16 20 10 Ne 35 56, 26Fe 89 110 17CI 39 16 48 Cd 141 Pr 59 180 12 209 19, 75 As 100, 12 14 33 42Mo 126 $2 Te Не 1. 5B 160 66 Dy 197 Au
The fusion reaction that holds most promise for the generation of electricity is the fusion of tritium 31 H and deuterium 21 H. The following equation shows the process:31 H + 21 H → 42 He + 11 HCalculate:a. The change in mass in the reactionb. The energy released in the reactionc. The energy
A nucleus of beryllium-10 (104 Be) decays into an isotope of boron by β− emission. The chemical symbol for boron is B.a. Write a nuclear decay equation for the nucleus of beryllium-10.b. Calculate the energy released in this decay and state its form.(Mass of 104 Be nucleus = 1.662 38 × 10−26
A carbon-12 atom consists of six protons, six neutrons and six electrons. The unified atomic mass unit (u) is defined as 1/12 the mass of the carbon-12 atom. Calculate:a. The mass defect in kilogramsb. The binding energyc. The binding energy per nucleon.(Mass of a proton = 1.007 276 u, mass of a
Table 29.3 gives the masses (in u) of several particles. (Avogadro constant NA = 6.02 × 1023 mol−1.) Use the table to determine to three significant figures:a. The mass in kg of a helium-4 nucleusb. The mass in gram (g) of 1.0 mole of uranium-235 nuclei. Nuclide Symbol Mass / u proton 1.007 276
The equation shows the radioactive decay of radon-222.22286Rn → 21884Po + 42 α + rCalculate the total energy output from this decay and state what forms of energy are produced.(Mass of 22286Rn = 221.970 u, mass of 22286Po = 217.963 u, mass of 4/2 α = 4.002u, 1 u is the unified atomic mass unit
a. The mass of an atom of 5626 Fe is 55.934 937 u. Calculate its mass in kg.b. The mass of an atom of 168 O is 2.656 015 × 10−26 kg. Calculate its mass in u.
In a nuclear reactor, the mass converted to energy takes place at a rate of 70 μg s−1. Calculate the maximum power output from the reactor assuming that it is 100% efficient.
The rest mass of a golf ball is 150 g. Calculate its increase in mass when it is travelling at 50 m s−1. What is this as a percentage of its rest mass?
Calculate the mass that would be annihilated to release 1 J of energy.
a. Calculate the energy released if a 42 He nucleus is formed from separate stationary protons and neutrons. The masses of the particles are given in Table 29.2.b. Calculate also the energy released per nucleon. Particle Mass / 10-27 kg 1.672 623 1.674 929 on He 6.644 661
An antiproton is identical to a proton except that it has negative charge. When a proton and an antiproton collide, they are annihilated and two photons are formed. In annihilation, all the mass of the particles is converted into energy.a. Calculate the energy released in the reaction.b. Calculate
The Sun releases vast amounts of energy. Its power output is 4.0 × 1026 W. Estimate how much its mass decreases each second because of this energy loss.
A student determines the half-life of an isotope to be 66 ± 5 s. What is the absolute uncertainty in the decay constant?A. 8.0 × 10−4 s−1B. 1.1 × 10−3 s−1C. 5.3 × 10−2 s−1D. 7.6 × 10−2 s−1
Copy and complete this equation for the β− decay of a nucleus of argon:4118 Ar → K+?
Which expression is correct for determining the energy (in electronvolt eV) produced from a mass change of 1 u?A. 1.0 × (3.00 × 108)2B. 1.66 × 10−27 × (3.00 × 108)2C. 1.66 × 10−27 × (3.00 × 108)2 × 1.60 × 10−19D. 1.66 x 10-27 x (3.00 x 108)2/ 1.60 x 10-19
Study the decay equations given in Worked examples 1 and 2, and write balanced equations for the following:a. A nucleus of radon-220 (22086 Rn) decays by α emission to form an isotope of polonium, Po.b. A nucleus of a sodium isotope (2511 Na) decays by β− emission to form an isotope of
A beam of electrons is accelerated from rest through a p.d. of 1.0 kV.a. What is the energy (in eV) of each electron in the beam?b. Calculate the speed, and hence the momentum (mv), of each electron.c. Calculate the de Broglie wavelength of each electron.d. Would you expect the beam to be
X-rays are used to find out about the spacings of atomic planes in crystalline materials.a. Describe how beams of electrons could be used for the same purpose.b. How might electron diffraction be used to identify a sample of a metal?
The line spectrum for a particular type of atom is found to include the following wavelengths:83 nm 50 nm 25 nma. Calculate the corresponding photon energies in eV.b. Sketch the energy levels that could give rise to these photons. On the diagram, indicate the corresponding electron transitions
a. Describe the importance of the Planck constant h in describing the behaviour of electromagnetic radiation and of electrons.b. Light of wavelength 550 nm is incident normally on a metal plate. The intensity of the light is 800 W m−2. All the incident light is absorbed by the metal plate. The
a. State what is meant by the de Broglie wavelength of an electron.b. The diagram shows the principles of an electron tube used to demonstrate electron diffraction.i. Calculate the kinetic energy E (in joules) of the electrons incident on the graphite film.ii. Show that the momentum of an electron
Figure 28.19 shows part of the energy level diagram for the electrons in an imaginary atom. The arrows represent three transitions between the energy levels. For each of these transitions:a. Calculate the energy of the photonb. Calculate the frequency and wavelength of the electromagnetic radiation
a. i. Explain what is meant by the wave–particle duality of electromagnetic radiation.ii. Explain how the photoelectric effect gives evidence for this phenomenon.The diagram shows the maximum kinetic energy E of the emitted photoelectrons as the frequency f of the incident radiation on a sodium
When electromagnetic radiation of wavelength 2000 nm is incident on a metal surface, the maximum kinetic energy of the electrons released is found to be 4.0 × 10−20 J.Calculate the work function of the metal in joules (J).You will need these values to answer questions:Speed of light in a vacuum
The diagram shows three of the energy levels in an isolated hydrogen atom. The lowest energy level is known as the ground state.a. Explain what happens to an electron in the ground state when it absorbs the energy from a photon energy 21.8 × 10−19 J.b. i. Explain why a photon is emitted when an
Electromagnetic waves of wavelength 2.4 × 10−7 m are incident on the surface of a metal whose work function is 2.8 × 10−19 J.a. Calculate the energy of a single photon.b. Calculate the maximum kinetic energy of electrons released from the metal.c. Determine the maximum speed of the emitted
Table 28.5 shows the work functions of several different metals.a. State which metal requires the highest frequency of electromagnetic waves to release electrons.b. State which metal will release electrons when the lowest frequency of electromagnetic waves is incident on it?c. Calculate the
The spectrum of sunlight has dark lines. These dark lines are due to the absorption of certain wavelengths by the cooler gases in the atmosphere of the Sun.a. One particular dark spectral line has a wavelength of 590 nm. Calculate the energy of a photon with this wavelength.b. The diagram shows
The diagram shows five of the energy levels in a helium ion. The lowest energy level is known as the ground state.a. Determine the energy, in joules, that is required to completely remove the remaining electron, originally in its ground state, from the helium ion.b. Determine the frequency of the
Photons of energies 1.0 eV, 2.0 eV and 3.0 eV strike a metal surface whose work function is 1.8 eV.a. State which of these photons could cause the release of an electron from the metal.b. Calculate the maximum kinetic energies of the electrons released in each case. Give your answers in eV and in
Calculate the minimum frequency of electromagnetic radiation that will cause the emission of photoelectrons from the surface of gold. (Work function for gold = 4.9 eV.)
In an experiment to determine the Planck constant h, LEDs of different colours were used. The p.d. required to make each conduct was determined, and the wavelength of their light was taken from the manufacturer’s catalogue. The results are shown in Table 28.3. For each LED, calculate the
Ultraviolet light with photons of energy 2.5 × 10−18 J is shone onto a zinc plate. The work function of zinc is 4.3 eV. Calculate the maximum energy with which an electron can be emitted from the zinc plate. Give your answer in:a. EVb. J.
A proton, initially at rest, is accelerated through a potential difference of 1500 V. A proton has charge + 1.60 × 10−19 C and mass 1.67 × 10−27 kg. Calculate:a. Its final kinetic energy in joules (J)b. Its final speed.
A helium nucleus (charge = + 3.2 × 10−19 C; mass = 6.8 × 10−27 kg) is accelerated through a potential difference of 7500 V. Calculate:a. Its kinetic energy in electronvoltsb. Its kinetic energy in joulesc. Its speed.
With the help of a calculation, identify the region of the electromagnetic spectrum (Figure 28.4) a photon of energy 10 eV belongs.To answer questions you will need these values:Speed of light in a vacuum c = 3.00 × 108 m s−1Planck constant h = 6.63 × 10−34 J s X-гаys visible microwaves
a. Alpha-particles of energy 5.0 MeV are emitted in the radioactive decay of radium. Express this energy in joules.b. Electrons in an cathode-ray tube are accelerated through a potential difference of 10 kV. Calculate their energy:i. In electronvoltsii. In joules.c. In a nuclear reactor, neutrons
Calculate the energy in eV of an X-ray photon of frequency 3.0 × 1018 Hz.To answer questions you will need these values:Speed of light in a vacuum c = 3.00 × 108 m s−1Planck constant h = 6.63 × 10−34 J s
In a microwave oven, the photons are used to warm food. Each photon has energy 1.02 × 10−5 eV.a. Calculate the energy of each photon in joule (J).b. Calculate the frequency of the photons.c. Calculate the wavelength of the photons.
An electron travels through a cell of e.m.f. 1.2 V. Calculate the energy is transferred to the electron. Give your answer in both eV and J.To answer question you will need these values:Speed of light in a vacuum c = 3.00 × 108 m s−1Planck constant h = 6.63 × 10−34 J s
The microwave region of the electromagnetic spectrum is considered to have wavelengths ranging from 5 mm to 50 cm. Calculate the range of energy of microwave photons.
A 1.0 mW laser produces red light of wavelength 6.48 × 10−7 m. Calculate how many photons the laser produces per second.To answer questions you will need these values:Speed of light in a vacuum c = 3.00 × 108 m s−1Planck constant h = 6.63 × 10−34 J s
Calculate the energy of a photon of frequency 4.0 × 1018 Hz.
Determine the wavelength of the electromagnetic waves for each photon, a to e. Then use Figure 28.4 to identify the region of the electromagnetic spectrum to which each belongs. The photon energy is:a. 10−12 Jb. 10−15 Jc. 10−18 Jd. 10−20 Je. 10−25 JTo answer questions 1 to 7 you will need
A researcher is carrying out an experiment on the photoelectric effect. Electromagnetic radiation of different frequencies is incident on a metal and the maximum kinetic energy of the emitted electrons is determined. The researcher plots a straight-line graph of maximum kinetic energy of the
Calculate the energy of a high-energy γ-photon, of frequency 1.0 × 1026 Hz.To answer questions you will need these values:Speed of light in a vacuum c = 3.00 × 108 m s−1Planck constant h = 6.63 × 10−34 J s
Visible light has wavelengths in the range 400 nm (violet) to 700 nm (red). Calculate the energy of a photon of red light and a photon of violet light.To answer questions you will need these values:Speed of light in a vacuum c = 3.00 × 108 m s−1Planck constant h = 6.63 × 10−34 J s
In which of the following can you use the term work function in your explanation?a. Diffraction of electrons by graphiteb. Interference of light from a diffraction gratingc. Photoelectric effectd. Reflection of light.
The Y-sensitivity and time-base settings are 5 V/cm and 10 ms/cm. The trace seen on the CRO screen is the one shown in Figure 27.7. Determine the amplitude, period and frequency of the signal applied to the Y-input of the CRO. Ilcm 1cm
Figure 28.26 shows the magnetic flux linkage and induced e.m.f. as a coil rotates. Explain why the induced e.m.f. is a maximum when there is no flux linkage and the induced e.m.f. is zero when the flux linkage is a maximum.
In an experiment to investigate the factors that affect the magnitude of an induced e.m.f., a student moves a wire back and forth between two magnets, as shown in Figure 26.14. State why the e.m.f. generated in this way is almost zero. movement of wire
A Van de Graaff generator produces sparks when the field strength at its surface is 4.0 × 104 V cm−1. If the diameter of the sphere is 40 cm, what is the charge on it?You will need the following data to answer the following questions. (You may take the charge of each sphere to be situated at its
This diagram shows a thin slice of metal of thickness t and width d. The metal slice is in a magnetic field of flux density B and carries a current I, as shown.a. Copy the diagram and mark:i. the side of the slice that becomes negative because of the Hall effectii. where a voltmeter needs to be
Use the idea of a conductor cutting magnetic field lines to explain how a current is caused by induced e.m.f. in a bicycle generator (Figure 26.7). fixed coil rotating magnet current
Which of the following units is not correct for magnetic flux?A. Kg m2 s−2 A−1B. TC. T m2D. Wb
The coil in Figure 26.11 is rotating in a uniform magnetic field. Predict the direction of the current caused by induced e.m.f. in sections AB and CD. State which terminal, X or Y, will become positive. magnetic field lines В A В
A student thinks that electrical current passes through the core in a transformer to the secondary coil. Describe how you might demonstrate that this is not true and explain how an electrical current is actually induced in the secondary coil. Use Faraday’s law in your explanation.
When an aircraft flies from east to west, its wings are an electrical conductor cutting across the Earth’s magnetic flux. In the northern hemisphere, state which wingtip (left or right) will become positive. State and explain what will happen to this wingtip in the southern hemisphere.
A square coil of 100 turns of wire has sides of length 5.0 cm. It is placed in a magnetic field of flux density 20 mT, so that the flux is perpendicular to the plane of the coil.a. Calculate the flux through the coil.b. The coil is now pulled from the magnetic field in a time of 0.10 s. Calculate
Use the idea of magnetic flux linkage to explain why, when a magnet is moved into a coil, the e.m.f. induced depends on the strength of the magnet and the speed at which it is moved.
An aircraft of wingspan 40 m flies horizontally at a speed of 300 ± 10 m s−1 in a region where the vertical component of the Earth’s magnetic field is 5.0 × 10−5 T.Calculate the magnitude of the e.m.f. induced between the aircraft’s wingtips; in your answer, include the absolute
In the type of generator found in a power station (Figure 26.15), a large electromagnet is made to rotate inside a fixed coil. An e.m.f. of 25 kV is induced; this is an alternating voltage of frequency 50 Hz.a. State the factor that determines the frequency.b. Suggest the factors that you think
a. Explain what is meant by a magnetic flux linkage of 1 Wb.b. This is a graph of magnetic flux density through a 240 turn coil with a cross-sectional area 1.2 × 10−4 m2 against timei. Determine the maximum rate of change of flux in the coil.ii. Determine the maximum magnitude of the induced
At the surface of the north pole of a bar magnet, the magnetic field is uniform with flux density 0.15 T. The pole has dimensions 1.0 cm × 1.5 cm. Calculate the magnetic flux at this pole.
This diagram shows a square coil about to enter a region of uniform magnetic field of magnetic flux density 0.30 T. The magnetic field is at right angles to the plane of the coil. The coil has 150 turns and each side is 2.0 cm in length. The coil moves at a constant speed of 0.50 m s−1.a. i.
A solenoid has diameter 5.0 cm, length 25 cm and 200 turns of wire (Figure 26.16). A current of 2.0 A creates a uniform magnetic field of flux density 2.0 × 10−5 T through the core of this solenoid.a. Calculate the magnetic flux linkage for this solenoid.b. The diameter of the solenoid is 5.0 ±
a. State Faraday’s law of electromagnetic induction.b. A circular coil of diameter 200 mm has 600 turns is shown. It is placed with its plane perpendicular to a horizontal magnetic field of uniform flux density 50 mT. The coil is then rotated through 90° about a vertical axis in a time of 120
A rectangular coil with 120 turns is placed at right angles to a magnetic field of flux density 1.2 T. The coil has dimensions 5.0 cm × 7.5 cm. Calculate the magnetic flux linkage for this coil.
A bicycle wheel is mounted vertically on a metal axle in a horizontal magnetic field, as shown in the diagram. Sliding connections are made to the metal edge of the wheel and to the metal axle.a. i. Explain why an e.m.f. is induced when the wheel rotates.ii. State and explain two ways in which this

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