Question

The Q value of a nuclear reaction 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. Calculate the Q-value of the reaction and state whether this reaction is exothermic or endothermic.

\[_1^1\mathrm{H}+_1^3\mathrm{H}\rightarrow_1^2\mathrm{H}+_1^2\mathrm{H}\]

Atomic masses are given to be

\[\mathrm{m(}_{1}^{1}\mathrm{H)}=1.007825\mathrm{u}\]

\[\mathrm{m(}_{1}^{2}\mathrm{H)}=2.014102\mathrm{u}\]

\[\mathrm{m(}_{1}^{3}\mathrm{H})=3.016049\mathrm{u}\]

विकल्प

• − 4.0334 MeV, endothermic

• 4.0334 MeV, exothermic

• − 4.334 MeV, endothermic

• 4.334 MeV, exothermic

Answer 1

− 4.0334 MeV, endothermic

Explanation:

The given nuclear reaction is:

\[_1^1\mathrm{H}+_1^3\mathrm{H}\to_1^2\mathrm{H}+_1^2\mathrm{H}\]

Its is given that

\[\text{Atomic mass }m(_1^1\mathrm{H})=1.007825\mathrm{u}\]

\[\text{Atomic mass }m(_1^3\mathrm{H})=3.016049\mathrm{u}\]

\[\text{Atomic mass }m(_1^2\mathrm{H})=2.014102\mathrm{u}\]

According to the question, the Q-value of the reaction can be a written as:

\[Q=[m(_1^1\mathrm{H})+m(_1^3\mathrm{H})-2m(_1^2\mathrm{H})]c^2\]

= [1.007825 + 3.016049 − 2 × 2.014102] c²

Q = (− 0.00433 c²)

But 1 u = 931.5 MeV/c²

Q = − 0.00433 × 931.5 = – 4.0334 MeV

The negative Q-value of the reaction shows that the reaction is endothermic.