Nuclei Test - 11

Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, $$^{2}_{1}\mathrm{H}$$ known as deuteron and denoted by $$\mathrm{D}$$ can be thought of as a candidate for fusion reactor. The $$\mathrm{D}-\mathrm{D}$$ reaction is $$^{2}_{1}\mathrm{H}+_{1}^{2}\mathrm{H}\rightarrow_{2}^{3} He +\mathrm{n}+$$ energy. In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of  $$^{2}_{1}\mathrm{H}$$ 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 $$k=8.6 \times 10^{-5} eV/K; \displaystyle \frac{\mathrm{e}^{2}}{4\pi\epsilon_{0}} =1.44\times 10^{9}\mathrm{e}\mathrm{V}\mathrm{m}$$.

Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, $$^{2}_{1}\mathrm{H}$$ known as deuteron and denoted by $$\mathrm{D}$$ can be thought of as a candidate for fusion reactor. The $$\mathrm{D}-\mathrm{D}$$ reaction is $$^{2}_{1}\mathrm{H}+_{1}^{2}\mathrm{H}\rightarrow_{2}^{3} He +\mathrm{n}+$$ energy. In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of  $$^{2}_{1}\mathrm{H}$$ 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 $$k=8.6 \times 10^{-5} eV/K; \displaystyle \frac{\mathrm{e}^{2}}{4\pi\epsilon_{0}} =1.44\times 10^{9}\mathrm{e}\mathrm{V}\mathrm{m}$$.

The mass of nucleus $$^{A}_{Z}X$$ is less than the sum of the masses of ($$\mathrm{A}-\mathrm{Z}$$) number of neutrons and $$\mathrm{Z}$$ number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. $$\mathrm{A}$$ heavy nucleus of mass $$\mathrm{M}$$ can break into two light nuclei of mass $$\mathrm{m}_{1}$$ and $$\mathrm{m}_{2}$$ only if $$(\mathrm{m}_{1}+\mathrm{m}_{2})<\mathrm{M}.$$ Also two light nuclei of masses $$\mathrm{m}_{3}$$ and $$\mathrm{m}_{4}$$ can undergo complete fusion and form a heavy nucleus of mass $$\mathrm{M}'$$ only if $$(\mathrm{m}_{3} +\mathrm{m}_{4})>\mathrm{M}'$$. The masses of some neutral atoms are given in the table above: