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 reactor , The D-D reaction is $_{1}^{2} H +_{1}^{2} H \to_{2}^{3} H e + n$ +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 nulear fusion to take place. Usually , the temperature in the reactors 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 $n t_{0}$ is called Lawson number. In one of the criteria , a reactor is termed successful if Lawson number is greater than $5 \times 10^{14} s / c m^{3}$ .
If may be helpful to use the following: Boltzmann constant $k = 8.6 \times 10^{- 5} e V / K, \frac{e ^{2}}{4 π ϵ _{0}} = 1.44 \times 10^{- 9} e V m$ .
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 $4 \times 10^{- 15}$ m is in the range

Question

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 reactor , The D-D reaction is

_{1}^{2} H +_{1}^{2} H \to_{2}^{3} H e + 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 nulear fusion to take place. Usually , the temperature in the reactors 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

n t_{0}

is called Lawson number. In one of the criteria , a reactor is termed successful if Lawson number is greater than

5 \times 10^{14} s / c m^{3}

.
If may be helpful to use the following: Boltzmann constant

k = 8.6 \times 10^{- 5} e V / K, \frac{e ^{2}}{4 π ϵ _{0}} = 1.44 \times 10^{- 9} e V m

.
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

4 \times 10^{- 15}

m is in the range

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