Answer Happy

This question asks you to consider neutrino capture reactions
used in neutrino detection experiments, in the form 𝜈+𝐴𝑋 → 𝑒 −+𝐴𝑋 ′
. a. (1 pts) Show that the Q-value, defined as 𝑄 = (∑ 𝑚𝑖 − ∑ 𝑚𝑓)𝑐 2
is just [𝑚( 𝐴𝑋) − 𝑚( 𝐴𝑋 ′ )]𝑐 2 , where m(AX) and m(AX’) are the
atomic masses. b. (3 pts) Neglecting the small kinetic energy given
to the final nucleus X’ (to conserve momentum), this Q-value is
equal to the minimum energy the neutrino must have to cause the
reaction. Compute the minimum neutrino energy necessary for capture
by 37Cl and 71Ga, looking up masses as required. c. (2 pts) One of
the processes responsible for the production of neutrinos in the
sun is the electron capture decay of 7Be. Looking up masses as
required, compute the energy of the emitted neutrino assuming the
recoil energy of the daughter nucleus is negligible. [Hint: HW 6 Q
2 could be helpful!] d. (2 pts) Defining the Q-value again as 𝑄 =
(∑ 𝑚𝑖 − ∑ 𝑚𝑓)𝑐 2 , compute the range of possible neutrino energies
from the solar fusion reaction 𝑝 + 𝑝 → 𝑑 + 𝑒 + + 𝜈, assuming the
protons have negligible kinetic energy. [Hint: consider the case
where the 𝜈 carries all the energy, and where it is produced at
rest. Make sure not to neglect the mass of the atomic electrons if
you use an atomic mass!] e. (2 pts) 37Cl was used in the Homestake
experiment to detect solar neutrinos, and 71Ga in the GALLEX
experiment. Using your answers from b, c, and d, comment on the
sensitivity of using these three nuclei to observe neutrinos from
7Be decay and from solar fusion.
1. (10 pts) This question asks you to consider neutrino capture reactions used in neutrino detection experiments, in the form v+^X → e+^X'. a. (1 pts) Show that the Q-value, defined as Q = ([m₂ - Σm,)c² is just [m(^X) - m(^X')]c², where m(^X) and m(^X') are the atomic masses. b. (3 pts) Neglecting the small kinetic energy given to the final nucleus X' (to conserve momentum), this Q-value is equal to the minimum energy the neutrino must have to cause the reaction. Compute the minimum neutrino energy necessary for capture by 37Cl and 7¹Ga, looking up masses as required. c. (2 pts) One of the processes responsible for the production of neutrinos in the sun is the electron capture decay of 'Be. Looking up masses as required, compute the energy of the emitted neutrino assuming the recoil energy of the daughter nucleus is negligible. [Hint: HW 6 Q 2 could be helpful!] d. (2 pts) Defining the Q-value again as Q = (Em₁ - Σm)c², compute the range of possible neutrino energies from the solar fusion reaction p + p → d+e++v, assuming the protons have negligible kinetic energy. [Hint: consider the case where the v carries all the energy, and where it is produced at rest. Make sure not to neglect the mass of the atomic electrons if you use an atomic mass!] e. (2 pts) ³7Cl was used in the Homestake experiment to detect solar neutrinos, and "¹Ga in the GALLEX experiment. Using your answers from b, c, and d, comment on the sensitivity of using these three nuclei to observe neutrinos from 'Be decay and from solar fusion.