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Question -

Consider the D−T reaction (deuterium−tritiumfusion)

(a) Calculate the energyreleased in MeV in this reaction from the data:

= 2.014102 u

= 3.016049 u

(b)Consider the radiusof both deuterium and tritium to be approximately 2.0 fm. What is the kineticenergy needed to overcome the coulomb repulsion between the two nuclei? To whattemperature must the gas be heated to initiate the reaction? (Hint: Kineticenergy required for one fusion event =average thermal kinetic energy availablewith the interacting particles = 2(3kT/2); =Boltzman’s constant, = absolute temperature.)



Answer -

(a) Take the D-T nuclear reaction 

It is given that:

Mass ofm1= 2.014102 u
Mass of, m= 3.016049 u
Mass of  m= 4.002603 u
Mass ofm= 1.008665 u

Q-value of the given D-T reaction is:

Q = [mm2− m3 −m4c2

= [2.014102 + 3.016049 − 4.002603 −1.008665] c2

= [0.018883 c2] u

But 1 u = 931.5 MeV/c2

Q = 0.018883 ×931.5 = 17.59 MeV

(b) Radius ofdeuterium and tritium, r ≈ 2.0 fm = 2 × 10−15 m

Distance between the two nuclei at the momentwhen they touch each other, d = r + r = 4 × 10−15 m

Charge on the deuterium nucleus = e

Charge on the tritium nucleus = e

Hence, the repulsive potential energy betweenthe two nuclei is given as:

Where,

0 = Permittivityof free space

Hence, 5.76 × 10−14 J or 

of kinetic energy (KE) is needed to overcomethe Coulomb repulsion between the two nuclei.

However, it is given that:

KE

Where,

k = Boltzmann constant = 1.38 × 10−23 m2 kgs−2 K−1

T = Temperature required for triggering thereaction

Hence, the gas must be heated to a temperatureof 1.39 × 109 K to initiate the reaction.

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