Question

Consider the following reaction
${ }_{1}^{1} H +{ }_{1}^{3} H \rightarrow{ }_{1}^{2} H +{ }_{1}^{2} H$
The atomic masses are given as
$m\left({ }_{1}^{1} H \right)=1.007825 \,u$
$m\left({ }_{1}^{2} H \right)=2.014102 \,u $
$m\left({ }_{1}^{3} H \right)=3.016049 \,u$
The $Q$ - value of the above reaction will be

• A. -4.03 MeV
• B. -2.01 MeV
• C. 2.01 MeV
• D. 4.03 MeV

Answer 1

Answer: (A)

${ }_{1}^{1} H +{ }_{1}^{3} H \rightarrow{ }_{1}^{2} H +{ }_{1}^{2} H$
The $Q$ -value of the above reaction is
$ Q =\Delta M c^{2}=[1.007825+3.016049-2 \times 2.014102] u \times c^{2} $
$=-4.33 \times 10^{-3} u \times c^{2} $
$\because 1 \,u =931 \,MeV / c ^{2} $
$\therefore Q=-4.33 \times 10^{-3} \times 931\, MeV $
$=-4.03\, MeV$