Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen, `._(1)^(2)H`, Known as deutreron and denoted by `D`, can be throught of as a candidate for fusion reactor. The `D-D` reaction is `._(1)^(2)H+._(1)^(2)Hrarr._(2)^(2)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 this core. If `n` is the density (number`//` volume) of deuterons, hte product `nt_(0)` is called Lawson number. In one of the criteria, a reactor is termed successful if Lawson is greater than `5xx10^(14)s//cm^(3)`.
It may be helpful to use the following. Boltzman constant `K=8.6xx10^(-5)eV//K, (e^(2))/(4piepsilon_(0))=1.44xx10^(-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 `4xx10^(-15)m` in the range.

Options

A. strong nuclear force acting between the deuterons
B. Coulomb force acting between the deuterons
C. Coulomb force acting between deuterons-electrons pairs
D. the high temperature maintained inside the reactor core

Answer

D

Explanation

From energy conservation
`2((3)/(2)kT)=(1)/(4piepsilon_(0))(e^(2))/(r )`
`rArr T=((1.44xx10^(-9)))/((8.6xx10^(-5)))xx(1)/(3xx4xx10^(-15))=1.39xx10^(9)K`