SCI 270: On Nuclear Technology Practice Problems
Answers are given for your reference only. Please do your part of the learning, because no one else will be able to do that for you.

Your skills of problem solving are tested and useful in the future. Answers are useless. Acquiring skills and abilities are the goals of learning, marks indications of your performances on these tasks.

# 8. Nuclear Reactions - Assignment

1. Is the reaction 14N + 4He ®   17O + 1H, endothermic or exothermic? Evaluate the energy, Q, of the reaction. Give this amount of energy per nuclear reaction and per mole of reactants.
Masses: H, 1.007825; n, 1.008665; He, 4.00260; 14N, 14.00307; and 17O, 16.99914.
Conversion factor and constant: 1 amu = 1.66053e-27 kg, c = 3.0e8 m s-1 (velocity of light).

 The reaction14N (a, p) 17O is _ endo-thermic Q = _ -1.207 _ MeV/reaction (negative indicating energy required)     = _ -1.17e11 _ J/mol (Energy required per mol of reactions)

2. Is the reaction 14N (n, p) 14C endothermic or exothermic? What is the mass of 14C if the beta decay energy is 0.156 MeV? Calculate the energy of the N (n, p) C reaction.

 The reaction14N (n, p) 14C is _exo-thermic Mass of 14C = _ 14.003241 _ amu Q = _ 0.623 _ MeV/reaction

3. Complete the following reaction by giving the symbol of the products.

 Now you have learned various types of nuclear reactions. 14B ( , b) _14C_ 18N ( , b a) _14C_ 9Be (6Li, p) _14C_ 9Be (7Li, d) _14C_ 11B (a, p) _14C_ 12C (a, 2p) _14C_ 12C (t, p) _14C_ 13C (d, p) _14C_ 13C (t, d) _14C_

Notes: a = 4He, b = 0e-, p = 1H, d = 2D, t = 3T.

4. Cobalt has only one stable isotope, 59Co, whose atomic mass is 58.9332 amu. According to the Handbook of Chemistry and Physics, the cross sections for the reaction 59Co (n, g) 60 mCo reaction is 20 b; the cross sections for the reaction 59Co (n, g) 60Co reaction is 17 b; the half life of 60mCo ( , g)60Co is 10.5 m; the half life of 60Co ( , b (followed by g)) 60Ni is 5.26 y; and the decay energy of 60Co 2.819 MeV. Estimate the amount of each produced, including those nuclei that have decayed during the time when 59.0 g of 59Co is irradiated by neutrons with an intensity of 1.0e15 neutron cm-2 s-1 in a nuclear reactor for 60 seconds. Assume all nuclei begin to decay after the irradiation is finished. Estimate the number of nuclei left after 24 hours.

Reaction Cross
section
Number of
nuclei produced
Number of Nuclei
remain after 24 hours
59Co (n, g) 60 mCo 20 b
__7.23e17_

_zero_
59Co (n, g) 60Co 17 b
__6.14e17__

_6.14e17 (almost no change)_

5. What are transuranium elements and transactinide elements? Give two nuclear reaction equations, one for the synthysis of a transuranium element, and one for the synthesis of a transactinide element. Explain your nuclear reactions for their synthesis.

Reaction for the synthesis of a transuranium element
Transuranium elements are those whose atomic number range from 93 to 103. Their atomic numbers are higher than that of uranium (92). Elements Ac to Lw are called actinides, they are a group as are the rare earth elements (atomic number 57-71).

Transuranium element Np and Pu were obtained using neutron bombardment of uranium. Heavier ones have been synthesized by bombarding Pu with neutrons. Yet, still heavier ones are made by bombarding heavy nuclei with light atomic nuclei:

246Cm + 12C = 254No102 + 4 n
252Cf + 10B = 247Lw103 + 5 n
252Cf + 11B = 247Lw103 + 6 n
Reaction for the synthesis of a transactinide element
Still heavier elements with atomic number greater than 103 are called transactinide elements. For example, 243Pu94 + 22Ne = 260Rf104 + 4 n
249Cf98 + 12C = 257Rf104 + 4 n

6. Why neutrons are the most important particles for the induction of nuclear reactions? What is a neutron source? What methods have been used to produce neutrons as neutron sources? What feature(s) shall be considered regarding the selection of a neutron source and why?

Hint
The most important particles for inducing nuclear reactions are neutrons, protons, alpha particles, and light atomic nuclei.

A neutron source provide neutrons for inducing nuclear reactions or for other purpose. It can be a mixture of alpha or gamma radionuclides and some light nuclides such as Be, Li, or B. These elements release neutrons when bombarded by alpha particles or gamma rays.

Another neutron source are (p, n) nuclear reactions. The protons from particle acclerators are used to bombard light nuclides, and the reactions release neutrons.

When selectron a neutron source, the energy of the neutrons is an important feature to consider, because the cross section of a nuclear reaction depends on the energy of the neutrons.