1000 Solved Problems in Modern Physics

444 8 Nuclear Physics – II The reaction above will take place for low energy incident deuterons in a s-wave state leaving the^12 ...

8.2 Problems 445 barns for a neutron velocityv= 2 ,200 m/s. If the counting rate is 250/min, calculate the value ofQ.GivenL=50 c ...

446 8 Nuclear Physics – II 8.86 Show that a homogeneous, natural uranium-graphite moderated assembly can not become critical. Us ...

8.3 Solutions 447 8.92 Assuming that the elastic scattering of low energy neutrons is isotropic, show that the mean energy of th ...

448 8 Nuclear Physics – II The mass of this ion is then 9. 98 × 10 −^27 kg 1. 66 × 10 −^27 kg/amu = 6 .012 amu Therefore the mas ...

8.3 Solutions 449 ΔEc= 3 5 1 4 πε 0 e^2 R [Z(Z+1)−Z(Z−1)] = 6 Ze^2 5 R e^2 4 πε 0 = 1. 2 × 1. 44 Z R MeV-fm EquatingΔEctoMSi−MA= ...

450 8 Nuclear Physics – II U= ∫ dU= 4 πρ^2 3 ε 0 ∫R 0 r^4 dr= 4 πρ^2 R^5 1. 5 ε 0 = 3 z^2 e^2 20 πε 0 R where we have substitute ...

8.3 Solutions 451 ThereforeJ= 2 ER ω = 2 × 537. 5 × 1. 6 × 10 −^13 2. 6 × 1023 = 6. 61 × 10 −^34 Js=h 8.10 (a) IfJbe the electro ...

452 8 Nuclear Physics – II Fig. 8.9Ellipsoid of revolution The equation of the ellipsoid is ( x′^2 b^2 ) + ( y′^2 b^2 ) + ( z′^2 ...

8.3 Solutions 453 8.15 (a) The electrical quadrupole moment is the expectation value of the operator Qij= ∑z k= 1 ek(3xixj−δijr^ ...

454 8 Nuclear Physics – II Therefore (a^2 −b^2 )= 14 .79 fm^2 (1) Now,A= 4 3 πab^2 ρ (2) The nuclear charge density,ρ= 0 .17 fm− ...

8.3 Solutions 455 8.20 Three types of decays are possible 64 29 Cu→ 64 30 Zn+β −+ν ̄ e (1) 64 29 Cu→ 64 28 Ni+β ++νe (2) 64 29 C ...

456 8 Nuclear Physics – II 8.22 The mass-energy equation for the positron decay gives MNa=MNe+ 2 me+ Tmax+Tγ 931. 5 = 21. 991385 ...

8.3 Solutions 457 8.3.7 Shell Model .................................... 8.26 A state with quantum numberjcan accommodate a maxi ...

458 8 Nuclear Physics – II 3 2 He : J π=(1/2)+ The state due to neutron hole is 1s 1 / 2 20 10 Ne : J π=(0)+ The protons and neu ...

8.3 Solutions 459 8.36 The difference in the binding energies of the two mirror nuclei is assumed to be the difference in the el ...

460 8 Nuclear Physics – II Hence the rest mass energy of the nucleus M(A,Z)c^2 =Zmpc^2 +(A−Z)mnc^2 −B = 92 × 938. 3 + 143 × 939. ...

8.3 Solutions 461 Multiply (1) byψ∗ ψ∗∇^2 ψ+ 2 m ^2 (E+U+iW)ψ∗ψ=0(2) Form the complex conjugate equation of (1) and multiply by ...

462 8 Nuclear Physics – II 8.3.10 Nuclear Reactions (General)......................... 8.45 The given decay is (^13) N→ (^13) C+ ...

8.3 Solutions 463 8.48 Given reaction is 4 2 He+ 14 7 N→ A ZX+ 1 1 H As the atomic number (Z) and mass number (A) are conserved ...