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The Q-value of a nuclear reaction A + b ...

The Q-value of a nuclear reaction A + b `to` 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 from the given data the Q-value of following reactions and state whether the reactions are exothermic or endothermic.
(i) `" "_(1)^(1)H+" "_(1)^(3)H (to) " "_(1)^(2)H+ " "_(1)^(2)H` (ii) `" "_(6)^(12)C+" "_(6)^(12)C (to) " "_(10)^(20)Ne + " "_(2)^(4)He`
Atomic masses are given to be m(`" "_(1)^(2)H) = 2.014102 u`, m(`" "_(1)^(3)H) = 3.016049 u`, `m(" "_(6)^(12)C) = 12.000000 u`, m(`" "_(10)^(20)Ne) = 19.992439 u`.

Text Solution

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`" "_(1)^(1)H+" "_(1)^(3)H to " "_(1)^(2)H+" "_(1)^(2)H`
In terms of atomic masses `Q =[{1.007825 + 3.016049}-{2.014102 + 2.014102}] xx 931.5 MeV =- 0.00433 xx 931.5 MeV = -4.03 MeV`
It is an endothermic reaction.
(ii) `" "_(6)^(12)C+" "_(6)^(12)C to " "_(10)^(20)Ne + " "_(2)^(4)He` `Q =[{12.0000 + 12.0000} - {19.992439 + 4.002603}] xx 931.5 MeV= 0.004958 xx 931.5 MeV = 4.62 MeV`
The reaction is exothermic.
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