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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 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

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#### 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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