Question

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?
$\text{A}\text{. deuteron density = }2\times {{10}^{12}}c{{m}^{-3}}\text{, confinement time}=5\times {{10}^{-3}}s$
$\text{B}\text{. deuteron density = 8}\times {{10}^{14}}c{{m}^{-3}}\text{, confinement time}=9\times {{10}^{-1}}s$
$\text{C}\text{. deuteron density = }4\times {{10}^{23}}c{{m}^{-3}}\text{, confinement time}=1\times {{10}^{-11}}s$
$\text{D}\text{. deuteron density = 1}\times {{10}^{24}}c{{m}^{-3}}\text{, confinement time}=4\times {{10}^{-12}}s$

Answer 1

Hint: A fusion reactor is a device that is used to generate large amounts of energy. In a fusion reactor energy is produced by nuclear fusion. According to Lawson criterion, the maximum yield of energy is obtained when the product of the deuteron density and the confinement time is less than $5\times {{10}^{14}}c{{m}^{-3}}s$.

Complete answer:
A fusion reactor is a device that is used to generate large amounts of energy. In a fusion reactor energy is produced by nuclear fusion.
Nuclear fission is a process in which a two lighter nuclei combine to form a single heavy nucleus. It is found that the mass of the single nucleus formed is less than the sum of the masses of the lighter nuclei. The missing mass is converted into a very large amount of energy.
Therefore, a fusion reaction results in the release of a tremendous amount of energy.
D-D fusion reaction, is the fusion reaction between deuterium nuclei.
Lawson criterion tells us about the ratio of rate of energy produced to the rate of energy lost in the process. It gives us the relation between nuclei density (deuteron density) and confinement time.
It is said that maximum yield of energy is obtained when $n\tau $> $5\times {{10}^{14}}c{{m}^{-3}}s$
Here, n is the deuteron density and $\tau $ is the confinement time.
Let us calculate the value of $n\tau $for the given options.
A- $n\tau =2\times {{10}^{12}}\times 5\times {{10}^{-3}}={{10}^{10}}c{{m}^{-3}}s$
B- $n\tau =8\times {{10}^{14}}\times 9\times {{10}^{-1}}=7.2\times {{10}^{14}}c{{m}^{-3}}s$
C- $n\tau =4\times {{10}^{23}}\times 1\times {{10}^{-11}}=0.04\times {{10}^{14}}c{{m}^{-3}}s$
D- $n\tau =1\times {{10}^{24}}\times 4\times {{10}^{-12}}=0.04\times {{10}^{14}}c{{m}^{-3}}s$.

So, the correct answer is “Option D”.

Note:
This was the case when the fusion reaction is between deuterium nuclei.
When the fusion reaction takes place between deuterium and tritium the value of $n\tau $> $5\times {{10}^{16}}c{{m}^{-3}}s$.
For maximum yield of energy, the temperature of the reactor must be maintained at a certain temperature called ignition temperature.