Nuclei Test - 62

The compound unstable nucleus $$_{92}^{236}U$$ often decays in accordance with the following reaction:
$$_{92}^{236}U\rightarrow _{54}^{140}Xe+_{38}^{94}Sr+$$ other particles
During the reaction, the Uranium nucleus "fissions" (splits) into the two smaller nucleii. The reaction is energetically favorable because the smaller nucleii have higher nuclear binding energy per nucleon (although the lighter nuclei have lower total nuclear binding energies, because they contain fewer nucleons).
Inside a nucleus, the nucleons (protons and neutrons) attract each other with a "strong nuclear" force. All nucleons exert approximately the same strong nuclear force on each other. This force holds the nucleus together. Importantly, the strong nuclear force becomes important only when the protons and neutrons are very close together at intranuclear distances.

All nuclei consist of two types of particles - protons and neutrons. The nuclear force is the strongest force. Stability of nucleus is determined by the neutron-proton ratio or mass defect or binding energy per nucleus or packing fraction. The shape of the nucleus is calculated by quadrupole moment. Spin of a nucleus depends on even or odd mass number. The volume of the nucleus depends on the mass number. The whole mass of the atom (nearly 99%) is centered at the nucleus. The magnetic moment of the nucleus is measured in terms of the nuclear magnetons.

A radionuclide with decay constant $$\lambda$$ is being produced in a nuclear reactor at a rate $$q_0t$$ per second, where $$q_0$$ is a positive constant and $$t$$ is the time. During each decay, $$E_0$$ energy is released. The production of radionuclide starts at time $$t=0$$.

The compound unstable nucleus $$_{92}^{236}U$$ often decays in accordance with the following reaction:
$$_{92}^{236}U\rightarrow _{54}^{140}Xe+_{38}^{94}Sr+$$ other particles
During the reaction, the Uranium nucleus "fissions" (splits) into the two smaller nucleii. The reaction is energetically favorable because the smaller nucleii have higher nuclear binding energy per nucleon (although the lighter nuclei have lower total nuclear binding energies, because they contain fewer nucleons).
Inside a nucleus, the nucleons (protons and neutrons) attract each other with a "strong nuclear" force. All nucleons exert approximately the same strong nuclear force on each other. This force holds the nucleus together. Importantly, the strong nuclear force becomes important only when the protons and neutrons are very close together at intranuclear distances.

The compound unstable nucleus $$_{92}^{236}U$$ often decays in accordance with the following reaction:
$$_{92}^{236}U\rightarrow _{54}^{140}Xe+_{38}^{94}Sr+$$ other particles
During the reaction, the Uranium nucleus "fissions" (splits) into the two smaller nucleii. The reaction is energetically favorable because the smaller nucleii have higher nuclear binding energy per nucleon (although the lighter nuclei have lower total nuclear binding energies, because they contain fewer nucleons).
Inside a nucleus, the nucleons (protons and neutrons) attract each other with a "strong nuclear" force. All nucleons exert approximately the same strong nuclear force on each other. This force holds the nucleus together. Importantly, the strong nuclear force becomes important only when the protons and neutrons are very close together at intranuclear distances.

Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, $$_1^2H$$, known as deuteron and denoted by D can be thought of as a candidate for fusion reactor. The D-D reaction is $$_1^2H+_1^2H\rightarrow _2^3He+n+energy$$. In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of $$_1^2H$$ nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually, the temperatures in the reactor core are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time $$t_0$$ before the particles fly away from the core. If n is the density (number /volume) of deuterons, the product $$nt_0$$ is called Lawson number. In one of the criteria, a reactor is termed successful if Lawson number is greater than $$5\times 10^{14} s cm^{-3}$$.
It may be helpful to use the following: Boltzmann constant, $$k=8.6\times 10^{-5} eV K^{-1}; \dfrac {e^2}{4\pi \epsilon_0}=1.44\times 10^{-9}eV m$$.

The mass of nucleus $$_Z^AX$$ is less than the sum of the masses of (A-Z) number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass $$M$$ can break into two light nuclei of mass $$m_1$$ and $$m_2$$ only if $$(m) < M.$$ Also two light nuclei of masses $$m_3$$ and $$m_4$$ can undergo complete fusion and form a heavy nucleus of mass $$M$$ "only if $$(m_3+m_4) > M$$". The masses of some neutral atoms are given in the table below:

$$_1H^2$$	1.007825 u	$$_1^2H$$	2.014102 u	$$_1^3H$$	3.016050 u	$$_2^4He$$	4.002603 u
$$_3^6Li$$	6.015123 u	$$_3^7Li$$	7.016004 u	$$_{30}^{70}Zn$$	69.925325 u	$$_{34}^{82}Se$$	81.916709 u
$$_{64}^{152}Gd$$	151.919803 u	$$_{82}^{206}Pb$$	205.974455 u	$$_{84}^{210}Po$$	209.982876 u