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 rector . The `D-D` reaction is `_(1)^(2) H + _(1)^(2) H rarr _(2)^(1) He + n+` energy. In the core of fusion reactor, a gas of heavy hydrogen of `_(1)^(2) H` 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 temperature in the reactor core are too high and no material will can be used to confine the to 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 then `5 xx 10^(14) s//cm^(2)`
it may be helpfull to use the following boltzmann constant
`lambda = 8.6 xx 10^(-5)eV//k, (e^(2))/(4 pi s_(0)) = 1.44 xx 10^(-9) eVm`
Assume that two deuteron nuclei in the core of fusion reactor at temperature energy `T` are moving toward each other, each with kinectic energy `1.5 kT` , when the seperation between them is large enough to neglect coulomb potential energy . Also neglate any interaction from other particle in the core . The minimum temperature `T` required for them to reach a separation of `4 xx 10^(-15) m ` is 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`