BACHELOR OF SCIENCE (B.Sc.) Term-End Examination December, li i,n PHYSICS PHE-11(S) : MODERN PHYSICS
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1 No. of Printed Pages : 8 BACHELOR OF SCIENCE (B.Sc.) Term-End Examination December, li i,n PHYSICS PHE-11(S) : MODERN PHYSICS I PHE-11(S) I Time : 2 hours Maximum Marks : 50 Note : Attempt all questions. The marks for each question are indicated against it. Symbols have their usual meanings. The values of physical constants are given at the end. 1. Answer any five parts : 5x3=15 (a) (b) (c) A particle at rest has a mean lifetime of 800 s. If we measure its mean lifetime as 2400 s, what is its speed relative to us? What is the uncertainty in the energy of an atom in an excited state having a lifetime of 10-9 s? What is the order of the natural width of the line emitted by the atoms? The rest mass of a free proton is 938 MeV/C2. A proton has a kinetic energy of 150 MeV. Calculate its total energy and relativistic mass. PHE-1 1 (S) 1 P.T.O.
2 (d) A ball of mass 100 g moves with a speed of 80 ms-1. Calculate the de Broglie wavelength associated with it. Would you be able to observe the wave characteristics? (e) Write down one use each of nuclear radiations from isotopes in agriculture, medicine and industry. (f) Determine the electronic configuration for the atoms having Z = 26 and Z = 45. (g) State, giving reasons, whether the following transitions are allowed or not for a multi-electron atom : (i) 2P /2 00 3s (h) Derive the expression for cyclotron frequency. 2. Answer any two parts : 2x5=10 (a) (b) Derive the relativistic velocity addition formula. A pion at rest decays into a muon and a neutrino (which is massless). Using the relativistic laws of conservation of energy and momentum, obtain the momentum of the muon in terms of m and m. TE PHE-11(S) 2
3 (c) The Doppler shift in the wavelength of the sodium line (5890 A) in the light observed from a distant star is 100 A. Determine the speed at which the star is receding. 3. Answer any two parts : 2x5=10 (a) (b) (c) Write the properties and boundary conditions that a wave function must satisfy in order to lr acceptable. Explain whether yr (x) = Ne" is an acceptable wave function or not. A particle with zero ;neigy has a wave function xi, (x) = A x e -x I L. Determine the potential function V(x). Define the parity operator. Determine whether the parity operator is Hermitian or not. 4. Answer any one part : / x10.10 (a) Write down the time independent Schrodinger equation for a one-dimensional simple harmonic oscillator with angular frequency w. What is its zero point energy? Calculate < x > and < px > for the oscillator in its ground state given by the wave function 1 (x) j a exp (- a2 2 x 2 ); MCO a2 = ) h PHE-1 1 (S) 3 P.T.O.
4 (b) State the selection rules for X-ray spectra. Explain with the help of a diagram, the transitions that give rise to K a lines. If the Ka line of Mo (Z = 42) has a wavelength of 0.71 A, calculate the wavelength of the Ka line for Cu (Z = 29). (Take a = 1) 5. Answer any one part : 1 x 5=5 (a) (b) What do you understand by radioactive equilibrium? Obtain the condition for transient equilibrium in the decay of 238U. Describe the liquid drop model of nuclear fission. Physical constants : h = 6.6 x Js me = 9.1 x kg PHE-11(S) 4
5 M11 wrm (.i nft.) wlia *ha itlyin, 2016 VIRE6'farrR.RV..-11(S) : a1tp-4 OM* ftft.1w.f.-11(s) I FFR1:2 WS' NAVA!' 31W : 50 : 70# k I A W i 3* sof frof 77 i / Nee 4- ar0 fl/h/^4 37ef Oft 4ifflio7 *R-R3iux7R7777g1 1. idef 3tii 1it : 5x3=15 () Ruiiicitvii -Pm. WIT T1 3141M qichirc 800 s t I zik VT WIT W. 31 fd siichchici 2400 s TrrEA f, a R10 aryl? (w) ANff ara-mr 7w wffita Actichle i0-9 s vi wrrigt=1.--at Afit-dffr TT ttft? timpiait vrt zmdfa - lur 3rit-1 w for cs;lfa? (71) 7 cf 34efq gatisii4 938 MeV/C2 tfft t I i431 z-4i 150 MeV t I VI silet4 1 1 Ott autlftr4t4 geepil4 TiuRr *INR I PHE-11(S) 5 P.T.O.
6 (T) 100 g airft t 80 ms-1 1 TU t I 'PT 4 tiainct AfT41 *Taut *r1=4r w wirr afirow6 k:fur trrg4? ffd,ctit dthir 4 tii.r-2act: RT1 idf4ruil*r 3T +T cictiv Z= K Z= 45 cite) TI:194 ch Atifftff *tra -R craul tii cf WdTiR '1* Alraweq tritituj i4hicirsm kisto i 3I 11 : for (i) 2 P /2 (ii) 3 s 1 1 so (i) kii*ctri atrin TT 0e4s,44, oerm *RR 2. ft;tf itfrff 39T ti*r : 2x 5=10 () 3TORT4tzt *-r *IT ogni *ti*r I NO Ti tuatt4, fiii ck.e t t, 90.4 * Rw Va--4 (f41:rwr pei RLRr t) 4 4T4I. IalTd-Wret tidit 3 davit * Timm Pepil mei 41 t-4 mp,* tra 4 9,3#4 1 1 'WI a* I PHE-11(S) 6
7 (Tr) v44 wrl A -4tATff 3r Iltwt -ffitits4 (5890 A) sikot 100 A t ti 0*MTARTATI147Wirgrt 3. it74f wr 3w1 tftr : 2x 5=10 ().RW ITTRI WiTT tb04 ati Uff 1 41a tritlforr ARditi *Err *fi yr (x) = Neax 2 1i TITRI *IT 'hilt 312T4T NO 7er sii 111 arr tur *-Tr th e4 f4.1012sci t : yr (x) = A x e-x2/1-2 fkit4 th-aa. v(x) -14%Tiftd -41* I CrO titwch 1taviin ti*i val. tat tithital 4411 t zrr 4. ftlft r4" ITT WF tr4r : 1 x1010 (t) Quilt+ atritt (.0 at 7- -f*frat TRa NTI% kia) TT faciasmtik wilchtui ofigq. 1 4ticP :11q IT t? Ti 1 (x) _ an )2 exp (_ a 2x 2 i; a2 mo) A trftitriirff AI TO ar4vati fer < atk < px > Trial TragriVA PHE-11(S) 7 P.T.O.
8 (I) X- VI TOT WYE *Pi iv I Ka Itc4I4 NICti 4i14 ATa NA AI- kmmir A wisflv I -zdt Mo (Z = 42) *I Ka IINT WiT At, t Cu (Z = 29)*1 Ka bg( cal 4 ~~nnr cf 014 I (a = 1 #07) 5. Wt vrtt T 3cTt : /x5=5 () -Qq.10(4 till-titcit-vif A 31-Fr wrr? 233U eirg fer 34FRX141 7T4 3rrRr*t* (is) ii ca41 is154 HISc.1 f4uiq O'AR I triftre hlwitc7 h = 6.6 x Js me = 9.1 x kg PHE-11(S) 8 500
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