1000 Solved Problems in Modern Physics

364 6 Special Theory of Relativity (λ′−λ)/λbecomes (1−γ)/γ Butγ= 1 +T/Mc^2 = 1 + 120 / 12 × 10 = 1. 01 Hence (λ′−λ)/λ=− 0. 01 / ...

6.3 Solutions 365 γ=Lx/Lx′=tanθ/tanθ=tan 45◦/tan 30◦= √ 3 β=(γ^2 −1)^1 /^2 /γ= √ 2 3 = 0. 816 The speed at which the rod is movi ...

366 6 Special Theory of Relativity 6.118 Tthreshold=[(mp+mp+mp)^2 −(mp+mp)^2 ]/ 2 mpby Eq. (6.53) mp= 1 , 837 me= 1 , 837 × 0. 0 ...

6.3 Solutions 367 6.125 Tthr=[(mk 0 +mk+mΩ−)^2 −(mk−+mp)^2 ]/ 2 mk− =[(0. 498 + 0. 494 + 1 .675)^2 −(0. 494 + 0 .938)^2 ]/ 2 × 0 ...

...

Chapter 7 Nuclear Physics – I 7.1 Basic Concepts and Formulae ................................ Solid angle In two dimensions the ...

370 7 Nuclear Physics – I The solid angle forθ 1 =0 andθ 2 =θis Ω= ∫ dΩ= ∫θ 0 2 πsinθdθ= 2 π(1−cosθ) The maximum solid angleΩ= 4 ...

7.1 Basic Concepts and Formulae 371 tanθ=sinθ∗/(cosθ∗+m 1 /m 2 ) (7.2) Ifm 2 >m 1 ;0<θ<π m 2 =m 1 ;0<θ<π/^2 m 2 & ...

372 7 Nuclear Physics – I Fig. 7.3Concept of differential cross-section The unit ofσis a Barn (B). 1 Barn= 10 −^24 cm^2 ,1mB= 10 ...

7.1 Basic Concepts and Formulae 373 Fig. 7.4Rutherford scattering R 0 is also the minimum distance of approach in head-on collis ...

374 7 Nuclear Physics – I Ionization Bethe’s quantum mechanical formula −dE/dx=(4πz^2 e^4 n/mv^2 )[ln (2mv^2 /I)−ln(1−β^2 )−β^2 ...

7.1 Basic Concepts and Formulae 375 Straggling When a mono-energetic beam of charged particles traverses a fixed absorber thick- ...

376 7 Nuclear Physics – I Motion of a charged particle in a magnetic field Centripetal force=Magnetic force mv^2 /ρ=qvB (7.30) M ...

7.1 Basic Concepts and Formulae 377 Bremsstrahlung When a relativistic particle of massm, chargezemoves close to a target nucleu ...

378 7 Nuclear Physics – I Maximum shift in wavelength (Δλ)max= 2 λc (7.38b) Shift in frequency ν=ν 0 /(1+α(1−cosθ)) (7.39a) wher ...

7.1 Basic Concepts and Formulae 379 At low Photon energy σph∝Z^5 /(hν)^7 /^2 (7.45) μph=Nσph (7.46) I=I 0 exp (−μphx) (7.47) Low ...

380 7 Nuclear Physics – I Nuclear resonance fluorescence IfE 0 is the transition energy in an atom of massM, the resonance energ ...

7.1 Basic Concepts and Formulae 381 Units 1 Curie (ci)= 3. 7 × 1010 disintegrations/s 1 Rutherford= 106 disintegrations/s 1 Becq ...

382 7 Nuclear Physics – I Selection rules Fermi rule:ΔI= 0 , Ii= 0 →If=0 allowed,Δπ= 0 (7.68) GT rule:ΔI= 0 ,± 1 ,Ii= 0 →If=0 fo ...

7.2 Problems 383 betweenθLand the angle of deflectionθM, in the center of mass frame is tanθL=sinθM/[m 1 /m 2 +cosθM] Show also ...