394
7 Nuclear Physics – I
Why 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 time t 1 = 2.0 s, the counting rate was N 1 and at t 2 = 6.0 s, the counting rate was N 2 = 2.66 N 1 .
Estimate the mean lifetime of the given nuclide.
7.108 Determine the half-life of β emitter
6 He whose end point energy is 3.5 MeV
and |M if |
2
= 6. Take G/(c)
3
= 1.166 × 10
−5 GeV
−2
7.109 The maximum energy E max of the electrons emitted in the decay of the isotope
14 C is 0.156 MeV. If the number of electrons with energy between E
and E + dE is assumed to have the approximate form
N(E)dE ∝
√
E (E max − E)
2 dE
find the rate of evolution of heat by a source of
14 C emitting 3.7 × 10
7 electrons per sec.
[University of Cambridge]
7.110 In the Kurie plot of the decay of the neutron, the end point energy of the electron 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 of β-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 the β-ray spectrum is represented by n(E)dE ∝
√
E (E max − E)
2 dE Show
that the most intense energy occurs at E = E max /5
7.3 Solutions
7.3.1 Kinematics of Scattering
7.1 We shall find an expression for the ratio of the masses M/m in terms of the
angles θ and ϕ. To this end we start with the equation for the transformation
of angle from CMS to LS.
tan θ = sin θ
∗
/(cos θ
∗
+ M/m)
( 1 )
θ
∗
= π − ϕ
∗
= π − 2ϕ
7 Nuclear Physics – I
Why 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 time t 1 = 2.0 s, the counting rate was N 1 and at t 2 = 6.0 s, the counting rate was N 2 = 2.66 N 1 .
Estimate the mean lifetime of the given nuclide.
7.108 Determine the half-life of β emitter
6 He whose end point energy is 3.5 MeV
and |M if |
2
= 6. Take G/(c)
3
= 1.166 × 10
−5 GeV
−2
7.109 The maximum energy E max of the electrons emitted in the decay of the isotope
14 C is 0.156 MeV. If the number of electrons with energy between E
and E + dE is assumed to have the approximate form
N(E)dE ∝
√
E (E max − E)
2 dE
find the rate of evolution of heat by a source of
14 C emitting 3.7 × 10
7 electrons per sec.
[University of Cambridge]
7.110 In the Kurie plot of the decay of the neutron, the end point energy of the electron 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 of β-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 the β-ray spectrum is represented by n(E)dE ∝
√
E (E max − E)
2 dE Show
that the most intense energy occurs at E = E max /5
7.3 Solutions
7.3.1 Kinematics of Scattering
7.1 We shall find an expression for the ratio of the masses M/m in terms of the
angles θ and ϕ. To this end we start with the equation for the transformation
of angle from CMS to LS.
tan θ = sin θ
∗
/(cos θ
∗
+ M/m)
( 1 )
θ
∗
= π − ϕ
∗
= π − 2ϕ