In the year 1939, German scientist Otto Hahn and Strassmann discovered that when an uranium isotope was bombarded with a neutron, it breaks into two intermediate mass fragments. It was observed that, the sum of the masses of new fragments formed were less than the mass of the original nuclei. This difference in the mass appeared as the energy released in the process. Thus, the phenomenon of splitting of a heavy nucleus (usually A> 230) into two or more lighter nuclei by the bombardment of proton, neutron, a-particle, etc with liberation of energy is called nuclear fission.
\({ }_{92} \mathrm{U}^{235}+{ }_{0} n^{1} \rightarrow \quad{ }_{92} \mathrm{U}^{236} \rightarrow{ }_{56} \mathrm{Ba}^{144}+{ }_{36} \mathrm{Kr}^{89}+3{ }_{0} n^{1}+Q\)
Unstable nucleus
(i) Nuclear fission can be explained on the basis of

(ii) For sustaining the nuclear fission chain reaction in a sample (of small size) \({ }_{92}^{235} \mathrm{U}\), it is desirable to slow down fast neutrons by

(iii) Which of the following is/are fission reaction(s)?
\(\text {(I) }{ }_{0}^{1} n+{ }_{92}^{235} \mathrm{U} \rightarrow{ }_{92}^{236} \mathrm{U} \rightarrow{ }_{51}^{133} \mathrm{Sb}+{ }_{41}^{99} \mathrm{Nb}+4_{0}^{1} n\)
\(\text {(II) }{ }_{0}^{1} n+{ }_{92}^{235} \mathrm{U} \rightarrow{ }_{54}^{1.40} \mathrm{Xe}+{ }_{38}^{94} \mathrm{Sr}+2{ }_{0}^{1} n\)
\((\mathrm{III}){ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \rightarrow{ }_{2}^{3} \mathrm{He}+{ }_{0}^{1} n\)

(iv) On an average, the number of neutrons and the energy of a neutron released per fission of a uranium atom are respectively

(v) In any fission process, ratio of mass of daughter nucleus to mass of parent nucleus is

The nucleus was first discovered in 1911 by Lord Rutherford and his associates by experiments on scattering of a-particles by atoms. He found that the scattering results could be explained, if atoms consist of a small, central, massive and positive core surrounded by orbiting electrons. The experimental results indicated that the size of the nucleus is of the order of 10^-14m and is thus 10000 times smaller than the size of atom.
(i) Ratio of mass of nucleus with mass of atom is approximately

(ii) Masses of nuclei of hydrogen, deuterium and tritium are in ratio

(iii) Nuclides with same neutron number but different atomic number are

(iv) If R is the radius and A is the mass number, then log R versus log A graph will be

(v) The ratio of the nuclear radii of the gold isotope \({ }_{79}^{197} \mathrm{Au}\) and silver isotope \({ }_{47}^{107} \mathrm{Au}\) is

A heavy nucleus breaks into comparatively lighter nuclei which are more stable compared to the original heavy nucleus. When a heavy nucleus like uranium is bombarded by slow moving neutrons, it splits into two parts releasing large amount of energy. The typical fission reaction of \({ }_{92} \mathrm{U}^{235}\).
\({ }_{92} \mathrm{U}^{235}+{ }_{0} n^{1} \rightarrow{ }_{56} \mathrm{Ba}^{141}+{ }_{36} \mathrm{Kr}^{92}+3{ }_{0} n^{1}+200 \mathrm{MeV}\)
The fission of ₉₂U²³⁵approximately released 200 MeV of energy.
(i) If 200 MeV energy is released in the fission of a single nucleus of \({ }_{92}^{235} \mathrm{U}\),the fissions which are required to produce a power of 1kW is

(ii) The release in energy in nuclear fission is consistent with the fact that uranium has

(iii) When ₉₂U²³⁵undergoes fission, about 0.1% of the original mass is converted into energy. The energy released when 1 kg of ₉₂U²³⁵undergoes fission is

(iv) A nuclear fission is said to be critical when multiplication factor or K

(v) Einstein's mass-energy conversion relation E = mc² is illustrated by

Neutrons and protons are identical particle in the sense that their masses are nearly the same and the force, called nuclear force, does into distinguish them. Nuclear force is the strongest force. Stability of nucleus is determined by the neutron proton ratio or mass defect or packing fraction. Shape of nucleus is calculated by quadrupole moment and spin of nucleus depends on even or odd mass number. Volume of nucleus depends on the mass number. Whole mass of the atom (nearly 99%) is centred at the nucleus.
(i) The correct statements about the nuclear force is/are

(ii) The range of nuclear force is the order of

(iii) A force between two protons is same as the force between proton and neutron. The nature of the force is

(iv) Two protons are kept at a separation of 40 \(\dot A\). Fn is the nuclear force and F_e is the electrostatic force between them. Then

(v) All the nucleons in an atom are held by

The density of nuclear matter is the ratio of the mass of a nucleus to its volume. As the volume of a nucleus is directly proportional to its mass number A, so the density of nuclear matter is independent of the size of the nucleus. Thus, the nuclear matter behaves like a liquid of constant density. Different nuclei are like drops of this liquid, of different sizes but of same density.
Let A be the mass number and R be the radius of a nucleus. If m is the average mass of a nucleon, then
Mass of nucleus = mA
\(\text { Volume of nucleus }=\frac{4}{3} \pi R^{3}=\frac{4}{3} \pi\left(R_{0} A^{1 / 3}\right)^{3}=\frac{4}{3} \pi R_{0}^{3} A\)
\(\text { Nuclear density, } \rho_{\mathrm{nu}}=\frac{\text { Mass of nucleus }}{\text { Volume of nucleus }} \text { or } \rho_{\mathrm{nu}}=\frac{m A}{\frac{4}{3} \pi R_{0}^{3} A}=\frac{3 m}{4 \pi R_{0}^{3}}\)
Clearly, nuclear density is independent of mass number A or the size of the nucleus. The nuclear mass density is of the order 10¹⁷ kg m^-3. This density is very large as compared to the density of ordinary matter, say water, for which p = 1.0 x 10³ kg m^-3.
(i) The nuclear radius of \({ }_{8}^{16} \mathrm{O}\) is 3 X 10^-15 m. The density of nuclear matter is

(ii) What is the density of hydrogen nucleus in SI units? Given R_o = 1.1 fermi and m_p = 1.007825 amu

(iii) Density of a nucleus is

(iv) The nuclear mass of \({ }_{26}^{56} \mathrm{Fe}\) is 55.85 amu. The its nuclear density is

(v) If the nucleus of \({ }_{13}^{27} \mathrm{Al}\) has a nuclear radius of about 3.6 fm, then \({ }_{52}^{125} \mathrm{Te}\) would have its radius approximately as

When subatomic particles undergo reactions, energy is conserved, but mass is not necessarily conserved.However, a particle's mass "contributes" to its total energy, in accordance with Einstein's famous equation, E = mc², In this equation, E denotes the energy carried by a particle because of its mass. The particle can also have additional energy due to its motion and its interactions with other particles. Consider a neutron at rest and well separated from other particles. It decays into a proton, an electron and an undetected third particle as given here: Neutron \(\rightarrow\) proton + electron + ???
The given table summarizes some data from a single neutron decay. Electron volt is a unit of energy. Column 2 shows the rest mass of the particle times the speed of light squared.

(i) From the given table, which properties of the undetected third particle can be calculate?

(ii) Assuming the table contains no major errors, what can we conclude about the (mass x c²) of the undetected third particle?

(iii) Could this reaction occur?
Proton \(\rightarrow\) neutron + other particles

(iv) How much mass has to be converted into energy to produce electric power of 500 MW for one hour?

(v) The equivalent energy of 1 g of substance is