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Question
The Q value of a nuclear reaction \[\ce{A + b → C + d}\] is defined by
Q = [ mA+ mb− mC− md]c2 where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic.
\[\ce{^1_1H + ^3_1H -> ^2_1H + ^2_1H}\]
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
Solution
The given nuclear reaction is:
\[\ce{^1_1H + ^3_1H -> ^2_1H + ^2_1H}\]
It is given that:
Atomic mass `m(""_1^1"H")` = 1.007825 u
Atomic mass `m(""_1^3"H")` = 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`
Q = (- 0.00433 c2)u
But 1 u = 931.5 MeV/c2
`= [1.007825 + 3.016049 - 2 xx 2.014102]c^2`
`"Q" = - 0.00433 xx 931.5 = - 4.0334` MeV
The negative Q-value of the reaction shows that the reaction is endothermic.
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