Question

The Q value of a nuclear reaction
A+b=C+d is defined by `Q=[m_A+m_b-m_C-m_d]c^2` where the masses refer to the respective nuclei. Determine form the given data the Q value of the following reactions and state whether the reactions are exothermic of endothermic.
(i) `._1H^(1)+._1H^3to ._1H^2+._1H^2`
(ii) `._6C^(12)+._6C^(12) to ._10Ne^(20)+._2He^4`
Atomic masses are given to be
`m(._1H^2)=2.014102u , m(._1H^3)=3.016049 u, m(._6C^(12))=12.000000u , m(._10Ne^(20))=19.992439u`

Answer 1

(i) the given nuclear reaction is :
`""_(1)H^(1)+""_(1)^(3)H to ""_(1)^(2)H +""_(1)^(2)H`
It is given that :
Atomic mass `m(""_(1)^(1)H) =1.007825 u`
Atomic mass `m(""_(1)^(1H)=3.016049 u`
Atomic mass `m(""_(1)^(2)H))=2.014102 u`
According to the question , the Q - value of the reaction can be written as :
`Q=[m(""_(1)^(1)H)+m(_(1)^(3)H)- 2 m(_(1)^(2)H)]c^(2)`
`=[1.007825 +3.016049 - 2xx2.0114102 ]c^(2)`
`Q=(-0.00433 c^(2))u`
But `1 u =931.5 Me V/V^(2) `
` therefore Q =- 0.00433xx931.5 =- 4.0334 MeV `
the nagative Q - value of the reaction shows that the reacion is endothermic
(ii) THe given nuclease reaction is :
`""_(6)^(12)C+_(6)^(12)C to _(10)^(20) NE + _(2)^(4)He `
it is given that : atomic mass of `m(""_(6)^(12)C) =12.0u`
Atomic mass of `m(""_(10)^(20)Ne )=19.992439 u`
Atomic mass of `m(""_(2)^(4)He He )=4.002603 u`
the Q- value of this reaction is given as :
`Q[2m (""_(6)^(12)C)-m(""_(10)^(20)Ne )-m(""_(2)^(4)He )]c^(2)`
`= [2xx10.0 -19.992439 - 4.002603]c^(2)`
`=(0.004958 c^(2))u`
`=0.004958 xx931.5 =4.618377 MeV`
the postive Q - value of the reaction shows that the reaction is exothermic .