Worksheet 26 Combine

26 Work Worksh shee eett (A2) Data needed to answer questions can be found in the Data, formulae and relationships sheet. 1

2

Calculate the force experienced experienced by an oil droplet with a charge of 3.2 3.2 × 10−19 C due to a uniform electric field of strength 5.0 × 105 V m−1. The diagram shows two parallel, horizontal horizontal plates separated by a vertical distance of 3.0 cm. The potential difference between the plates is 600 V.

a b c

Calculate the magnitude and direction of the electric field between the plates. Describe the electric field between the plates. A charged oil droplet of weight 6.4 × 10−15 N is held stationary between the two plates. i

ii 3

4

[2]

State whether the charge on the droplet is positive or negative. Explain your answer. Determine the charge on the oil droplet.

Calculate the force experienced experienced by an electron travelling at a velocity of 4.0 4.0 × 106 m s−1 at right angles to a magnetic field of magnetic flux density 0.18 T.

[3] [2]

[2] [2] [3]

The diagram shows an electron moving moving at a constant speed of 8.0 × 106 m s−1 in a plane  perpendicular to a uniform magnetic field of magnetic magnetic flux density 4.0 mT.

a  b c

Calculate the force acting on the electron due to the magnetic field. [3] What is the centripetal acceleration of the electron? [2] Use your answer to b to determine the radius of the circular path described by the electron. [2]

26 Worksheet (A2) 5

The diagram shows the trajectory of an electron travelling into a region of uniform magnetic field of flux density 2.0 mT. The electron enters the region of magnetic field at 90°.

a b

c

d

6

[1] [1] [5] [2]

A proton of kinetic energy 15 keV travelling at right angles to a magnetic field describes a circle of radius of 5.0 cm. The mass of a proton is 1.7 × 10−27 kg. a b c

d 7

Draw the direction of the the force experienced by the electron at points A and B. Explain why the electron describes part of a circular path while in the region of the magnetic field. The radius of curvature of the path of the electron in the magnetic field is 5.0 cm. Calculate the speed v of the electron. Explain how your answer to c would change if the electron described a circular path of radius 2.5 cm.

Show that the speed of the proton is 1.7 × 106 m s−1. For this proton, calculate the centripetal force provided by the magnetic field. Determine the magnetic flux density of the magnetic field that keeps the proton moving in its circular orbit. How long does it take for the proton to complete one orbit?

[3] [3] [3] [2]

The diagram shows a velocity-selector for for charged charged ions. ions. Ions Ions of speed v emerge from the slit.

a

b

The parallel plates have a separation of 2.4 cm and are connected to a 5.0 kV supply. A magnetic field is applied at right angles to the electric field between the plates such that the positively charged ions emerge from the slit of the velocity-selector at a speed of 6.0 × 106 m s−1. Calculate the magnetic flux density of the magnetic field. [6] Ions from the velocity-selector pass into a mass s pectrometer which contains another magnetic field, of flux density  B. The ions all have charge Q but either have mass m1 or mass m2. Show that the difference in the radius of the two isotopes in the magnetic field is given by:  = ∆r  =

(m1 − m 2 )v  BQ

[2]

26 Worksheet (A2) 8

An electron describes a circular orbit in a plane perpendicular to a uniform magnetic field. a

Show that the time T  taken by an electron to complete one orbit in the magnetic field is independent of its speed and its radius, and is given by: T  =

2πm  Be

where B is the magnetic flux density of the magnetic field, e is the charge on an electron and m is the mass of an electron. b

[5]

Explain in words how a faster electron takes the same time to complete one orbit as a slower electron. [1]

Total:

55

Score:

%

27 Worksheet (A2) 1

A flat coil of N  turns and cross-sectional area  A is placed in a uniform magnetic fie ld of flux density B. The plane of the coil is normal to the magnetic field. a Write an equation for: the magnetic flux Φ  through the coil [1] i ii the magnetic flux linkage for the coil. [1] b The diagram shows the coil when the magnetic field is at an angle θ  to the normal of the plane of the coil. What is the flux linkage for the coil? [1]

2

A square coil of N  turns is placed in a uniform magnetic field of magnetic flux density  B. Each side of the coil has length  x. What is the magnetic flux linkage for this coil?

3

4

The diagram shows a magnet placed close to a flat circular coil. a Explain why there is no induced e.m.f. even though there is magnetic flux linking the coil. b Explain why there is an induced e.m.f. when the magnet is  pushed towards the coil.

[2]

[1]

[2]

A coil of cross-sectional area 4.0 × 10−4 m2 and 70 turns is placed in a uniform magnetic field. a The plane of the coil is at rightangles to the magnetic field. Calculate the magnetic flux density when the flux linkage for the coil is 1.4 × 10−4 Wb. [3] b The coil is placed in a magnetic field of flux density 0.50 T. The normal to the coil is at an angle of 60° to the magnetic field, as shown in the diagram. Calculate the flux linkage for the coil. [3]

27 Worksheet (A2) 5

A square coil is placed in a uniform magnetic field of flux density 40 mT. The plane of the coil is normal to the magnetic field. The coil has 200 turns and the length of each side of the coil is 3.0 cm. a  Calculate: i the magnetic flux Φ  through the coil [2] ii the magnetic flux linkage for the coil. [2] b The plane of the coil is turned through 90°. What is the change in the magnetic flux linkage for the coil? [2]

6

A flat circular coil of 1200 turns and of mean radius 8.0 mm is connected to an ammeter of negligible resistance. The coil has a resistance of 6.3 Ω. The plane of the coil is placed at right angles to a magnetic field of flux density 0.15 T from a solenoid. The current in the solenoid is switched off. It takes 20 ms for the magnetic field to decrease from its maximum value to zero. Calculate: a

b

7

the average magnitude of the induced e.m.f. across the ends of the coil the average current measured by the ammeter.

The diagram shows a straight wire of length 10 cm moved at a constant speed of 2.0 m s −1 in a uniform magnetic field of flux density 0.050 T.

For a period of 1 second, calculate: a the distance travelled by the wire b the area swept by the wire the change in the magnetic flux for the wire (or the magnetic flux ‘cut’ by the wire) c d the e.m.f. induced across the ends of the wire using your answer to c  e the e.m.f. induced across the ends of the wire using  E = Blv. 8

[5] [2]

[1] [1] [2] [2] [1]

A circular coil of radius 1.2 cm has 2000 turns. The coil is placed at right angles to a magnetic field of flux density 60 mT. Calculate the average magnitude of the induced e.m.f. across the ends of the coil when the direction of the magnetic field is  reversed in a time of 30 ms. [5]

27 Worksheet (A2) 9

The diagram shows a step-up transformer. The ends AB of the  primary coil are connected to a 1.5 V cell and a switch. The switch is initially closed and the lamp is off. The switch is suddenly opened and the lamp illuminates for a short time.

Explain why the lamp illuminates only for a short period. State one change to the apparatus that would allow the lamp to illuminate normally.

[4] [1]

A wire of length L is placed in a uniform magnetic field of flux density  B. The wire is moved at a constant velocity v at right angles to the magnetic field. Use Faraday’s law of electromagnetic induction to show that the induced e.m.f.  E  across the ends of the wire is given by  E = BLv. Hence calculate the e.m.f. induced across the ends of a 20 cm long rod rolling along a horizontal table at a speed of 0.30 m s −1. (The vertical component of the Earth’s magnetic flux density is about 40 µT.)

[8]

a b 10

11 a b c

State Faraday’s law of electromagnetic induction. Lenz’s law expresses an important conservation law. Name this conservation law. i Define magnetic flux for a coil placed at right angles to a magnetic field. ii Determine for which of the two coils X and Y, each placed at right angles to the magnetic field, is the magnetic flux linkage the greatest.

Total:

59

Score:

[1] [1] [1] [4]

%

28 Worksheet (A2) 1

2

An alternating voltage is given by the equation V = V 0 sin 2π ft  where V 0 = 5.0 V and f = 10 Hz. a Calculate the period of the alternating voltage. b Calculate the values of t  during the first cycle of the voltage (from t = 0) for which the value of V  is: i 0 ii +V 0 iii −V 0  iv +V rms

4

5

[1] [2] [1] [2]

The graph shows how an alternating voltage V  and an alternating current I change with time t .

a b 3

[2]

V  and I  are in phase with each other. Explain what is meant by in phase. Copy the graph and add a waveform to show how the power dissipated varies with t .

An electric drill is marked 230 V r.m.s., 690 W. Calculate: a i the r.m.s. current in the wire connecting the drill to the mains ii the peak current in the wire connecting the drill to the mains iii the peak value of the potential difference across the drill. b Sketch a graph of the power drawn by the drill over one cycle of the current. Mark on the graph the values of peak power and average power. The diagram shows the variation of voltage with time across a resistor. a State and explain whether the current in the resistor is a.c. or d.c. [2] +2 V b Explain why the power dissipated in the resistor is the same as the power produced  by a steady voltage of 2 V. [1] 0 c For the voltage variation shown, state: i the peak value [1] −2 V ii the r.m.s. value. [1] Calculate the value of the average power dissipated in a resistor when the alternating supply to the resistor has a peak current of 2.5A and a peak voltage of 6.0 V.

[1] [3]

[2] [1] [1] [3]

t  / s

[2]

28 Worksheet (A2)

6

The diagram shows the trace obtained on the screen of an oscilloscope connected to a signal generator. The time-base of the oscilloscope is set at 20 ms per division and the Y-gain at 1.5 V per division. a

b

7

For the signal generator, calculate: i the frequency [2] ii the r.m.s. voltage. [2] The equation of the waveform can be written in the form V = V 0 sin (ωt ). Determine the values of V 0 and ω. [2]

1 division

The diagram shows a step-down transformer. The primary coil has 1150 turns and the secondary coil has 30 turns. The ends of the secondary coil are connected to a lamp labelled ‘6.0 V, 24 W’. The ends AB of the  primary coil are connected to an alternating voltage supply. The  potential difference across the lamp is 6.0 V. a b c d e

Calculate the current in the lamp. Calculate the input voltage to the primary coil. Calculate the current in the primary coil, assuming the transformer is 100% efficient. Calculate the maximum p.d. across the lamp during one cycle of the a.c. A student suggests that to avoid the production of heat in the transformer the wires should be coated in a material that is a poor conductor of heat. Explain why this is not a sensible suggestion.

[2] [2] [2] [2]

[1]

8

An electrician uses a transformer to step the 230 V r.m.s. mains voltage down to 115 V r.m.s. The secondary coil has 500 turns and is connected to a resistor of 5000 Ω. a Calculate the number of turns on the primary coil. [1] [1] b Calculate the current in the secondary coil. [1] c Calculate the current in the primary coil. Assume that the transformer is 100 % efficient. d The electrician connects cables to the secondary coil that break down when the p.d.  between the wire and earth is larger than 130 V. Explain whether the cables will break down when the transformer is switched on. [2]

9

A consumer receives 1000 W of power at 100 V r.m.s. through a 5.0 Ω cable. a Calculate the rate of heat production in the cable. b Explain why transmitting the same amount of power at a higher voltage produces less heat dissipation in the cable.

Total:

50

Score:

[2] [2]

%

29 Worksheet (A2) Data needed to answer questions can be found in the Data, formulae and relationships sheet. 1

What is a photon?

2

γ-rays

3

4

5

6

[1]

from a radioactive material have higher frequency than visible light. Explain why this means that γ-rays are more harmful.

[2]

State one piece of evidence that electromagnetic radiation has: a wave-like properties b particle-like properties.

[1] [1]

A light-emitting diode emits red light of wavelength 6.4 × 10−7 m. Calculate: a the frequency of the red light b the energy of a photon of red light.

[2] [3]

Using the terms photons and work function, describe why electrons are emitted from the surface of a zinc plate when it is illuminated by ultraviolet radiation but not when it is illuminated by visible light.

[3]

The figure below shows an electron making a transition between two energy levels and the bright spectral emission line observed.

Explain why electromagnetic radiation is emitted when an electron jumps from energy level E 1 to energy level  E 2. b Derive an expression for the frequency  f of the radiation emitted. c State and explain the position of the spectral line when an electron makes a transition  between energy levels E 1 and E 3. a

[2] [2] [2]

7

An electron in an atom can occupy four energy levels. With the help of an energy level diagram, determine the maximum number of spectral emission lines from this atom. [2]

8

Lithium atoms emit red light of wavelength 670 nm. Calculate the difference between the energy levels responsible for this red light.

[3]

29 Worksheet (A2)

9 The diagram below shows a hot solid, at a t emperature of 5000 K, emitting a continuous spectrum.

State the type of spectrum observed from: a  position X b  position Y c position Z.

[1] [1] [1]

10

What experimental evidence is there that suggests that electrons behave as waves?

[1]

11 

The electronvolt is a convenient unit of energy for particles and photons. Define the electronvolt.

[1]

An electron is accelerated through a potential difference of 6.0 V. According to a student, this electron has kinetic energy greater than the energy of a photon of ultraviolet radiation of wavelength 2.5 × 10−7 m. With the aid of calculations, explain whether or not the student is correct.

[5]

12

13 a b

Define threshold frequency for a metal. The work function of caesium is 1.9 eV. Calculate the threshold frequency.

[1] [3]

14 A particular filament lamp of rating 60 W emits 5.0% of this power as visible light. The average wavelength of visible light is 550 nm. Calculate: a the average energy of a single photon of visible light b the number of photons of visible light emitted per second from the lamp.

[3] [3]

− 15 A plate of zinc is illuminated by electromagnetic radiation of wavelength 2.1 × 10 7 m. The work function of zinc is 4.3 eV. Calculate the maximum kinetic energy of a photoelectron.

[4]

16 Neutrons travelling through matter get diffracted just as electrons do when travelling through graphite. In order to show diffraction effects, the neutrons need to have a de Broglie wavelength that is comparable to the spacing between the atoms. Calculate the speed of a neutron that has a de Broglie wavelength of 2.0 × 10−11 m.

[3]

17 A yellow light-emitting diode (LED) is connected to a d.c. power supply. The output voltage from the supply is slowly increased from zero until the LED just starts to glow. The yellow light from the LED has a wavelength of about 5.8 × 10−7 m. Estimate the potential difference across the LED when it just starts to glow.

[4]

29 Worksheet (A2)

18 a

In an electron-diffraction experiment, electrons are accelerated through a p.d. V . Show that the de Broglie wavelength λ  of an electron is given by: h λ  =

b

2meVe

where me is the mass of the electron and e is the elementary charge. Calculate the accelerating p.d. V  that gives an electron a de Broglie wavelength of 4.0 × 10−11 m.

[3] [3]

19 In an experiment on the photoelectric effect, a metal is illuminated by visible light of different wavelengths. A photoelectron has a maximum kinetic energy of 0.9 eV when red light of wavelength 640 nm is used. With blue light of wavelength 420 nm, the maximum kinetic energy of the photoelectron is 1.9 eV. Use this information to calculate an experimental value for the Planck constant h. [5] 20 The diagram below shows the some of the energy levels for a helium atom.

a b

c

Explain the significance of the energy levels being negative. When a helium atom is not excited, the electrons have an energy of −3.00 eV. This is known as the stable state of the electrons. Calculate the minimum energy, in j oules, required to free an electron at this energy level. Explain your answer. The helium atom absorbs a photon of energy 1.41 eV. i State the transition made by an electron. ii Calculate the wavelength of the radiation absorbed by the helium atom.

21 The figure below shows the energy level diagram for an atom of mercury. a Explain what is meant by the ground [1] state. b Calculate the shortest wavelength emitted by the atom. Explain your answer. [4]

[1]

[3] [2] [3]

29 Worksheet (A2)

22 For the hydrogen atom, the energy level  E n in joules is given by the equation  E n

=−

2.18 ×10 −18

n2 where n is an integer, known as the principal quantum number. a b

c

Calculate the energy level of the ground state (n = 1) and the energy level of the first excited state (n = 2). Determine the wavelength of radiation emitted when an electron makes a transition from the first excited state to the ground state. In which region of the electromagnetic spectrum would you find a spectral line with this wavelength? In which region of the electromagnetic spectrum would you find the spectral line corresponding to an electron transition between energy levels with principal quantum numbers of 6 and 7? Justify your answer.

Total:

90

Score:

[2]

[4]

[4]

%

30 Worksheet (A2) Data needed to answer questions can be found in the Data, formulae and relationships sheet. 1

2

a b

Write down Einstein’s famous equation relating mass and energy. Determine the change in energy equivalent to a change in mass: i of 1.0 g −31 ii equal to that of an electron (9.1 × 10 kg).

[1] [2] [2]

In nuclear physics, it is common practice to quote the mass of a nuclear particle in terms of the unified atomic mass unit, u. The unified atomic mass unit u is defined as one-twelfth of the mass of an atom of the carbon isotope a

b

12 6C

.

Determine the mass of each of the following particles in terms of u: −27 i an α-particle of mass 6.65 × 10 kg −26 ii a carbon-13 atom of mass 2.16 × 10 kg. Determine the mass of each of the following particles in kilograms: i a proton of mass 1.01 u ii a uranium-235 nucleus of mass 234.99 u.

[1] [1] [1] [1]

3  State three quantities conserved in all nuclear reactions. 4

5

6

a b

Explain why external energy is required to ‘split’ a nucleus. Define the binding energy of a nucleus.

c

The binding energy of the nuclide

a b

16 8O

[3] [1] [1]

 is 128 MeV. Calculate the binding energy

 per nucleon.

[2]

Define the half-life of a radioactive isotope. The half-life of a particular isotope is 20 minutes. A sample initially contains  N 0 nuclei of this isotope. Determine the number of nuclei of the isotope left in the sample after: i 20 minutes ii 1.0 hour.

[1]

The activity of an α-source is 540 Bq. The kinetic energy of each α-particle is 8.6 × 10 The isotope in the source has a very long half-life. a Calculate the number of α-particles emitted by the source in: i 1 second ii 1 hour. b Determine the total energy released by the source in a time of 1 second. c State the rate at which energy is emitted from this α-source.

[1] [2]

−14

 J.

[1] [1] [3] [1]

30 Worksheet (A2)

7

The binding energy per nucleon against nucleon number graph for some common nuclides is shown below.

a

Identify the most stable nuclide. Explain your answer.

[2] 12 6C

b

Use the graph to estimate the binding energy for the nucleus of

.

c

Use the graph to estimate the energy released in the following fusion reaction.

[2] [4]

2 2 4 1 H + 1H → 2 He

d

8

The fusion reaction shown in c is one of the many that occur in the interior of stars. State the conditions necessary to initiate such reactions in stars.

[2]

Use the data given below to determine the binding energy and the binding energy per nucleon of the nuclide

235 92 U

.

mass of proton = 1.007 u mass of neutron = 1.009 u

[7] mass of uranium-235 nucleus = 234.992 u

30 Worksheet (A2)

9

a b

Describe the process of induced nuclear fission. The diagram shows the fission of uranium-235 in accordance with the nuclear equation: 235 1 95 139 92 U + 0 n → 38 Sr + 54 Xe +

i ii

[1]

2 01 n

Copy the diagram, adding labels to identify the neutrons, the strontium nuclide and the xenon nuclide. Explain why energy is released in the reaction above.

[1] [2]

iii Use the following data to determine the energy released in a single fission reaction

involving

235 92 U

mass of

and 01 n .

[5]

−25 235  kg 92 U = 3.902 × 10

mass of 01 n

−27

 1.675 × 10

=

 kg

mass of

−25 95  kg 38 Sr  = 1.575 × 10

mass of

−25 139  kg 54 Xe = 2.306 × 10

10 One of the neutron-induced fission reactions of uranium-235 may be represented by the following nuclear equations. 235 92 U

 + 01 n

→

236 146 92 U → 57 La

236 92 U

 +

87 35 Br  +

3 01 n

The binding energies per nucleon for these nuclides are: 236 92 U,

7.59 MeV;

146 57 La,

8.41 MeV;

87 35 Br,

 8.59 MeV.

Calculate the energy released in MeV when the 11 The half-life of the radon isotope a b

220 86 Rn −1

236 92 U

nucleus undergoes fission.

[3]

 is 56 s.

Determine the decay constant in s .

[3] 10

Calculate the activity of a sample containing 6.0 × 10 nuclei of

220 86 Rn

.

[3]

14 9 12 The activity of a radioactive source containing 8.0 × 10  undecayed nuclei is 5.0 × 10  Bq. −1 a Determine the decay constant in s . b Calculate the half-life of the nucleus. c How many undecayed nuclei will be left after 40 hours?

13 a b

Define the decay constant of a nucleus. The thorium isotope

227 90 Th

[1]

 has a half-life of 18 days.

A particular radioactive source contains 4.0 × 1012 nuclei of the isotope i

[3] [3] [3]

Determine the decay constant for the thorium isotope

227 90 Th

227 90 Th

.

in s−1.

ii What is the initial activity of the source? iii Calculate the activity of the source after 36 days.

[3] [3] [2]

14 A sample of rock is known to contain 1.0 µg of the radioactive radium isotope 226 88 Ra .

The half-life of this particular isotope is 1600 years. The molar mass of radium-226 is 226 g. 226 88 Ra

a

Determine the number of nuclei of the isotope

in the rock sample.

b

Calculate the activity from decay of the radium-226 in the sample.

[2] [3]

30 Worksheet (A2)

15 In a process referred to as ‘annihilation’, a particle interacts with its antiparticle and the entire mass of the combined particles is transformed into energy in the form of photons. The following equation represents the interaction of a proton (p) and its antiparticle, the antiproton ( p ). 1 1 1 p + −1 p → γ + γ

The antiproton has the same mass as a proton – the only difference is that it has a negative charge. Determine the wavelength λ  of each of the two identical photons emitted in the − reaction above. (Mass of a proton = 1.7 × 10 27 kg.)

[5]

16 Does fusion or fission produce more energy per kilogram of fuel? Answer this question by considering the fusion reaction in 7 c and the fission reaction in 9 b. (The molar masses of hydrogen-2 and uranium-235 are 2 g and 235 g, respectively.)

[7]

17 Some astronomers believe that our solar system was formed 5.0 × 109 years ago. Assuming that all uranium-238 nuclei were formed before this time, what fraction of the original uranium-238 nuclei remain in the solar system today? The isotope of uranium 238 92 U

 has a half-life of 4.5 × 109 y.

[4]

Total:

100

Score:

%

31 Worksheet (A2) 1

The flowchart below shows the components that make up an electronic sensor. sensing device

What are the names of the missing components? 2

3

A thermistor is an example of a sensing device. a b

Sketch the temperature characteristic of a negative temperature coefficient thermistor. State the name of one other sensing device.

[2] [1]

a

Describe the structure of a metal-wire strain gauge.

[2]

b

A strain gauge contains 15 cm of wire of resistivity 5.0 strain gauge is 150 Ω. i ii

4

5

[2]

−7

× 10

Ω m.

The resistance of the

Calculate the cross-sectional area of the wire in the strain gauge. Calculate the increase in resistance when the wire extends by 0.1 cm, assuming that the cross-sectional area and resistivity remain constant.

[2] [1]

a

What is meant by negative feedback ?

[2]

b

State two advantages of negative feedback in an operational amplifier.

[2]

The circuit shown is used to produce a graph of V out against V in by moving the slider on the variable resistor. The supply voltage to the op-amp is + V s.

31

Worksheet

The graph obtained is shown.

a b c d

e

f 

6

[2] [1] [1]

i  Rin is halved in value but  Rf  is kept unchanged ii  Rf  is halved in value but  Rin is unchanged from the initial value iii the supply voltage V s is increased.

[2] [1] [1]

The variable resistor is removed and an a.c. signal of maximum voltage ±1.0 V is applied to the input of the amplifier circuit. Sketch the output voltage and input voltage on the same graph. Explain why the amplifier circuit produces distortion if an a.c. signal with a maximum voltage of 3.0 V is applied to the input.

[2]

In the circuit shown in question 5 the input voltage a b c d e

7

State the type of amplifier drawn. Explain how the graph shows that the amplifier is of this type. State why the graph flattens at the ends. Suggest the value that was used for the supply voltage V s. State what changes occur to the graph if:

V in is

[2]

1.0 V and  Rin is 2.0 k Ω.

Explain why the potential at the inverting input ( −) is almost zero. State the value of the fall in potential across Rin. Calculate the current in Rin. Explain why the current in  Rf  is the same as the current in  Rin. Determine the value of Rf . You will need to use the graph from question 5.

[2] [1] [1] [1] [1]

An electrical device generates a potential of +1.0 mV at point P.

a b

State two properties of an ideal operational amplifier. Assuming that the operational amplifier is ideal, calculate:

[2]

the current in the 10 k Ω resistor the potential at R   the gain of the amplifier using your answer to b ii  the potential difference between R  and Q.

[2] [1] [1] [1]

i ii iii iv

31

8

The circuit shows a non-inverting amplifier with an output voltage of 8.0 V.

a b c d e 9

Worksheet

State two differences between an op-amp used as an inverting amplifier and as a non-inverting amplifier. Calculate the gain of the amplifier shown in the circuit. Calculate the value of the input voltage V in. Calculate the value of the current in the 40 k Ω resistor. Determine the voltage across the 20 k Ω resistor.

[2] [2] [1] [2] [1]

The circuit shows an op-amp used as a comparator.

a b c

Explain how the op-amp acts as a comparator. [2] + − State the value of V out when V   is larger than V  . [1] The resistors and the thermistors are all chosen to have the same resistance, as closely as can  be measured. i ii

Explain why the value of V out is uncertain. The temperature of thermistor X falls. Explain what, if anything, happens to V −, V + and V out.

[1] [3]

10 A device is to be placed on the output of the circuit shown in question 9, such that when the output voltage is +9 V green light is emitted and when the output voltage is −9 V the light emitted is red. a b

Draw the circuit diagram of the device. Explain how the device works.

[2] [2]

Total:

58

Score:

%

32 Worksheet (A2) Data needed to answer questions can be found in the Data, formulae and relationships sheet. 1 State the nature of X-ray radiation.

[2]

2 The energy of an X-ray photon is 50 keV. a b

Calculate the energy of the photon in joules. Calculate the wavelength of the X-rays.

[2] [2]

3 One of the interaction mechanisms between X-rays and matter is the photoelectric effect.  Name the two other interaction mechanisms.

[2]

4 State one main difference between the images produced by a normal X-ray machine and by a CAT scan.

[1]

5 Briefly explain what is meant by a non-invasive technique.

[1]

6 State what is meant by ultrasound.

[2]

7 The speed of ultrasound in soft tissue is 1.5 km s −1. a b

Calculate the wavelength of ultrasound of frequency 1.8 MHz. Use your answer to part a to explain why high-frequency ultrasound is suitable for medical scans.

8  Define acoustic impedance. 

[2] [1] [1]

9 The table below shows useful data for biological materials. Material

Density / kg m−3

soft tissue

1060

1540

1.63

muscle

1075

1590

1.71

 bone

?

4000

6.40

 blood

1060

1570

1.66

Speed of ultrasound / m s−1

Acoustic impedance Z / 106 kg m−2 s−1

Calculate the density of bone. Calculate the percentage of intensity of ultrasound reflected at the blood–soft tissue  boundary. (Assume the waves are incident at right angles to the boundary.) c Explain why it would be difficult to distinguish between blood and soft tissue in an ultrasound scan. a b

10 Name the five main components of an MRI scanner.

[2] [3] [2] [5]

11 Protons have a precession frequency of 40 MHz in a strong uniform magnetic field. a b c

Describe what is meant by precession. State the frequency of the radio frequency (RF) radiation that will cause the protons to resonate. Use your answer to b to determine the wavelength of the RF radiation.

[1] [1] [2]

32 Worksheet (A2)

12 Briefly describe the production of X-rays and explain why an X-ray spectrum may consist of a continuous spectrum and a line spectrum.

[7]

2 13 The intensity of a collimated X-ray beam is 250 W m .

a  Define intensity. b The diameter of the X-ray beam is 4.0 mm. Calculate the power transmitted by the beam.

[1] [2]

14 Describe what is meant by a contrast medium and state why it is used in X-ray scans.

[2]

15 The potential difference between the cathode and the anode of an X-ray tube is 80 kV. Calculate the minimum wavelength of the X-rays emitted from this tube.

[3]

16 The photoelectric effect is one of the attenuation mechanisms by which X-ray photons interact with the atoms in the body. Describe some of the characteristics of this mechanism.

[3]

17 A collimated X-ray beam is incident on a metal block. The incident intensity of the beam is  I 0. a b c

18 a b

Draw a sketch graph to show the variation with thickness  x of the intensity  I of the beam. Write down an expression for the intensity  I in terms of I 0 and x. Explain any other symbol you use. The linear absorption coefficient of a beam of 80 keV X-rays is 0.693 mm 1 in copper. Calculate the thickness of copper necessary to reduce the intensi ty of the beam to 0.10  I 0.

[3] [2]

Describe the use of a CAT scanner.

[5]

Compare the image formed in X-ray diagnosis with that produced by a CAT scanner.

[3]

[3]

19 Outline how ultrasound may be used in medical diagnosis.

[5]

20 Explain why, in medical diagnosis using ultrasound, a coupling medium is necessary  between the ultrasound probe and the skin.

[6]

21 a

b 22 a b

When an ultrasound pulse reflects from the front and back edges of a bone, it produces two peaks on an A-scan. The time interval between these two peaks is 13 µs. The speed of the ultrasound in bone is 4000 m s 1. Calculate the thickness of the bone.

[3]

Describe how a B-scan differs from an A-scan.

[2]

Outline the principles of magnetic resonance.

[6]

Outline, with the aid of a sketch diagram, the use of MRI (magnetic resonance imaging) to obtain diagnostic information about internal body structures.

23 X-Rays, ultrasound and MRI are all used in medical diagnosis. State one situation in which each of these techniques is preferred and give reasons, one in each case, for the choice.

Total:

104

Score:

[10]

[6]

%

33 Worksheet (A2) 1

Two amplitude-modulated radio waves are shown. Each wave has the same carrier frequency and is carrying an audio signal.

a

State and explain one similarity and one difference between the audio signals that they carry. b  Explain how the graphs show that the carrier frequency is the same. 2

a b

c

3

Describe the difference between amplitude and frequency modulation. A carrier wave has a frequency 800 kHz. It is modulated in frequency by an audio signal of frequency 6 kHz and amplitude 2.0 V. The frequency deviation of the carrier wave is 30 kHz V−1. i Determine the maximum frequency shift produced. ii Determine the minimum frequency of the modulated carrier wave. iii Describe how the frequency of the carrier wave changes. A country intends to start a new broadcasting system. State two reasons why it is more expensive to set up an FM broadcasting system rather than an AM system.

[4] [1] [2]

[1] [1] [1] [2]

The graph shows the frequency spectrum of an AM radio wave carrying an a udio signal of a single frequency.

35 a

b

c

40

45

Frequency / kHz

i

State the name of the component with frequency 40 kHz. ii State the name of the components with frequency 35 and 45 kHz. iii Determine the frequency of the audio signal. Calculate the time for one complete carrier wave. i ii Calculate the time for one complete wave of the audio signal. iii Sketch a graph of the variation of the signal with time. On your graph mark the values obtained in b i and b ii. The frequency spectrum shown above is formed from a carrier wave and an audio signal of one frequency. Draw the frequency spectrum formed at one instant if the audio signal contains a range of frequencies up to 15 kHz.

AS and A Level Physics

Original material © Cambridge University Press 2010

[1] [1] [1] [1] [1] [3]

[2]

1

33 Worksheet (A2) 4

5

Data is often produced as an analogue signal and then converted into digital form for transmission. a Explain, with the aid of sketch graphs, the difference between an analogue and a digital signal. b Explain the process of sampling in which an analogue signal is turned into a digital signal.

[4] [3]

The diagram shows the analogue signal from a microphone.

For transmission, the signal is digitally sampled every 0.5 ms starting at time t  = 0 s. In the analogue-to-digital (ADC) converter, 0 to 0.99 mV produces a digital output 0000 1 to 1.99 mV produces a digital output 0001 and so on. a b

c

6

7

State the value of the digital out put when t  = 0 s and when t  = 0.5 ms. The digital signal from the ADC is eventually converted back into analogue form. Draw a sketch diagram showing the final analogue signal produced. i Explain how increasing the sampling frequency improves the final analogue signal  produced and suggest a suitable maximum value for the sampling frequency. ii Telephone systems use 8-bit numbers, rather than 4-bit numbers. Explain why this improves the final analogue signal produced.

A laser provides power input of 6.0 mW into an optic fibre, where the average noise is 2.0 × 10−19 W. Calculate the signal-to-noise ratio in dB. A signal has a power of 1.0 mW and a noise of 0.001 mW. a What is the signal-to-noise ratio in dB? b The signal is attenuated by 30 dB and the noise remains constant. What is the new signal-to noise ratio in dB?

AS and A Level Physics

Original material © Cambridge University Press 2010

[2] [3] [3] [2] [1] [1] [2]

2

33 Worksheet (A2) 8

9

In the modern telephone system, more and more coaxial cable has been replaced for long-distance transmission of telephone signals by optic fibre. State and explain two reasons for this change. a

b

10 a b

c

11

State a typical value of wavelength for: i space waves ii sky waves. Explain why satellite communication is more reliable than a sky wave for long-distance communication between two points on the Earth’s surface. Describe the orbit of a geostationary satellite. State a typical wavelength for communication between the Earth’s surface and a geostationary satellite. State one advantage and one disadvantage of the use of a geostationary satellite rather than a satellite in polar orbit for telephone communication.

In the original telephone system of 1876, every telephone was connected to every other telephone by a pair of wires. Today the telephone is used worldwide as the result of the invention of the exchange and the use of sampling using digital electronics. Describe how each of these developments has meant that many telephone conversations can take place at once.

Total:

AS and A Level Physics

61

Score:

Original material © Cambridge University Press 2010

[4]

[2] [2] [3] [1] [2]

[4]

%

3