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`
Result of calculations for four different design of a fusion reactor using `D-D` reaction are given below. which of these is most promising based on Lawson criterion ?

Options

A. deuteron density `= 2.0 xx 10^(12) cm^(-3)`, cofinement time `= 5.0 xx 10^(-3) s`
B. deuteron density `= 8.0 xx 10^(14) cm^(-3)`, cofinement time `= 9.0 xx 10^(-1) s`
C. deuteron density `= 4.0 xx 10^(23) cm^(-3)`, confinement time `= 1.0 xx 10^(-11) s`
D. deuteron density `= 1.0 xx 10^(24) cm^(-3)`, confinement time `= 4.0 xx 10^(-12) s`

Answer

B

Explanation

`nt_(0) gt 5 xx 10_(14) s//cm_(3)`
for deuteron density `= 8.0 xx 10_(-4) cm_(-3)` confinement time `= 9.0 xx 10_(-1) s`
`n t_(0) = 7.2 xx 10_(14) s//cm_(3)`