The Q value of a nuclear reaction, A + b $\to$ C + d, is defined by
$Q = [m_{A} + m_{b}] - [m_{C} + m_{d}]$
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) $_{1}^{1} H +_{3}^{1} H \to_{1}^{2} H +_{1}^{2} H$
(ii) $_{6}^{12} C +_{6}^{12} C \to_{10}^{20} N e +_{2}^{4} H e$
Atomic masses are given to be
$m (_{1}^{2} H) = 2.014102 u$
$m (_{1}^{3} H) = 3.016049 u$
$m (_{6}^{12} C) = 12.000000 u$
$m (_{10}^{20} N e) = 19.992439 u$

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Solution

(i) $_{1}^{1} H +_{1}^{3} H \to_{1}^{2} H +_{1}^{2} H$
$Q = [m_{_{1}^{1} H} + m_{_{1}^{3} H}] - [m_{_{1}^{2}} + m_{_{1}^{2} H}]$
$Q = 1.00758 + 3.016049 - [2.014102 + 2.014102]$
$Q = - 0.0046$ u
Since, Q is negative, some mass is converted into energy. Hence, the reaction is endothermic.
(ii) $_{6}^{12} C +_{6}^{12} C \to_{10}^{20} N e +_{2}^{4} H e$
$Q = [m_{_{6}^{12} C} + m_{_{6}^{12} C}] - [m_{_{10}^{20} N e} + m_{_{2}^{4} H e}]$
$Q = 12.000000 + 12.000000 - [19.992439 + 4.00387]$
$Q = 0.00369$ u
Since, Q is positive, some mass is converted into energy. Hence, the reaction is exothermic.

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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]c²where 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)

(ii)

Atomic masses are given to be

Q. The Q value of a nuclear reaction A + b → C + d is defined by Q = [ mA + mb – mC – md ]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. (i) 1 3 2 2 1 1 1 1 H+ H H+ H → (ii) 12 12 20 4 6 6 10 2 C+ C Ne+ 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

Q. Fusion reaction is given by

_{6}^{12} C +_{6}^{12} C \to_{10}^{20} N e +_{2}^{4} H e

.
If B.E. per nucleon for

_{6}^{12} C

is X, B.E. per nucleon for

_{10}^{20} N e

is Y and B.E. per nucleon for

_{2}^{4} H e

is Z, then Q value of reaction is

Q. Distinguish between nuclear fission and fusion. Show how in both these processes energy is released. Calculate the energy release in MeV in the deuterium-tritium fusion reaction :

_{1}^{2} H +_{1}^{3} H \to_{1}^{4} H e +_{0} n^{1}

Using the data:

m (_{1}^{2} H) = 2.014102 u

m (_{1}^{3} H) = 3.016049 u

m (_{2}^{4} H e) = 4.002603 u

m n = 1.008665 u

l u = 931.5 M e V / c 2

Calculate the Q-values of the following fusion reactions:

(a) $_{1}^{2} H +_{1}^{2} H \to_{1}^{3} H +_{1}^{1} H$

(b) $_{1}^{2} H +_{1}^{2} H \to_{3}^{2} H e + n$

Atomic masses are $m (_{1}^{2} H e) = 2.014102 u, m (_{1}^{3} H e) = 3.016049 u, m (_{2}^{3} H e) = 3.016029 u, m (_{2}^{4} H e) = 4.002603 u$ .

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