A formula sheet and table of physical constants is attached to this paper. Linear graph paper is available.

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1 DEPARTMENT OF PHYSICS AND ASTRONOMY Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. Liner grph pper is vilble. Spring Semester PHYSICS PHY009: 3 HOURS Answer questions ONE nd FIVE plus TWO others from section A, nd TWO others from section B, SIX questions in ll. Answers to different sections must be written in seprte books, the books tied together nd hnded in s one. All questions re mrked out of twenty. The brekdown on the right-hnd side of the pper is ment s guide to the mrks tht cn be obtined from ech prt. Plese clerly indicte the question numbers on which you would like to be exmined on the front cover of your nswer book. Cross through ny work tht you do not wish to be exmined. 1 PHY009 TURN OVER

1. COMPULSORY SECTION A () The reltive tomic mss of Aluminium is 26.98 u. Clculte the mss of n Aluminium tom in kg. [2] Describe wht thermometric property is.

2 1. COMPULSORY SECTION A () The reltive tomic mss of Aluminium is u. Clculte the mss of n Aluminium tom in kg. [2] Describe wht thermometric property is. [2] (c) A cylinder open to the ir contins freely moving seled piston. The volume underneth the piston contins fixed mount of gs. Initilly this gs is t temperture T of 20 C nd occupies volume V of m 3. The initil pressure of the gs is equl to P. (i) Clculte the volume of the trpped gs when its temperture hs risen to 90 C. [3] The mss of ech gs molecule in the cylinder is kg. Clculte the totl mss of gs contined within the trpped prt of the cylinder. [3] (d) (i) A long unlgged copper rod hs het source t one end nd het sink t the other. Sketch grph showing the vrition in temperture of the rod ssuming stedy stte conditions hve been reched. [2] The rod is now lgged. Sketch nother grph showing the vrition in temperture of the rod ssuming stedy stte conditions hve been reched. [2] (e) Define in full the liner expnsivity α of mteril. [3] (f) Clculte the tensile stress produced in wire of dimeter 1.20 mm when it is subjected to lod of 250 N. [3] PHY009 2 CONTINUED

2. () The Serle s Br method is to be used to experimentlly determine the coefficient of therml conductivity of n unknown mteril. (i) Define the coefficient of therml conductivity of mteril.

3 2. () The Serle s Br method is to be used to experimentlly determine the coefficient of therml conductivity of n unknown mteril. (i) Define the coefficient of therml conductivity of mteril. [2] A cylindricl metl br with rdius r = 3 cm is cooled using wter flowing t rte of m 3 s 1 through the cooling pipes. By referring to dt in the digrm bove determine the coefficient of therml conductivity of the mteril in the br. You my ssume tht the br is perfectly insulted nd tht the experiment is t therml equilibrium. [8] A 2.0 kw electric kettle is filled with 1.5 litres of wter t temperture of 8 C, switched on, nd left unttended. (i) How long will it tke for the wter to rech boiling point? [3] As the wter reches boiling point, the therml switch fils tht is supposed to switch the kettle s heting element off. How much time will it tke until the kettle hs boiled itself dry? [3] (c) Define the ultimte tensile strength of mteril. [2] (d) Define the reltive tomic mss of n element. [2] Density of liquid wter = 1000 kg m -3 Specific het cpcity of liquid wter = 4200 J kg -1 K -1 Specific ltent het of vporistion of wter = 2260 kj kg -1 3 PHY009 TURN OVER

4 3. () Describe n electricl experiment to determine the specific het cpcity of liquid. In your nswer you must include the following: A cler nd lbelled digrm of the pprtus A list of the mesurements to be tken An explntion of how c cn be determined from the results Possible sources of uncertinty in the mesurements nd how these cn be reduced [12] A solid wll is 1.8 m high nd 4.0 m wide nd 0.6 m thick. It is mde from brick with coefficient of therml conductivity of 1.40 W m -1 K -1. Clculte the rte of het flow through the wll when the temperture difference cross it is 40 C. [4] (c) (d) The surfce temperture of str is determined to be 4800K. Clculte the wvelength t which pek rdince occurs. Stte ny ssumptions tht you mke. [3] Give n exmple of thermometer tht would be suitble for mesuring tempertures in excess of 1000 C. [1] PHY009 4 CONTINUED

5 4. COMPULSORY SECTION B () (i) Both electromgnetic nd sound wves cn be reflected. Stte two other wve phenomen tht pply to both electromgnetic nd sound wves. [2] Explin why electromgnetic wves cn be polrised but sound wves cnnot. [1] Resonnce is lrge mplitude forced vibrtion produced when the frequency of the periodic driving force is equl to the nturl frequency of the system. (i) Explin the mening of the two highlighted terms. [4] Describe n exmple of resonnce, giving detils of the driving force nd the consequences of the resonnce. [3] (c) (d) Monochromtic light with wvelength of 580 nm psses through pir of nrrow, prllel slits 0.60 mm prt. Clculte the spcing of the bright fringes formed on screen 1.40 m wy from the slits. [3] Light, in vcuum, is incident t n ngle of 42.0 on plne plstic surfce. Clculte: (i) The refrctive index of the plstic, given tht the ngle of refrction is [2] The criticl ngle for the plstic/ir interfce. [2] (e) Explin wht is ment by totl internl reflection nd stte the circumstnces under which it occurs. [3] 5 PHY009 TURN OVER

5. () Define the term frequency. [1] (c) Explin, with the id of simple sketch, the difference between trnsverse nd longitudinl wves. Give n exmple of ech type of wve.

6 5. () Define the term frequency. [1] (c) Explin, with the id of simple sketch, the difference between trnsverse nd longitudinl wves. Give n exmple of ech type of wve. [4] A mss m is suspended verticlly by spring. (i) The mss is currently in equilibrium. By referring to the forces cting upon the mss explin wht is ment by equilibrium. [2] The mss is pulled down by verticl distnce of 12 mm from its equilibrium position nd relesed. The mss oscilltes with simple hrmonic motion. Define simple hrmonic motion. [2] The displcement x, in mm, t time t seconds fter relese is given by the formul: x = 12 cos(7.85 t) Clculte: (iii) The frequency of the oscilltion. [3] (iv) The mximum velocity of the mss m. [2] An experiment is set up in drkened room where single nrrow slit is illuminted from behind by monochromtic light source. A diffrction imge is observed upon screen tht hs been plced some distnce in front of the slit. (i) Explin wht is ment by diffrction. [2] Sketch the diffrction pttern tht you would expect to observe upon the screen. [2] (iii) How wide would the slit need to be to be ble to produce first-order diffrction minimum t ngles of ± 5 from the centrl mximum if the wvelength of the light source ws 603 nm? [2] PHY009 6 CONTINUED

7 6. () The digrm below shows string of length L fixed t one end nd plced under tension with suspended mss m. The frequency of the mechnicl oscilltor t one end is ltered until stnding wve is formed on the string s illustrted. (i) Explin with reference to progressive wve how the sttionry wve is formed. Ensure tht you include reference to both the nodes nd ntinodes in your nswer. [4] Stte the number of ntinodes on the string bove. [1] The length L of the string is 0.9 m nd the frequency of the oscilltor is 120 Hz. (iii) Clculte the speed of the progressive wves on the string. [2] (iv) The weight of the suspended mss is currently 4.0 N. If the weight ws incresed to 9.0 N clculte whether sttionry wve would still be observed. [5] QUESTION 6 IS CONTINUED ON THE NEXT PAGE 7 PHY009 TURN OVER

8 6 (continued) QUESTION 6 CONTINUED FROM THE PREVIOUS PAGE A prllel monochromtic bem of light with wvelength of 630 nm is incident normlly upon diffrction grting s shown in the figure below. Bright spots re observed on the curved screen which curves round the ±90 in front of the grting. The diffrction grting hs 300 lines per mm. Clculte: (i) The spcing of the lines on the grting. [2] The ngle θ t which the first order spot is observed. [3] (iii) The number of bright spots observed on the screen [3] PHY009 8 CONTINUED

9 7. COMPULSORY SECTION C () A lser emits light with wvelength of 630 nm. Clculte the number of photons emitted every seconds to give lser power of 0.5 mw [4] (c) Describe two fetures of the Rutherford model of the tom tht distinguished it from previous tomic models nd describe the evidence tht supported this model. [3] The tomic spectr of Hydrogen cn be described by the Rydberg eqution 1 λ = R ( 1 n n 2 2 ) n 2 > n 1 The Rydberg constnt R equls m -1 Clculte: (i) The wvelength of the second trnsition of the Lymn series. [3] The shortest wvelength emitted by the Lymn series. [2] (d) (i) Describe the pprtus tht produces X-Rys nd how it functions. Ensure tht you reference the efficiency of the production of the X-rys nd the consequences of this with respect to the design of the pprtus. [3] (iii) Describe both the types of rdition observed in typicl X-Ry spectrum nd give n explntion of how these chrcteristics re produced. [3] Sketch grph illustrting typicl spectrum for X-rys emitted by tube with metl trget (numericl vlues re NOT required) clerly mrking the loction of the minimum wvelength. [2] 9 PHY009 TURN OVER

10 8. () A chrged oil-droplet (mss kg) is between pir of prllel, horizontl pltes 4.00 cm prt. The droplet is sttionry when the lower plte is t potentil of +130 V reltive to the upper plte. Clculte the mgnitude nd sign of the chrge on the droplet, given tht buoyncy effects re negligible. [4] In 1905 Einstein presented theory to explin the photoelectric effect using the concept of quntistion of rdition by Plnck in (i) (iii) Show with the id of suitbly lbelled digrm, the rrngement of the pprtus tht could be used to demonstrte the photoelectric effect. [3] Describe how this pprtus would be used to demonstrte the effect nd wht would be observed. [2] Describe how the photoelectric effect cn be explined in terms of the physics of quntum behviour. You my use the photoelectric eqution in your nswer but be sure to fully explin ny symbols used. [5] (c) (i) Stte wht is ment by nucler fusion. [2] In terms of the forces between nuclei, explin why the fusion of two nuclei cn only occur t high tempertures. [2] (iii) In terms of the nucler msses, explin why energy is relesed in fusion rection. [2] PHY CONTINUED

11 9. () 197 How mny neutrons re there in the nucleus of 79Au? [1] A smple of mteril initilly consists of N 0 rdioctive toms of single isotope. After time t the number N of rdioctive toms of the isotope is given by: N = N 0 exp( λt) (i) Sketch grph of this eqution. Lbel the points representing N 0 nd mrk the first two hlf-lives on the grph. [4] Explin wht is ment by the decy rte of the smple. [2] This smple is found to hve n initil ctivity of 15 kbq. Three hours lter its ctivity hs dropped to 4 kbq. Clculte: (iii) The hlf-life of this smple in seconds. [5] (iv) If the smple hs to drop to below 3750 Bq before it is considered sfe how long will it tke before this smple is deemed to be sfe? [1] (c) In n exmple of neutron induced fission of Urnium-235 the fission products re isotopes of Cesium (Cs) nd Rubidium (Rb) with n excess of neutrons n U 55Cs + ZRb + X( 0n) Z nd X re integer vlues. (i) Determine the vlues of Z nd X [2] Clculte the energy relesed per fission, given the following msses U = u Cs = u 95 ZRb = u 1 0n = u [5] END OF EXAMINATION PAPER 11 PHY009 TURN OVER

12 PHYSICAL CONSTANTS & MATHEMATICAL FORMULAE Physicl Constnts electron chrge e = C electron mss m e = kg = MeV c 2 proton mss m p = kg = MeV c 2 neutron mss m n = kg = MeV c 2 Plnck s constnt h = J s Dirc s constnt ( = h/2π) = J s Boltzmnn s constnt k B = J K 1 = ev K 1 speed of light in free spce c = m s m s 1 permittivity of free spce ε 0 = F m 1 permebility of free spce µ 0 = 4π 10 7 H m 1 Avogdro s constnt N A = mol 1 gs constnt R = J mol 1 K 1 idel gs volume (STP) V 0 = 22.4 l mol 1 grvittionl constnt G = N m 2 kg 2 Rydberg constnt R = m 1 Rydberg energy of hydrogen R H = 13.6 ev Bohr rdius 0 = m Bohr mgneton µ B = J T 1 fine structure constnt α 1/137 Wien displcement lw constnt b = m K Stefn s constnt σ = W m 2 K 4 rdition density constnt = J m 3 K 4 mss of the Sun M = kg rdius of the Sun R = m luminosity of the Sun L = W mss of the Erth M = kg rdius of the Erth R = m Conversion Fctors 1 u (tomic mss unit) = kg = MeV c 2 1 Å (ngstrom) = m 1 stronomicl unit = m 1 g (grvity) = 9.81 m s 2 1 ev = J 1 prsec = m 1 tmosphere = P 1 yer = s

13 Polr Coordintes x = r cos θ y = r sin θ da = r dr dθ 2 = 1 ( r ) + 1r 2 r r r 2 θ 2 Sphericl Coordintes Clculus x = r sin θ cos φ y = r sin θ sin φ z = r cos θ dv = r 2 sin θ dr dθ dφ 2 = 1 ( r 2 ) + 1 r 2 r r r 2 sin θ ( sin θ ) + θ θ 1 r 2 sin 2 θ 2 φ 2 f(x) f (x) f(x) f (x) x n nx n 1 tn x sec 2 x e x e x sin ( ) 1 x ln x = log e x 1 x cos 1 ( x sin x cos x tn ( 1 x cos x sin x sinh ( ) 1 x cosh x sinh x cosh ( ) 1 x sinh x cosh x tnh ( ) 1 x ) ) 1 2 x x 2 2 +x 2 1 x x x 2 cosec x cosec x cot x uv u v + uv sec x sec x tn x u/v u v uv v 2 Definite Integrls x n e x dx = n! (n 0 nd > 0) n+1 π e x2 dx = π x 2 e x2 dx = 1 2 Integrtion by Prts: 3 b u(x) dv(x) dx dx = u(x)v(x) b b du(x) v(x) dx dx

14 Series Expnsions (x ) Tylor series: f(x) = f() + f () + 1! n Binomil expnsion: (x + y) n = (1 + x) n = 1 + nx + k=0 ( ) n x n k y k k n(n 1) x 2 + ( x < 1) 2! (x )2 f () + 2! nd (x )3 f () + 3! ( ) n n! = k (n k)!k! e x = 1+x+ x2 2! + x3 x3 +, sin x = x 3! 3! + x5 x2 nd cos x = 1 5! 2! + x4 4! ln(1 + x) = log e (1 + x) = x x2 2 + x3 3 n Geometric series: r k = 1 rn+1 1 r k=0 ( x < 1) Stirling s formul: log e N! = N log e N N or ln N! = N ln N N Trigonometry sin( ± b) = sin cos b ± cos sin b cos( ± b) = cos cos b sin sin b tn ± tn b tn( ± b) = 1 tn tn b sin 2 = 2 sin cos cos 2 = cos 2 sin 2 = 2 cos 2 1 = 1 2 sin 2 sin + sin b = 2 sin 1( + b) cos 1 ( b) 2 2 sin sin b = 2 cos 1( + b) sin 1 ( b) 2 2 cos + cos b = 2 cos 1( + b) cos 1 ( b) 2 2 cos cos b = 2 sin 1( + b) sin 1 ( b) 2 2 e iθ = cos θ + i sin θ cos θ = 1 ( e iθ + e iθ) 2 nd sin θ = 1 ( e iθ e iθ) 2i cosh θ = 1 ( e θ + e θ) 2 nd sinh θ = 1 ( e θ e θ) 2 Sphericl geometry: sin sin A = sin b sin B = sin c sin C nd cos = cos b cos c+sin b sin c cos A

15 Vector Clculus A B = A x B x + A y B y + A z B z = A j B j A B = (A y B z A z B y ) î + (A zb x A x B z ) ĵ + (A xb y A y B x ) ˆk = ɛ ijk A j B k A (B C) = (A C)B (A B)C A (B C) = B (C A) = C (A B) grd φ = φ = j φ = φ x î + φ y ĵ + φ z ˆk div A = A = j A j = A x x + A y y + A z z ) curl A = A = ɛ ijk j A k = ( Az y A y z φ = 2 φ = 2 φ x + 2 φ 2 y + 2 φ 2 z 2 ( φ) = 0 nd ( A) = 0 ( A) = ( A) 2 A ( Ax î + z A ) ( z Ay ĵ + x x A ) x y ˆk

Data Provided: A formula sheet and table of physical constants is attached to this paper.

Data Provided: A formula sheet and table of physical constants is attached to this paper. PHY15-B PHY47 Dt Provided: Formul sheet nd physicl constnts Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. DEPARTMENT OF PHYSICS & Autumn Semester 009-010 ASTRONOMY DEPARTMENT