THE ATOMIC NUCLEUS

Chapter – 19

Q.1: How many neutrons and protons do the following nuclei contain?

Nuclide	Protons	Neutrons
$^{27}_{13}Al$	13	$27 - 13 = 14$
$^{40}_{18}Ar$	18	$40 - 18 = 22$
$^{138}_{56}Ba$	56	$138 - 56 = 82$
$^{207}_{82}Pb$	82	$207 - 82 = 125$
$^{28}_{14}Si$	14	$28 - 14 = 14$
$^{238}_{92}U$	92	$238 - 92 = 146$

Q.2: Do $\alpha$, $\beta$, and gamma rays come from the same element? Why do we find all three in many radioactive samples?
Ans: A radioactive element either emits $\alpha$-particles or $\beta$-particles, but never both. Gamma radiations generally accompany $\beta$-emission and, in some cases, with $\alpha$-emission.

A radioactive element (or sample) is a mixture of various nuclides of different relative abundances and with different modes of disintegration. Hence, we can find all the three types of radiations in a radioactive sample at the same time. For example, R-226 is an $\alpha$-emitter, but Ra-25 is a $\beta$-emitter.

Q.3: It is more difficult to start fusion reaction than fission. Why?
Ans: Fission is caused by captured neutrons by heavy nuclei. Neutrons, being electrically neutral, are highly penetrating particles for nuclei. But in fusion of two light nuclei, the positively charged nuclei are repelled by the repulsive forces. So work has to be done against the repulsive forces of the two nuclei.

Q.4: Is it possible that fusion of two small nuclei may occur without collision at extremely high energy?
Ans: No. Two nuclei must collide with sufficient kinetic energy to penetrate their mutual “Coulomb Barrier” and come within the range of the nuclear forces.

Q.5: Explain how a nuclear reactor produces heat as a result of fission?
Ans: In fission, the difference of binding energies of reactants and products is converted into energy. The difference of mass (0.22u) appears as energy (200 MeV). If fission takes place in a bulk solid, most of the disintegration energy appears as an increase in the internal energy of the solid, which shows a corresponding rise in temperature. This thermal energy is carried away to the heat exchanger by circulating the coolant through the reactor.

Q.6: What are the benefits and risks of nuclear reactors? Which reactor is relatively better from the point of safety?
Ans: Nuclear reactors are used to produce (i) electricity, (ii) nuclear fuels, and (iii) radioisotopes. These are peaceful uses of nuclear energy; the reactor fuel is clean burning and relatively easy to transport.

The risks of reactors include the possibility of safety hazards for the workers, environmental damage near the plant, the problem of storing highly radioactive wastes, and a limited supply of raw materials. Nuclear reactors have built-in safety devices. The accidental problems, such as leakage of radioactive substances, could occur if safety features malfunctioned. Pressurized water reactors, using water as a moderator and coolant, are safer with shut-off control rods and liquid "poison."

Q.7: Both fission and fusion apparently produce energy. How can you reconcile this with the law of conservation of energy?
Ans: In fission of U-235 with thermal neutrons, the loss of mass (0.2153 u) is converted into energy, producing about 200 MeV per fission.

In fusion, four protons may be combined to produce one helium nucleus and two positrons. Here, the losses of mass (0.027 u) are converted into energy, producing about 26 MeV. Thus, in both cases, the total "mass-energy" remains conserved.

Q.8: When a photon disappears in producing an electron and a positron, is the energy of a photon equivalent to that of the particles produced? Explain.
Ans: No, the energy of the photon is always greater than the rest mass energy of elements (electron and positron pair, 1.02 MeV). The surplus energy is taken by the two particles as their kinetic energy.

Q.9: When a neutron decays into a proton and an electron, there would be a loss of mass. What would be the energies of the products and their relative directions of motion?
Ans: Neutron is not a stable particle outside nuclei. It decays into a proton, an electron, and an antineutrino. The half-life of the free neutron is 10.8 min.

$$^0n^1 \rightarrow ^1p^1 + e^0 + \nu$$

• Mass of neutron = 1.008649 u = 939.58 MeV
• Mass of proton = 1.0072766 u = 938.23 MeV
• Mass of electron = 0.000549 u = 0.511 MeV
• Mass of proton + electron = 1.0078256 u
• Loss of mass = 1.0086469 - 1.0078256 = 0.0008393 u = 0.78 x 18 MeV

These would be the energies of the products. Due to their kinetic energies, the two particles will move apart (and not be attracted).

Q.10: Why do most moderators, used in nuclear reactors, are light atoms like $H^1, H^2,$ $C^{12}$ slow down the neutrons, and hence they are slowed?
Ans: Fast moving neutrons can be stopped when they make elastic collisions with stationary particles of the same mass. Since the mass of protons, deuterons, or graphite nuclei is comparable to the mass of neutrons, hence they are slowed.

Q.11: Can a conventional fission reactor ever explode like a bomb does? Why?
Ans: In a nuclear reactor, a fission explosion is not possible because the amount of fuel (e.g., U-235 or Pu-239) is of sub-critical mass and it can shut off control rods in emergencies. Also, liquid "poison" can be inserted directly into the moderator if other safety devices fail.

Q.12: In LMFBR, would you expect the radioactivity of the sodium coolant to include the life time of the reactor?
Ans: Yes, because sodium can capture neutrons.

$$^{11}\text{Na}^{12} + ^0\text{n}^1 \rightarrow ^{11}\text{Na}^{24} + \gamma$$

Here, Na-24 is radioactive (beta and gamma emitter) with a half-life of 15.0 h.

Q.13: Consider a sample of 1000 radioactive nuclei with a half-life T. Approximately, how many will be left after a time 3T?
Ans: The number of nuclei decayed in one half-life (T = T) are 500. Also, the number of nuclei that decay in three periods of half-life are $1000/2^3$. Hence, the number of nuclei left undecided is 125.

Q.14: What is the condition for “critical mass?”
Ans: If the mass of fissile material is such that the multiplication factor k > 1, then fission is said to occur in a critical mass. The multiplication factor is the ratio of the number of neutrons in any particular generation to the number of neutrons in the preceding generation. In a reactor, it is slightly above 1; but in a fission bomb, it is about 2.5.

Q.15: Why is heavy water more efficient as a moderator than ordinary water?
Ans: Heavy water (D₂O) has a much lower probability of capturing neutrons, but it can slow down neutrons. In fact, heavy water is 1600 times more efficient as a moderator than ordinary water (H₂O).

Q.16: In LMFBR, why is water not used as a coolant instead of liquid metal?
Ans: If water is used as a coolant in LMFBR, it slows down the neutrons through collisions and hinders the process of breeding (which requires less neutrons to convert U-238 into Pu-239). Also, the probability of capturing neutrons for water is high. Moreover, high pressure is needed to stop vaporization of water, and the core is heated up.

Sodium is a solid at room temperature but becomes liquid at 98°C. Hence, there is no need to pressurize the reactor to keep the sodium from vaporizing. Sodium is highly valued for thermal conductivity and heat transfer coefficient.

Q.17: Why are breeder reactors a necessity?
Ans: The world’s deposit of fossil fuels may not last more than 500 years, and nuclear fuels may not last for more than 5000 years. So, reactors that generate more nuclear fuels than they consume—breeder reactors—are a necessity.