Binding Energy per Nucleon (BEA) andStabilityThe experimental results give the following binding energy per nucleon vs. nucleon number () graph: Figure ANuclear Fusion1 1H + H4 1In nuclear fusion, two light nuclei join together to form one heavier nucleus. FissionExample92 0141 92 1Ba + Kr + 3 n + energyIn nuclear fis massnuclides; whereas nuclides of nucleon number greater than 56 tend to undergo nuclear fission toproduce more stable nuclides (see Fig. total nucleon no. of reactants = total nucleon no. of productstotal mass-energy of reactants = total mass-energy of productstotal momentum of reactants = total momentum of productsThe energy released (∆E) in a nuclear reaction may be calculated by:2 E m cwhere: mThe energy released (∆E) in a nuclear reaction may also be calculated by:E BE EB………. (i)B A= binding energy per nucleon ×  :B:of total reactantsto for thenuclear take place.CL

2 Radioactive Decay  spontaneously emits ionisingradiations (or alpha/beta/gamma radiations). [2 or 3]Radioactive decay is a random process; that is, it cannot be predicted when a particular nucleus[1 or 2]Radioactive decay is a random process because each nucleus in the sample (of a radioactiveisotope) has the same probability of decay, which remains constant over time. aspressure). ) and Decay Co)=A………. (i)where ∆is the number of nuclei decayed in time interval ∆. As all undecayed nuclei (N=………. (ii)/=tSo, decay constant (of a radioactive isotope) is the probability of decay of a nucleus per unit time. [2]Note( X)Zcontaining N nuclei is given by: = × uwhere 1u (= 1.66 × 10 kg) is the unified atomic mass unit.Decay Curveand Half)N N………. (iii)where N0 is the initial number of undecayed nuclei in the sample (i.e. at , tC), activity (Ato each other (i.e. A so count rate (C) and activity (A) after time can also be given by the ………. (iv)= expA A………. (v)NUCLEAR PPage of

UCLEAR PHYSICSEq. (iv) gives count rate vs. time graph of the following shape: Figure .3 (a) 23.3Notes (or the [2]t) by:1/2=tPutting the above expression for  into Eq. (v) gives: 1/20.693= expttSample ProblemShow that the half-life (1/2) and decay constant (1/20.693=[2 or 3]In one half-life, the number of undecayed nuclei (N) left in the sample reduces to one half of its initial value (NNt= t1/21/20NtN1/2= exp2tln(1/ 2) =tHence: 1/2103 of

M PHYSICS1 Generation and Detection of Ultrasound WavesPiezo-A is a device that converts energy from one form to another.For example, piezo-electric microphone that converts sound to electrical energy is a transducer. of which are coated with thin layers of a metal (e.g. silver) to provide electrical connections, as shown in Fig. 24.1.Figure 24.1. The magnitude of theatmospheric pressure; and the polarity of the voltage depends on whether the crystal is compressed .2). (a)(b) compressed(c) extended24.2Piezo-electric MicrophoneFigure 24.3.3. Here, the crystal and the amplifier act as a simple microphone. specific acoustic impedance of the medium:the attenuation of ultrasound in matterZ c=2R 2 11Z Z)I Z ZIthe r:X-ray photon energy = KE of colliding electronc=ccof

M PGeneration and Detection of UltrasoundWave usinga Piezo-Figure 24.4When a conalternating voltage of ultrasound frequency (range) is applied across it, it starts vibratingtage. In other words, it starts generating ultraso(of the same frequency as that of the incident ultrasound pulseis induced across it, which can beNotesThin layers of silver on the opposite sides of the crystal act as electrical contacts.range. This is done so that resonance would take place at theuency, and[5 or 6]

2 Specific Acoustic Impedance (Z) IfFigure .5then specific acoustic impedance of the medium is given by: So, the specific acoustic impedance (Z) of a medium may be defined as the product of . [2]3 Intensity Reflection Coefficient () Figure .6TI………. (i)The experimental results show that: 221( )=(+)I Z ZIZ Z………. (ii)where IRI is the fraction of incident wave intensity reflected from the boundary; it is commonly known 22 1(=)………. (iii)Dividing Eq. (i) by IT1=I ITI IT=1Iwhere ‘I is the fraction of incident wave intensity transmitted across the boundary; it is commonly known as the intensity transmission coefficientNotesmedia (i.e. Z2[2]M PHYSICS106

MEDICALHYSICS4 Linear Absorption (or Attenuation) Coefficient () Figure .7I0I I………. (i)where is the linear absorption coefficient (also known as the linear attenuation coefficient) of the 0= eIn the above equation, ‘II0x beam of ultrasound (or X-rays).Half-value Thickness (Eq. (i) gives the following Ix graph: Figure The half-value thickness (x1/2) of a medium is related to its linear absorption coefficient () by: 1/2i.e. 1/20.693=Page 132

5 Writing Expression for Fraction of Incident Wave Intensity Finally Received Example 1If: we can writ31 3 2 1= × ×I1 1II  (where:2 1()=( + )) Example 2If: Figure 2410then we can write:4 4 231 3 2 1= × ×I I III I I I2 2IIMEDICAL Pof 132

MEDICAL PHYSICS6 Ultrasound Scan It is of two types: 1 A-scan 2 B-scan Figure 24.11Figure (b)A short pulsemedium (e.g. gel) is applied to the skin to reduce reflection (or to increase transmission) at theskin (see Fig. 24.11 (a)).bone boundary).The reflected pulses are detected by the same transducer.The detected pulses are then processed and displayed on the screen of CRO (see Fig. t) between the transmission and receipt of the pulse gives information about the of the boundary beneath the skin (corresponding to each reflection). of the boundary,as the degree of reflection depends upon the specific acoustic impedances of the two media atthe boundary.skin is very small (i.e. Z1of ultrasound is transmitted into the body. This also allows gnal to be distinguishedfrom the emitted signal, and hence the depth of the boundary to be determined. B-109

7 Production of X-Rays Fig. 2412 shows a schematic diagram of the arrangement used to produc-rays. Figure 12X-ray production takes place by two processes: When a charged particle, such as an electron, accelerates (or decelerates), EM radiation ismagnitude of acceleration of the charged particle.As the electrons hitting the target metal have a continuous distribution (i.e. range) ofaccelerations, the EM radiation (i.e. X-rays) produced has a continuous distribution ofwavelengths. [3]2.DeThe subsequent de-excitation of these electrons results in the production of X-ray photons.de-excitation ofelectrons have discrete wavelengths.243 shows a typical spectrum (i.e. intensity vs. wavelength graph) of the X-rays produced by 24.12. Figure 24Notes Electrons that give up all of their kinetic energy in a single collision undergo maximumdeceleration; this results in the production of X-ray photons of maximum energy or of minimumwavelength cut-wavelength[2]By energy conservation:max. X-ray photon energy = KE of colliding electron chceVwhere ceanode voltage (see Fig. 12MHYSICSPage of

8 Modern X-Ray Tube Fig. 24.14 shows the design of a typical modern X-ray tube. .14The X-rayThe intensity of X-ray beam is controlled by changing the current in the filament. The greater the current in the filament (or voltage Vand [2 or 3]the more penetrating it is. [1]It is controlled by changing the anode voltage (V2). The greater the anode voltage, the greater the KE energy of X-ray photons, and hence the greater the hardnesMEDICAL PHYSICSPage 111

MEDICAL PHYSICS9 Linear Absorption (or Attenuation) Coefficient (Figure 24.15 and I0 are rel= eI I………. (i)where [3]Notes[1] of a wave is the (gradual) reduction in the power (or intensity or amplitude) of the[2]Half-value Thickness (1/2)Eq. (i) gives the following I vs. x graph: Figure .16x1/2) of a medium is related to its linear absorption coefficient (1/2ln2=xi.e. 1/20.693x112

10 X-Ray Scan [3]24A beam of X-rays in[4 or 5]ContrastAn X-ray image is said to have 'good' contrast (or high contrast) if it has areas of both: little blackening and heavy blackening (see Fig. 24.20).Figure 24.[1]The larger the difference between ‘x’ values along different lines (e.g.21), the better the contrast of the X-ray image. Figure 21Contrast of an X-r1.using a contrast medium (e.g. stomach may be examined by giving the patient a drink containingincreasing the exposure time3. P

12 PETAnnihilation2430Figure 24Notes 2ewhere h is the Planck constant, is the frequency of -ray photon, mand TracerTracer is a substance containing radioactive nuclei that can be introduced into the body to be absorbed by the tissue being studied. [2] decay.most commonly used tracer in PET scanning is fluorodeoxyglucose. It is a glucose-based tracer. Different tissues/organs absorb it at different rates. For example, cancer cells that are metabolically more active than the surrounding healthy cells absorb it at a higher rate and thus emit + radiation at agreater rate) CT Scanning of Patient’s bodyFigure 24.29from different angles.The procedure is repeated for successive slices.can be rotated and viewed from any angle. M

MEDICAL PPET ScanFigure 24.31In the PET sshort distancetons travelling in the oppositedirections-ray photons from the annihilation event travel outside the body and are detected by an24.31The detected signals are then fed to a computer that uses the time lapse between the twoing at the detectors to determine the position of the annihilation event (on the line ofresponse).of the tracer inregion; so the image formed by the computer is actually the image of thetracer concentration in the tissue. [6]Note from the inside. [1]115 of 132

ASTRONOMYAND COSMOLOGY 1 Standard Candles Luminosity ()itAccording to the , the luminosity of a star is given by the expression: = 4where  (= 5.67 × 10 W m–) is Stn constantThe luminosity of the Sun is about 3.83 × 1026W.In astronomy, an object of known luminosity is called a .Two well-known standard candles are:2.Radiant Flux Intensity (Figure d from 2=(as: intensity = powerareaStefan-Boltzmann law:Radiant flux intensity:Wien’s Displacement Law:L= 42maxmax1fvSo, the radiant flux intensity may be defined as the radiant power passing normally through a surface [1 or 2]Page

ASTRONOMYAND COSMOLOGYNotesThe above expression for radiant flux intensity assumes that:1.the 2.there is negligible absorption of this radiated power between the star and the Earth. is constant, so we can write:F2dthat is, the radiant flux intensity (Frse square law with F) the Earth, NOT on itsDetermining Distance () of a StaMeasure the radiant flux intensity (F) of light received on the Earth from the star.d2=4d1

2 Stellar Radii Black BA black body is an idealised object that absorbs all electromagnetic radiation falling on it. Figure Note that the higher the surface temperature of a (black) body: 1.the shorter the wavelength at the peak (i.e. maximum) intensity;the greater the intensity of the electromagnetic radiation at each wavelength.TtheT………. (i)The above relationship is known as the Wien’s displacement law.The experimental value of the constant in Eq. (i) is 2.9 × 10 m K.T andT, we can write:. = .………. (ii)max2L)2.temperature TL2TASTRONOMY118 of 132

Now it's your turn1 State two factors that affect radiant flux intensity from a star. 2 The radiant flux intensity F23 –9 W m–the star is 5.0 × 10 W. Calculate the distance of this star from the Earth.4 nm. Calculate the surface temperature of a star with wavelength 350 nm at peak intensity. 5 The luminosity of a star is 520 times that of the Sun. The wavelength of light at peak intensity for the star is 740 nm and the wavelength of light at peak intensity for the Sun is 500 nm. (a) (b) radius of the starradius of the SunAnswers1 luminosity of the stardistance from the centre of the star2, soFd0.32 × ()= F14 W m–22=Fdd= × = constant5 (a) maxT = constant As max is longer for the star than for the Sun, so the star is cooler than the Sun (i.e. has lower (b)L = 42T44=4Lr4and Tmax1, so: r4Lradius of the star=4×500= 50 ASTRONOMYANDPage 119

ASTRONOMYAND COSMOLOGY3 Redshift of Electromagnetic Radiation from Distant Stars and the Expansion of Universe When a source of waves moves towards a stationary observer, the observed wavelength isshorter than the actual wavelength of the waves. [1]longer than the actual wavelength of the waves. [1]NoteGalaxiesFig. 25.3 shows the absorption line spectrum of light from the Sun, and Fig. 25absorption line spectrum of light from a distant galaxy. Note that the observed wavelengths of allspectral lines from the distant galaxy are longer than the ones from the Sun. This is known as Figure .3The galaxies are receding (i.e.moving away) from us. In other words, the Universe is expanding. The fractional change in the wavelength (or frequency) of a spectral line from a galaxy is relatedto its recession speed v by:fvcwhere c is the speed of light in a vacuum. 6 7 The Tadpole galaxy has a recession speed of 9400 km s1wavelength of the observed spectrum. Answers6 v8= × = 0.15×(3.0×10 ) = 4.5×10 m s7 v38== 0.0313.0×10(a)absorption from the absorption lines

4 Hubble’s Law andthe Big Bang Theory billion years ago). The event that marks the birth of the Universe is called the Big Bang, and the idea Hubble’s LawWhat’s more is that the more distant a galaxy, the faster it moves. Hubble’s law states that the recession speed v of a galaxy is proportional to its distance d from us. [1]Mathematically: d =0where H018 s–All galaxies in the Universe are moving away from us. This implies that, at some point in the past, they [2]Examplevapproximate time interval t between the Big Bang and the current time (i.e. the age of the Universe) =dvNoteIn the above example, we assumed that the recession speed of the galaxy had remained unchanged 8 ×10m from us and is moving away at–.(a) Calculate the Hubble constant based on this data. (b) 25m.Answerv= H0718 1= = = 2.2×10 s9.5×10v (b)v= constantv7=1.9×10 9.5×10vv = 4.2 × 107ASTRONOMYPage 121

Collection of Explanation Questions 12 Motion in a circle Define the radian. an arc of length equal to the radius of the circle. Angular speed is the angle swept out per unit time. 13 Gravitational fields State what is meant by a . force acting between two masses OR force on a mass in a gravitational field Define bringingunit mass from infinity to that point Define gravitational field Distinguish between free oscillations and forced oscillations. ies associated with its molecules

pV = nRT. State what is meant by the symbol. the symbol the symbol Tthermal energy per unit mass per unit change in temperature hange the temperature of substance by one degree Define specific latent heatDefine specific latent heat of vaporization. thermal energy per unit mass to gas at constant temperature Gas molecules are hard elastic identical spheres. thermal equilibrium. Force per unit charge acting on Define electric potential Work done per unit charge in bringing unit positive charge fromcapacitancesmoothing direct current Explain why the capacitor is said to store energy but not charge. The plates of the capacitor havThe work is done to separate the opposite charges. The work done is stored in the capacitor in the form of energy.Explain the exponential decay of with Current causes capacitor to lose charge.

20 Magnetic fields Explain what is meant by a field of forceA region of space where a force is experienced by a body. e a force acts on a current-cahere a force acts on a moving charge tron in the magnetic field is tcular to direction of motion. Magnitude of force is constant. Magnetic force provides the centripetal force. Newton per ampere per metre when a current-carrying conductor is placed perpendicular to C). change that is producing it. Define magnetic flux. Magnetic flux is the product of magnetic flux density andto the direction ofthe magnetic flux density voltage when the Hall probe is roThe Hall voltage is zero when prIt is maximum when probe is perpenA and B are held above the tubes simultaneously. A falls through a plastic tube and B passes through an aluminium tube. Explain why magnet B takes much longer than magnet A to fall through the tube. As magnet falls, metal tube cuts magnetic flux. Current is induced in metal tube. 132

21 Alternating currents Explain what is meant by the root-mean-square r.sSuggest why high voltages are usl energy For the same power, current is low when high voltages are used.Lower current causes less power loss in transmission cables. easily stepped up and down. Transformers only work with a.c. causes emission of electronsState what is meant by the etic energy below a maximum value. Electrons below surface requireonstant. State and explain the effect Shorter wavelength means each photon has more energy. Intensity of light is kept constant, and each photon has more energy, so the amount of photon ited. ence in energy of two energy levels. State what is meant by the de Broglie wavelendth. Wavelength associated with a moving particle Evidence for the particulate nature of electromagnetic radiation photoelectric effect Page

23 Nuclear physics State what is meant by nuclear fissionA large nucleus splits into two nuclei of approximatelyTwo light nuclei combine to form a more massive nucleus. e of the deuterium and the tritium must be high. High temperature means high kinetic energy of nuclei. State what is meant by the Energy required to separate nucucleon for the neutron is not quoted. Neutron is a single particle, s, so mass of α-particle is less. Distinguish, for an atom, between a nucleus and a nucleon. nucleus:State what is meant by isotopes. neutrons. Explain what is meant by (γ State what is meant by: ticular nucleus will decay spontaneousdecay is not affected by external factors half-life. Mean time taken for half of the active nuclei in a sample to de of the sample is not equal to the measured the gradient in the figure of number

25 Astronomy and cosmology State what is meant by the luminosity of a star. State what is meant by a standard candle. reasons why some stars appear brighter than others. The brighter star could have a greater luminosity. redshiftApparent wavelength is greater due to the movement of star awaya distant star has undergone redshift. Compare with known spectrum. ure of a distant star may be determined from the wavelength spectrum of the light from the star. Wavelength of peak intensity is r. Wavelength of peak intensity from object of known temperatureis determined. Use Wien’s displacement law (wavelength of peak intensity inversely proportional to Speed of recession of galaxy is directly proportional todistance of galaxy away from the Explain how Hubble’s law and the idea of the expanding Universe lead to the Big Bang theory of the origin of the Universe. All parts of the Universe are mMatter must have been close together in the past. Page 127

Define what is contrast in X-ray imaging. difference in degree of blackState and explain how, in an X-ray tube, the hareases their kinetic energy. Explain why an aluminium filter may be placed in the X-ray beam when producing an X-ray image of a patient. X-ray beam contains may wavelengths. Long wavelength X-ray radiation would be absorbed by bodybut no contribute to image. attenuationState why the expression of exy to a parallel beam. Intensity decreases wlinear absorption coefficient 0 e, where I0absorptionExplain the principles behind ternal body structures. 1. X-ray beam is directed through body onto detector. erent attenuation coefficientsThese image build up an image of a slice through the body. Series of images of slices form 3-dimensional image. 3D image can be rotated and viewed from different angles. Suggest why the ultrasound from the transducer is pulsed. The transducer transmits pulses and then receives the reflectedspecific acoustic impedancePage 128 of 132

use of ultrasound to obtain diagnostic information about internal body structures. The transducer made of piezo-electric crystal can transmitand receive ultrasound. ected pulse gives information about boundaTime delay gives information about depth. State and explain one advantage of the use of high frequency ultrasound as compared with low frequency ultrasound for medical diagnosis.Higher frequency means Shorter wavelength can resoignal received later at the detector The later signal has passed through greater thickness ofExplain the principles behind the The transducer is made of piezo-electric crystal. P.d. across the crystal causes it to distort. the crystal to oscillate. When applied p.d. frequency equalstal,the crystal resonates. Position of the tracer in body can be detected. Mass of particles is converted into gamma photons. Explain how the detection of the gamma-ray photons is used to produce an image of the tissue being ocessed to establish the positioPage 129

131233m <22 = 2πfv = ω v2r ; F = mv = oscillations 2 ; fa0sinx02 – x2gravitational field g = FmF = – GMmGMGMmrastrophysics max1LσTNewtonian world and astrophysicsthermal physics ideal gases E = E = 2∆v2= –E2x

capacitance and capacitors CQVC1 + C21= 1C11QVW1Q ; = 12CCRx = x0e–tCRx = 0t)electric field E = FF = Qqπε0rE = Q4πε = V = Q4π0renergy = Qq40rF = BILsinθF = BQvsinθVHqBθΔ2

radioactivityA = N; ∆ = – N1/20tN = N∆mc2I0–ρI =(Z2 – Z12(Z1hcλhf = KEmaxλ = hE = E= 1132 132