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GCE MAY 2009 : A2 2 Electromagnetism and Nuclear Physics

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Centre Number 71 Candidate Number ADVANCED General Certificate of Education 2009 Physics assessing Module 5: Electromagnetism and Nuclear Physics A2Y21 Assessment Unit A2 2 [A2Y21] THURSDAY 28 MAY, MORNING TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number in the spaces provided at the top of this page. Answer all five questions. Write your answers in the spaces provided in this question paper. INFORMATION FOR CANDIDATES The total mark for this paper is 90. Quality of written communication will be assessed in question 5. Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question. Your attention is drawn to the Data and Formulae Sheet which is inside this question paper. You may use an electronic calculator. Question 5 contributes to the synoptic assessment requirement of the Specification. You are advised to spend about 45 minutes in answering questions 1 4, and about 45 minutes in answering question 5. 4865 For Examiner s use only Question Number 1 2 3 4 5 Total Marks Marks If you need the values of physical constants to answer any questions in this paper, they may be found on the Data and Formulae Sheet. Examiner Only Marks Remark Answer all five questions 1 Two capacitors, C1 of capacitance 2.00 F and C2 of capacitance of 8.00 F are charged so that the energy stored in each capacitor is 5.76 10 4 J. This energy remains stored in the capacitors as they are connected in the circuit of Fig. 1.1 with switch S open. 2.00 F C1 S X Y C2 8.00 F Fig. 1 (a) Calculate the potential difference across each of the capacitors. Reminder: the switch is open at this stage. Potential difference across C1 (2.00 F) capacitor = _____________ V Potential difference across C2 (8.00 F) capacitor = _____________ V [4] 4865 2 [Turn over (b) Switch S is now closed. Examiner Only Marks Remark (i) Find the potential difference between the terminals X and Y after the switch is closed. Potential difference = _________ V [5] (ii) Describe and explain the transfer of charge between the capacitors after the switch is closed. ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ___________________________________________________ [4] 4865 3 [Turn over 2 (a) (i) State, in words, Faraday s law of electromagnetic induction. Examiner Only Marks Remark _____________________________________________________ _____________________________________________________ ___________________________________________________ [2] (ii) A flat coil of wire is placed with its plane perpendicular to a magnetic field. The flux through the coil is initially constant, but changes with time t as shown in Fig. 2.1. On the blank axes below this graph, draw a graph to show how the induced e.m.f. E in the coil changes with time t from t = 0 to t = tf + 0 tf E + 0 4865 tf Fig. 2.1 [3] 4 [Turn over (b) The output voltage E of a simple a.c. generator changes with time t as given by Equation 2.1. E = 320 sin (314t) Examiner Only Marks Remark Equation 2.1 (i) Calculate the frequency of the generator. Frequency = ________ Hz [2] (ii) Calculate the minimum time, in ms, for the output of the generator to rise from zero to 160 V in each cycle of operation. Minimum time = ________ ms 4865 [3] 5 [Turn over 3 (a) (i) State what is meant by the specific charge of the electron. Examiner Only Marks Remark _____________________________________________________ ___________________________________________________ [1] (ii) Obtain the magnitude of the specific charge of the electron to two significant figures and state its unit. Specific charge = ____________ Unit = ____________ [3] (b) The specific charge of an electron may be measured by passing a fine beam of electrons through an electric and a magnetic field which are at right angles to each other and the path of the electrons (i.e. crossed fields). Fig. 3.1 indicates a fine beam of electrons travelling perpendicularly outward from the plane of the paper between two metal plates which create a uniform electric field. On Fig. 3.1, mark the polarity of these plates to create an electric field and mark clearly using an arrow head labelled E the corresponding direction of the electric field. Mark clearly with another arrowhead on Fig. 3.1 the direction of a corresponding magnetic field B which would be needed to produce null deflection of the electron beam. [2] Fig. 3.1 4865 6 [Turn over The beam of electrons is replaced by an identical beam of positrons. (A positron is a particle identical to an electron, but with a positive charge.) State and explain whether this beam would still experience null deflection for the E and B fields you have indicated. Examiner Only Marks Remark _________________________________________________________ _______________________________________________________ [1] (c) A fine beam of electrons moves through a region where an electric field and a magnetic field act perpendicularly to each other. The electrons in the beam are not deflected when passing through this region. The magnetic field has a flux density of 1.50 10 3 T, and the electric field strength is 1.78 104 V m 1. Calculate the velocity of the electrons in the beam. Velocity = ____________ m s 1 4865 [3] 7 [Turn over 4 (a) -particles, -particles and -radiation are the common types of radioactive emissions. Some of their properties are to be summarised in Table 4.1. Possible magnitudes of their speed and range in air are stated below, along with their ionisation ability. Speed/m s 1: 3 108; 2 108; 2 103; 2; Remark 2 107 Range/cm: Examiner Only Marks 10 The ionisation ability can be classified as: low, medium, or high. After considering the given information, complete Table 4.1 below by selecting and entering the appropriate data in the blank spaces of the table. Table 4.1 Radiation Speed/m s 1 Range/cm Ionisation ability -particles -particles -radiation [3] (b) A uranium nucleus 238 U undergoes a series of radioactive decays 92 before it attains a final stable state which is a nucleus of lead (Pb). The succession of particles emitted during its decay is listed below in the order in which they occur. alpha, beta, beta, alpha, alpha, alpha, alpha, alpha, beta, beta, alpha, beta, beta, alpha Find the nucleon number and the proton number of the final stable Pb nucleus. Nucleon number = ____________ Proton number = ____________ 4865 [2] 8 [Turn over (c) (i) Define the becquerel, the unit of activity for a radioactive sample. Examiner Only Marks Remark _____________________________________________________ ___________________________________________________ [1] (ii) Define the decay constant of a radioactive sample. _____________________________________________________ _____________________________________________________ ___________________________________________________ [2] (iii) The half-life of bismuth-210 for -particle emission is 5.0 days. Find the percentage loss of activity in a sample after 15 hours. Percentage loss of activity = _____ % 4865 9 [4] [Turn over 5 Comprehension question This question contributes to the synoptic assessment requirement of the Specification. In your answer, you will be expected to bring together and apply principles and contexts from different areas of physics, and to use the skills of physics, in the particular situation described. You are advised to spend about 45 minutes in answering this question. Read the passage carefully and answer all the questions which follow. In parts (c)(i) and (ii) and (d)(ii) of this question you should answer in continuous prose. You will be assessed on the quality of your written communication. Thermal aspects of X-ray tubes In X-ray tubes, fast moving electrons bombard metal targets to produce X-rays. This process is very inefficient and most of the energy of the electrons (about 99%) is converted to heat in the metal anodes of the tubes. 1 The anodes are designed to maximise heat loss by different methods. Heat transfer by conduction (mainly in solids), convection (only in fluids) and radiation 5 (by electromagnetic waves) contribute to the removal of heat from the anodes of tubes to prevent thermal damage during operation. Two anode designs are considered here, the stationary type of anode and the rotating type. Fig. 5.1 shows a labelled diagram of a stationary anode tube immersed in oil coolant within its housing enclosure. 10 Oil coolant Glass tube Enclosure Tungsten target Cathode e path Copper anode Vacuum Seal X-rays Fig. 5.1 When the tube is operating, the thin tungsten target embedded in the anode becomes very hot. It quickly transfers its heat to the massive copper anode which then transfers it to the oil. After further heat transfer processes, the heat eventually escapes to the 4865 10 [Turn over surrounding air. Thermal expansion at the seal where the copper anode passes through the glass into the oil is an important consideration. The thermal expansion of materials is governed by Equation 5.1. Lt = Lo(1 + t) 15 Equation 5.1 where Lt is the length of an object at t C, Lo is the length of the object at 0 C, is the coefficient of linear expansivity, i.e. the fractional increase of length per C temperature rise and t is the temperature of the object in C. The melting point of copper is 1083 C 20 and this imposes a practical limit on the amount of heat which may accumulate in the anode. This restricts the intensity of the X-rays the stationary anode tube can produce. Fig. 5.2 is a labelled diagram of a rotating anode tube. This design permits the anode to withstand increased power input and higher temperatures. The target for the electrons 25 to produce X-rays is a small area on the bevelled edge of the rotating anode disc. The tungsten anode disc is attached to the rotor of an induction motor which can rotate at different speeds. Oil coolant Motor coils Glass tube Enclosure Vacuum Rotor Cathode e path Rotating anode disc Target area X-rays Fig. 5.2 The anode disc is tungsten with a melting point of 3380 C. As the disc rotates, each area on the anode is exposed to the bombarding electron beam for only a short time in 30 each revolution. Each successive area on the anode can radiate X-rays when impacted by electrons, but cools by radiation for most of the time in one revolution. The anode can thus withstand a higher mean temperature and consequently generates higher intensity X-rays from a higher energy electron beam. Similar methods of heat removal apply to this tube as for the stationary type, but radiation is the main agent of heat loss. 35 The anode may operate safely at a temperature higher than the melting point of copper, in fact the anode may reach a high enough temperature to glow without causing thermal damage. The greatest heat loss from the hot rotating surface is controlled by Stefan s law of radiation (Equation 5.2) Q = T4 4865 11 Equation 5.2 40 [Turn over where Q is the rate of emission of radiation energy from unit area of a surface in W m 2. T is the temperature of the surface in K and is the Stefan constant, 5.70 10 8 W m 2 K 4. To avoid damage due to overheating the anode of an X-ray tube, rating charts are used. These charts indicate appropriate safe limits for the operation of the tube. A rating chart 45 displays tube current in mA on its vertical axis and tube operating time in seconds on its horizontal axis. Each curve on a chart indicates the limit of safe operating conditions for a given tube anode voltage. 4865 12 [Turn over Answer ALL the following questions Examiner Only Marks Remark (a) Write a few words, or a short sentence, to show the meaning of the following words or phrases as they are used in the passage. (i) bombard (line 1) ____________________________________________________ __________________________________________________ [1] (ii) anode/s (lines 3, 4, 6 & others) ____________________________________________________ __________________________________________________ [1] (iii) oil coolant (line 9) ____________________________________________________ __________________________________________________ [1] (iv) seal (line 14) ____________________________________________________ __________________________________________________ [1] (v) melting point (lines 20 and 29) ____________________________________________________ __________________________________________________ [1] (vi) intensity (lines 22 and 34) ____________________________________________________ __________________________________________________ [1] (vii) bevelled edge (line 26) ____________________________________________________ __________________________________________________ [1] 4865 13 [Turn over (viii) glow (line 37) Examiner Only Marks Remark ____________________________________________________ __________________________________________________ [1] (b) (i) An electron current of 75.0 mA strikes the anode of the X-ray tube shown in Fig. 5.1 for a time of 1.50 s. Estimate the number of these electrons which generate X-rays (line 2). ____________________________________________________ ____________________________________________________ ____________________________________________________ Number of electrons = _______________________________ [4] (ii) The tungsten target (line 11) has a mass of 11.3 10 4 kg and its specific heat capacity is 142 J kg 1 K 1. Electrons which strike the target have been accelerated through a potential difference of 60.0 kV. Calculate the temperature rise in the tungsten target when a single electron loses all its energy to heat. Temperature rise = ________ K [4] (iii) How many simultaneous electron impacts similar to those in (ii) are required to raise the temperature of the target by 1.30 K? No. of impacts = __________ 4865 [2] 14 [Turn over (c) The tube of Fig. 5.1 has been operating for a period of time and the tungsten target in the anode has reached a high temperature. You are to consider how the heat at the hot end of the anode may be removed (line 6). For example, it could be stated that some of the energy is radiated (by electromagnetic waves) away from the anode through the vacuum to the glass of the tube. However, your task is to consider Fig. 5.1 carefully, then identify and state the direction of heat flow in two instances in the fixed anode tube where the process of conduction is used to transfer heat energy. You will then identify and state the direction of heat flow in one instance of convection for the tube. (i) Examiner Only Marks Remark Conduction considerations Identify and state the direction of heat flow in two instances of conduction for the tube. 1. __________________________________________________ ____________________________________________________ 2. __________________________________________________ __________________________________________________ [4] (ii) Convection considerations Identify and state the direction of heat flow in one instance of convection for the tube. ____________________________________________________ __________________________________________________ [2] 4865 15 [Turn over (d) (i) In Fig. 5.1, the copper anode at the end where there is a seal with the glass has a diameter of 48.5 mm at 0 C. The internal diameter of the glass at the seal is also 48.5 mm at 0 C. Differential expansion occurs between the copper anode and the glass, i.e. the copper and the glass expand by different amounts for any temperature change. Examiner Only Marks Remark The coefficients of linear expansivity (line 19) of copper and glass are 1.71 10 5 C 1 and 1.63 10 5 C 1 respectively. It is possible this seal may fracture when the difference in expansion between the copper and the glass diameters is 4.50 10 3 mm. Using this value and Equation 5.1, calculate the temperature at the seal when this difference in diameter size occurs. Temperature = __________ C [4] (ii) Normally the X-ray tube is immersed in oil. It is also possible to remove the oil and operate the tube in air. If the tube were used in air when the seal fractured, write a brief account of how this would affect the operation of the tube as it generated X-rays. ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ __________________________________________________ [4] Quality of written communication 4865 16 [2] [Turn over (e) The rotating anode of the tube shown in Fig. 5.2 rotates at high speed when the tube is in operation. A glowing ring is completely visible around the bevelled edge of the anode. The temperature of this glowing ring is 1200 C. The ring has a mean radius of rotation of 42.0 mm and is 2.30 mm wide. (i) Examiner Only Marks Remark Calculate the area of the glowing ring around the anode. Hint: consider the mean circumference and the width of the ring. Area = __________ m2 [2] (ii) Use Stefan s law (Equation 5.2) to calculate the total radiation heat loss from the glowing area of the anode in 1.50 s. Heat loss __________ J [3] (iii) The absolute temperature of the glowing ring is reduced by 10%. Calculate the corresponding percentage reduction in the rate of emission from the glowing ring for this temperature decrease. Percentage reduction = __________ % 4865 17 [2] [Turn over (f) You are now to consider curves on an X-ray tube rating chart (lines 45 48). On Fig. 5.3 is a curve which shows the limit of safe operating conditions to avoid overheating the anode in a given tube for an anode operating voltage of 60 kV. (i) Examiner Only Marks Remark On Fig. 5.3, starting at the point P (150 mA), sketch another curve for an anode operating voltage of 40 kV. Label the curve you have drawn 40 kV . [2] (ii) On Fig. 5.3, considering the curve you have drawn and the given curve, shade the area which indicates the safe operating region for the anode for both operating voltages, 40 kV and 60 kV. Tube current/mA 150 P 100 50 60 kV 0 0.1 1.0 Tube operating time/s 10 Fig. 5.3 20 [2] THIS IS THE END OF THE QUESTION PAPER 4865 18 [Turn over 937-052-1 [Turn over

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Additional Info : Gce Physics May 2009 Assessment Unit A2 2, Module 5: Electromagnetism and Nuclear Physics
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