Unit 15: Modern Physics
Weightage : 15–18%
How many neutrons are contained in the isotope \(^{238}_{92}\mathrm{U}\)?
Correct Answer: \( \boxed{\mathrm{C}} \)
The mass number \(A\) is the total number of nucleons (protons + neutrons), while the atomic number \(Z\) is the number of protons.
Number of neutrons:
\( N=A-Z=238-92=146 \)
Therefore, the uranium-238 nucleus contains \(146\) neutrons and \(92\) protons.
Therefore, the correct answer is (C).
What is the function of a moderator in a fission reactor?
Correct Answer: \( \boxed{\mathrm{A}} \)
A moderator slows down the fast neutrons produced during nuclear fission. Slow (thermal) neutrons are much more likely to induce further fission in nuclei such as \(^{235}\mathrm{U}\), allowing the chain reaction to continue at a controlled rate.
Common moderator materials include graphite and heavy water. By reducing the speed of neutrons, the moderator helps regulate the neutron population and maintain a stable chain reaction.
Note: Although the moderator primarily slows neutrons rather than absorbing them, its overall role is to help control the neutron population and sustain the reactor safely. (Control rods are the components that primarily absorb excess neutrons.)
Therefore, the correct answer is (A).
Correct statements about the binding energy of a nucleus include which of the following?
I. It is the energy needed to separate the nucleus into its individual protons and neutrons.
II. It is the energy liberated when the nucleus is formed from the original nucleons.
III. It is the energy equivalent of the apparent loss of mass of its nucleon constituents.
Correct Answer: \( \boxed{\mathrm{D}} \)
The binding energy of a nucleus is the energy required to completely separate the nucleus into its individual protons and neutrons. It is also the energy released when the nucleus is formed from free nucleons.
The binding energy is related to the mass defect by Einstein’s mass-energy relation:
\( E_{\mathrm{b}}=\Delta mc^2 \)
where \(\Delta m\) is the difference between the total mass of the free nucleons and the mass of the bound nucleus.
Therefore:
I. True. Binding energy is the energy required to separate a nucleus into individual nucleons.
II. True. The same amount of energy is released when the nucleus is formed.
III. True. The binding energy is the energy equivalent of the mass defect, \( \Delta mc^2 \).
Therefore, the correct answer is (D).
