Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, $$_1^2$$H, known as deuteron and denoted by D, can be thought of as a candidate for fusion reactor. The D-D reaction is $$_1^2$$H + $$_1^2$$H $$\to$$ $$_2^3$$He + $$n$$ + energy. In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of $$_1^2$$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; $${{{e^2}} \over {4\pi {\varepsilon _0}}} = 1.44 \times {10^9}$$ eVm.
Assume that two deuteron nuclei in the core of fusion reactor at temperature T are moving towards each other, each with kinetic energy 1.5 kT, when the separation between them is large enough to neglect Coulomb potential energy. Also neglect any interaction from other particles in the core. The minimum temperature T required for them to reach a separation of 4 $$\times$$ 10$$^{-15}$$ m is in the range
Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, $$_1^2$$H, known as deuteron and denoted by D, can be thought of as a candidate for fusion reactor. The D-D reaction is $$_1^2$$H + $$_1^2$$H $$\to$$ $$_2^3$$He + $$n$$ + energy. In the core of fusion reactor, a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of $$_1^2$$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; $${{{e^2}} \over {4\pi {\varepsilon _0}}} = 1.44 \times {10^9}$$ eVm.
Results of calculations for four different designs of a fusion reactor using D-D reaction are given below. Which of these is most promising based on Lawson criterion?
A radioactive sample S1 having activity of 5 $$\mu$$Ci has twice the number of nuclei as another sample S2 which has an activity of 10 $$\mu$$Ci. The half lives of S1 and S2 can be :
In a mixture of H - He$$^+$$ gas (He$$^+$$ is singly ionized He atom), H atoms and He$$^+$$ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He$$^+$$ ions (by collisions). Assume that the Bohr model of atom is exactly valid.
The quantum number n of the state finally populated in He$$^+$$ ions is :