Question

The Q value of a nuclear reaction \[\ce{A + b → C + d}\] is defined by

Q = [ m_A+ m_b− m_C− m_d]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

Answer 1

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.