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Question
The Q value of a nuclear reaction 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.
\[\ce{^12_6C + ^12_6C ->^20_10Ne + ^4_2He}\]
Atomic masses are given to be
`"m"(""_1^2"H")` = 2.014102 u
`"m"(""_1^3"H")` = 3.016049 u
`"m"(""_6^12C)` = 12.000000 u
`"m"(""_10^20"Ne")` = 19.992439 u
Solution
The given nuclear reaction is:
\[\ce{^12_6C + ^12_6C ->^20_10Ne + ^4_2He}\]
t is given that:
Atomic mass of `"m"(""_6^12"C") = 12.0 u`
Atomic mass of `"m"(""_10^20"Ne")` = 19.992439 u
Atomic mass of `"m"(""_2^4"He")` = 4.002603 u
The Q-value of this reaction is given as:
`"Q" = [2"m"(""_6^12"C") - "m"(""_10^20"Ne") - "m"(""_2^4"He")]"c"^2`
`= [2 xx 12.0 - 19.992439 - 4.002603]"c"^2`
`= (0.004958 c^2)"u"`
`= 0.004958 xx 931.5 = 4.618377` MeV
The positive Q-value of the reaction shows that the reaction is exothermic.
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