1000 Solved Problems in Modern Physics

404 7 Nuclear Physics – I 7.3.3 Ionization, Range and Straggling ..................... 7.33 The rate of loss of energy due to ra ...

7.3 Solutions 405 As the straggling is inversely proportional to the square root of particle mass, the straggling for^3 He will ...

406 7 Nuclear Physics – I 7.42 The proton velocityvp=(2Ep/mp)^1 /^2 = √ 2 × 4 /mp The deuteron velocityvd =(2Ed/md)^1 /^2 = √ 2 ...

7.3 Solutions 407 (b) Over the whole path total number of ion pairs =Total energy lost/Ionization energy of each pair= 5. 0 × 10 ...

408 7 Nuclear Physics – I Fig. 7.15 hν 0 /c=hνcosθ/c+Pecosφ (2) 0 =−hνsinθ/c+Pesinφ (3) wherePeis the electron momentum Re-arran ...

7.3 Solutions 409 Forhν 0 =30 keV,α=hν 0 /mc^2 = 30 / 511 = 0 .0587 andθ= 30 ◦ We findhν= 29 .766 keV Therefore the kinetic ener ...

410 7 Nuclear Physics – I E 2 ′′= 2 E′′ 1 2 +α′′ = 4 E 0 (2+α)(4)(1+α)(2+α) = E 0 (1+α) 0 Photon energy after the third scatteri ...

7.3 Solutions 411 7.3.5 Photoelectric Effect ................................ 7.63 According to Einsteins’s equation, kinetic en ...

412 7 Nuclear Physics – I 7.67 Number of gamma rays absorbed in the thicknessxcm of lead N=N 0 (1−e−μx) whereN 0 is the initial ...

7.3 Solutions 413 V λ× 10 −^10 m(1/λ)× 106 1.48 3,660 2,732 1.15 4,050 2,469 0.93 4,360 2,293 0.62 4,920 2,032 0.36 5,460 1,831 ...

414 7 Nuclear Physics – I T 2 =hc/λ 2 −W T 2 −T 1 =hc(1/λ 2 − 1 /λ 1 ) (4. 0 − 1 .8)× 1. 6 × 10 −^19 J=hc ( 1 700 × 10 −^10 − 1 ...

7.3 Solutions 415 Fig. 7.17 hν/c≤p++p− (2) Or (hν)^2 ≤(cp++cp−)^2 By virtue of (1) (E++E−)^2 ≤c^2 p+^2 +c^2 p−^2 + 2 c^2 p+p− Or ...

416 7 Nuclear Physics – I 7.80 For electronz=−1. The given integral is easily evaluated assuming that this refractive indexμis i ...

7.3 Solutions 417 Optical Doppler effect is given by hν=hν 0 (1+βcosθ∗) The maximum and minimum energy of photons will behν 0 (1 ...

418 7 Nuclear Physics – I Fig. 7.18 7.86 The flow of heat in a material placed between the walls of a coaxial cylinder is given ...

7.3 Solutions 419 GivenNB/NA= 2. 2 / 0. 53 = 4. 15 λA= 0. 693 /T 1 / 2 (A)= 0. 693 / 12 = 0 .05775 year−^1 λB= 0. 693 /T 1 / 2 ( ...

420 7 Nuclear Physics – I Now at timet NE=NE^0 exp(−λEt) (3) Solution of (2) is NF=Aexp(−λEt)+Bexp(−λFt)(4) whereAandBare consta ...

7.3 Solutions 421 7.95 Let the proportion of^235 U and^238 Uatt=0bex:(1−x). Present day radioactive atoms for the two components ...

422 7 Nuclear Physics – I Usingλ 238 = 1 /τ 238 = 1 / 6. 52 × 109 ,λ 235 = 1 /τ 235 = 1 / 1. 02 × 109 And solving (3) we get the ...

7.3 Solutions 423 wherec 1 is another constant. k log 3. 36 +log(1622×365)=c 1 (2) k log 3. 85 +log 138=c 1 (3) Solving (2) and ...