Question 1
Find the binding energy of a nitrogen-14 nucleus. Its atomic mass is 14.00307 u. Use the nuclear data given in the exercise.
Steps only
Δm=7m_H+7m_n−m(N)=0.112360 u; E_b=0.112360×931.5≈104.7 MeV.
Answer
104.7 MeV.
CLASS 12 · PHYSICS · CHAPTER 13
Nuclei
Easy-to-follow worked answers to all ten exercises on nuclear masses, binding energy, and nuclear reactions.
10 worked answersComplete chapter answers
10 worked answers · short steps first, explanations when you need them
Chapter 13 Exercises
Textbook pages 321–322
Question 2
Find the binding energies of iron-56 and bismuth-209 in MeV. Their atomic masses are 55.934939 u and 208.980388 u, respectively.
Steps only
Δm_Fe=0.528461 u, so E_b≈492.3 MeV. Δm_Bi=1.760877 u, so E_b≈1640.3 MeV.
Answer
Fe-56: 492.3 MeV; Bi-209: 1640 MeV.
Question 3
A coin has mass 3.0 g. Estimate the nuclear energy needed to separate all its neutrons and protons. Assume it is entirely made of copper-63 atoms of mass 62.92960 u.
Steps only
E_b per Cu-63 nucleus≈551.4 MeV; number of atoms≈2.87×10²². Total≈1.58×10²⁵ MeV≈2.54×10¹² J.
Answer
2.54×10¹² J (about 1.58×10²⁵ MeV).
Question 4
Find approximately the ratio of the nuclear radii of gold-197 and silver-107.
Steps only
R_Au/R_Ag=(197/107)^(1/3)≈1.23.
Answer
About 1.23:1.
Question 5
For each reaction, calculate Q=[initial masses−final masses]c² and say whether it is exothermic or endothermic: (i) deuterium + tritium → helium-4 + neutron; (ii) carbon-12 + carbon-12 → neon-20 + helium-4. Use the atomic masses given in the exercise.
Steps only
(i) Δm=5.030151−5.011268=0.018883 u, Q=+17.59 MeV. (ii) Δm=24−23.995042=0.004958 u, Q=+4.62 MeV.
Answer
Both reactions are exothermic: +17.6 MeV and +4.62 MeV.
Question 6
Could an iron-56 nucleus split into two aluminium-28 nuclei and release energy? Calculate the Q-value. The given atomic masses are 55.93494 u for iron-56 and 27.98191 u for aluminium-28.
Steps only
Q=[55.93494−2(27.98191)]×931.5≈−26.9 MeV.
Answer
No. It would require about 26.9 MeV.
Question 7
Each fission of plutonium-239 releases an average of 180 MeV. How much energy is released if all atoms in 1 kg of pure plutonium-239 undergo fission? Give the answer in MeV.
Steps only
N=(1000/239)(6.023×10²³)=2.52×10²⁴; E=180N≈4.54×10²⁶ MeV.
Answer
4.54×10²⁶ MeV.
Question 8
How long can a 100 W lamp glow using the fusion of 2.0 kg of deuterium? Use the reaction deuterium + deuterium → helium-3 + neutron + 3.27 MeV.
Steps only
Number of reactions≈2.99×10²⁶; energy≈1.57×10¹⁴ J. For a 100 W lamp, t=E/P≈1.57×10¹² s≈49,700 years.
Answer
About 50,000 years.
Question 9
Estimate the potential barrier for a head-on collision between two deuterons. Treat them as hard spheres of radius 2.0 fm that just touch.
Steps only
At contact r=4 fm. U=(1.44 MeV·fm)/(4 fm)=0.36 MeV.
Answer
0.36 MeV.
Question 10
From R=R₀A^(1/3), where A is the mass number, show that nuclear matter density is nearly independent of A.
Steps only
M≈Am_N; V=(4/3)πR₀³A. Thus ρ=M/V=3m_N/(4πR₀³), independent of A.
Answer
Nuclear matter density is nearly constant, ≈2.3×10¹⁷ kg/m³.