Solutions to Nuclear Chemistry Homework Problems
1. Explanation should include most of the following and how they are related:
protons, neutrons, pions, strong forces, binding energy, magic numbers and the concepts in the semi-empirical binding energy (coulombic, pairing, etc.)
2. They are effectively the same particle. However, each term is associated with a different location. Beta particles are associated with the nucleus, electrons with the quantum shells outside the nucleus.
3. mass of neutron = 1.0086641; mass of p+e = 1.008374; 1 Da = 931.7 MeV
for 136Xe: p = e = 54 and n = 82 so predicted mass = 137.16265 Da
Δm = 1.2555 Da = 1169.7 MeV
8.601 MeV/nucleon
for 208Pb: p = e=82, n = 126 so predicted mass = 209.77834
Δm = 1.8017 Da = 1678.7 MeV
8.071 MeV/nucleon
for 28Si: p=e=14; n=14 so predicted mass = 28.23853
Δm = 0.26160 Da = 243.73 MeV
8.705 MeV/nucleon
So silicon-28 is the most stable nucleus
4a. 
4b. 
4c. 
4d. 
4e. 
4f. 
4g. 
5a. 238U (see natural decay chains)
5b.
5c. Alpha particles, while large and destructive, are not very penetrating. They travel only cm and can be blocked by skin. However, radon is a gas, so it can get into the lungs were there is no skin to protect sensitive parts of the body from radiation. All other members of that decay chain are solids.
6a. 243Am.... a very large nuclei, so alpha decay is predicted
6b. 17F....Fluoride’s average mw is 19, so this atom is light on neutron. A positron decay is predicted because it’s rather light for an electron capture.
6c. 49Ca....Calcium average mw is 40, so this very neutron heavy, so negatron decay
6d. 181Ir...Iridium’s average mw is 192, so the atom is neutron light. As a heavier element it is more likely to undergo electron capture than positron decay.
7. 87.74 yr X (365.25 day/1 yr) X (24 hr/1 day) X (60 min/1 hr) X (60s/1 min) =
2.769 X 109 s
λ = ln 2/t1/2 = ln2/(2.769 X 109s) = 2.503 X 10-10 s-1
0.25 g X (1 mol/238 g) X (6.20 X 1023 atoms/1 mol) = 6.3 X 1020 atoms
activity = λN = (2.503 X 10-10)(6.3 X 1020) = 1.6 X 1011 Bq (or dps)
1.6 X 1011 Bq X (1 Ci/3.7 X 1010 Bq) = 4.3 Ci
In a pacemaker: 1) a very small amount of fuel is required; 2) as an a emitter its easily sheilded and 3) it lasts a very long time.
8. For γ radiation, 6AEn/d2 = dose in mrad/hr
d = 1.0 m X (100 cm/1 m) X (1 in/2.54 cm) X (1 ft/12 in) = 3.3 ft
337 = 6A(1.67)(1)/(3.3)2
A = 24 mCi = 0.24 Ci
9 5.2714 yr X (365.25 day/1 yr) X (24 hr/1 day) X (3600 s/1 hr) = 1.664 X 108 s
λ = ln 2/t1/2 = 4.16 X 10-7 s-1
A0 = 5.0 Ci X (3.7 X 1010/1 Ci) = 1.85 X 1011 dps
1.85 X 1011 = (4.16 X 10-9)N
N = 4.44 X 1019 atoms
15 yr = 4.73 X 108 s and 3.0 ft = 91.4 cm
ln N0 – ln N = λt so
ln(4.44 X 10) – ln N = (4.16 X 10-9 s-1)(4.73 X 108 s)
N = 5.9 X 1018
A = λN = (4.16 X 10-9)(5.9 X 1018) = 0.67 Ci or 670 mCi
β = (338,000)(670)/(91.4)2 = 2.7 X 104 mrem/hr
γ1 =
6(670)(1.3325)(1)/9 = 595 mrem/hr
γ2 = 6(670)(1.1732)(1)/9 = 524 mrem/hr
total exposure rate = 2.8 X 104 mrem/hr = 24 rem/hr
10. a pion is made of a down and an anti-up quark
11. For heavier isotopes, the effect of charge becomes significant in the coulomb term (Z2/A), but is decreased if A is large. A similar (although lesser) effect occurs in the correction for surface effects.
12. For isotopes lighter than 56Fe, fusion is exothermic and will lead to a more stable atom. For isotopes heavier than 56Fe, fission will create the more stable atom. This is shown in the graph of binding energy versus mass number.
In the semi-empirical binding energy equation, the factors that decrease binding energy become larger as A and Z increase and increase faster than the gain in strong force.
13. 135Xe has p = 54 and n = 81, capturing one
neutron makes the number of neutrons “magic” which is very favorable.