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.
(i) $^{1}_{ 1} H + ^{3} _{1}H → ^{2}_{1} H + ^{2}_{1} H$
(ii) $^{12}_{6} C + ^{12}_{6} C → ^{12}_{10} Ne + ^{4}_{2} He$
Atomic masses are given to be
$m (^{2}_{ 1} H)$ = 2.014102 u
$m (^{3}_{1} H)$= 3.016049 u
$m (^{12}_{ 6} C)$= 12.000000 u
$m (^{20}_{10} Ne)$ = 19.992439 u

Answer 1

(i) The given nuclear reaction is:
$^{1} _{1} H + ^{3}_{1} H → ^{2}_{1} H + ^{2} _{1} H$
It is given that:
Atomic mass $m (^{1}_{1} H)$= 1.0078 25 u
Atomic mass $m (^{3}_{1} H)$ = 3.016049 u
Atomic mass $m (^{2}_{1} H)$ = 2.014102 u
According to the question, the Q-value of the reaction can be written as:
Q = [$m (^{1}_{1} H)$ + $m (^{3}_{1} H)$- $m (^{2}_{1} H)$]c2
Q = [1.0078 25 + 3.016049 -2 x 2.014102]c2
Q = (-0.00433 c2)u
But 1u = 931.5 $\frac{Mev}{c^{2}}$
Q = -0.00433 x 931.5 = -4.0334 MeV
The negative Q-value of the reaction shows that the reaction is endothermic.

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(ii) The given nuclear reaction is:
$^{12}_{6} C + ^{12}_ {6} C → ^{12}_{10} Ne + ^{4 }_{2} He$
It is given that:
Atomic mass of m $(^{12}_{6} C) = 12.000000 u$
Atomic mass of $m (^{20}_{10} Ne)$ = 19.992439 u
Atomic mass of $m (^{4}_{2} He)$ = 4.002603 u
The Q-value of this reaction is given as:
Q = [2m$(^{12}_{6}C)$ - $m(^{20}_{10}Ne)$ - $m(^{4}_{2}He)]c^2$
Q = [2 x 12.0 -19.992439 - 4.002603]c2
Q = (0.004958 c2) u
Q = 0.004958 x 931.5
Q = 4.618377 MeV
The positive Q-value of the reaction shows that the reaction is exothermic.