Question

A nuclear reaction is given as
$p{+}^{15}N{\to }_Z^{A}X+n$
Find the Q value of the reaction

Answer 1

The nuclear reaction will be ${}_1^{1}p{+}_7^{15}N{=}_Z^{A}X{+}_0^{1}n$

Now, $1+15=A+1\Rightarrow A=15$ and $1+7=Z+0\Rightarrow Z=8$

The nucleus would be isotope of oxygen i.e ${}_8^{15}O$

The atomic mass of proton $=1.00727$ amu ; atomic mass of neutron $=1.00866$ amu ; atomic mass of ${}^{15}O=15.9994$ amu and atomic mass of ${}^{15}N=15.000108$ amu

Sum of masses of reactants $=1.00727+15.000108=16.0074$ amu

Sum of masses of products $=15.9994+1.00866=17.0081$ amu

The Q-value $=$Mass difference $\Delta M=17.0081-16.0074=1.0007$ amu$=1.0007\times 931MeV=931.65MeV$