A deuterium reaction that occurs in an experimental fusion reactor is in two stage:
(a) Two deuterium `(._1^2D)` nuclei fuse together to form a tritium nucleus, with a proton as a by product written as `D(D,p)T`.
(b) A tritium nucleus fuses with another deuterium nucleus to form a helium `._2^4He` nucleus with neutron as a by - product, written as T (D,n) `._2^4He`.
Compute (a) the energy released in each of the two stages, (b) the energy released in the combined reaction per deutrium. (c ) What percentage of the mass energy of the initial deuterium is released. Given,
`{:(._1^2D=2.014102 am u),(._1^3 T=3.016049), (._2^4 He =4.002603 am u),(._1^1 H =1.007825 am u),(._0^1 n =1.00665 am u):}`.

Explanation

(i) The reaction involved in the process is
` ._1^2D._1^2Drarr _1^3T+._1^1p+._1^1p+E_(1)`.
Mass defect of the above reaction is
`Delta m=[2(2.01402)-(3.016049+1.007825)]`
`=0.00433 am u`
Energy released in the process is
`E_(1) =0.004333 xx 931.2 MeV=4.0333 MeV`
ii. The reaction involved in the process is
` ._1^3T+._1^2Drarr ._2^4He +._0^1n+E_(2)`
Mass defect of above reaction is
` Delta m =[(3.-01049 +2.014102)`
`-(4.002603 +1.008665)]`
`=0.01888 am u`
Energy releasd in the process is
`E_(2) =0.01888 xx 931 MeV=17.585 MeV`
Total energy released in both processes is
` 17.585 +4.033 =21.618 MeV`
b. Energy released per decterium atom is
`E_(1) =(21.618)/(1) =7. 206 MeV`
c. `%` of rest mass of `._1^2D` released
`f=(7.206)/(2.014102xx931) =0.385%`.