Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen , `._(1)^(2)H`, known as deuteron and denoted by D, cab be throught of as a candidate for fusion reactor, The D-D reaction `._(1)^(2)H+_(1)^(2)H rarr_(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 collector 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. one of criteria, a reactor is termed successful it Lawson number is greater than `5 xx 10^(14) s//cm^(3)`
It may be helpful to use to following : Boltzman constant `k = 8.6 xx 10^(-5) wV//K , (e^(2))/(4 pi epsilon_(0)) = 1.44 xx 10^(-9) eVm`.
In the core of nuclear fusion reactor, the gas becomes plasma because of

Options

A. deuteron density `= 2.0xx10^(12)cm^(-3)`, confinement time `=5.0xx10^(-3)s`
B. deuteron density `= 8.0xx10^(14)cm^(-3)`, confinement time `=9.0xx10^(-1)s`
C. deuteron density `= 4.0xx10^(23)cm^(-3)`, confinement time `=1.0xx10^(-11)s`
D. deuteron density `= 1.0xx10^(24)cm^(-3)`, confinement time `=4.0xx10^(-12)s`

Answer

B

Explanation

`nt_(0) gt 5xx10^(14)s//cm^(3)`
for deuteron density `=8.0xx10^(14)cm^(-3)m`, confinement time `=9.0xx10^(-1)s`
`nt_(0)=7.2xx10^(14)s//cm^(3)`