394 7 Nuclear Physics – IWhy is the transition(^17) F→ (^17) O+e−+ν(5/ 2 +→ 5 / 2 +)
called a super-allowed transition?
7.107 Beta particles were counted from Mg nuclide. At timet 1 = 2 .0 s, the count-
ingratewasN 1 and att 2 = 6 .0 s, the counting rate wasN 2 = 2 .66 N 1.
Estimate the mean lifetime of the given nuclide.
7.108 Determine the half-life ofβemitter^6 He whose end point energy is 3.5 MeV
and|Mif|^2 =6. TakeG/(c)^3 = 1. 166 × 10 −^5 GeV−^2
7.109 The maximum energyEmaxof the electrons emitted in the decay of the iso-
tope^14 C is 0.156 MeV. If the number of electrons with energy betweenE
andE+dEis assumed to have the approximate form
N(E)dE∝
√
E(Emax−E)^2 dE
find the rate of evolution of heat by a source of^14 C emitting 3. 7 × 107 elec-
trons per sec.
[University of Cambridge]
7.110 In the Kurie plot of the decay of the neutron, the end point energy of the elec-
tron is 0.79 MeV. What is the threshold energy required by an antineutrino
for the inverse reaction.
ν ̄+p→n+e+
[University of Durham]
7.111 36 Kr^88 decays to 37 Rb^88 with the emission ofβ-rays with a maximum energy
of 2.4 MeV. The track of a particular electron from the nuclear process has a
curvature in a field of 10^3 gauss of 6.1 cm. Determine
i. the energy of this electron in eV and that of the associated neutrino.
ii. the maximum possible kinetic energy of the recoiling nucleus
[University of Bristol]7.112 If theβ-ray spectrum is represented byn(E)dE∝
√
E(Emax−E)^2 dEShow
that the most intense energy occurs atE=Emax/ 57.3 Solutions..................................................
7.3.1 KinematicsofScattering............................
7.1 We shall find an expression for the ratio of the massesM/min terms of the
anglesθandφ. To this end we start with the equation for the transformation
of angle from CMS to LS.
tanθ=sinθ∗/(cosθ∗+M/m)(1)
θ∗=π−φ∗=π− 2 φ