Physics

Problem

Consider the following nuclear reaction:

\;^7\!\mathrm{Li}\;\rightarrow\;^4\!\mathrm{He}+\;^3\!\mathrm{H}

The nuclear masses are:

^7\!\mathrm{Li}:\;7.01436\,\text{u}

^4\!\mathrm{He}:\;4.00151\,\text{u}

^3\!\mathrm{H}:\;3.01550\,\text{u}

. Take

\mathrm{m_p}=1.00727\,\text{u}

\mathrm{m_n}=1.00866\,\text{u}

and

1\,\text{u}=931.5\,\text{MeV}/c^{2}

. a. (i) Calculate the binding energy per nucleon for

^7\!\mathrm{Li}

. (Show all steps.) b. (ii) Calculate the binding energy per nucleon for

^4\!\mathrm{He}

and for

^3\!\mathrm{H}

separately. c. (iii) Using your results, find the

Q

-value of the reaction above and state whether the reaction is energetically allowed (exothermic) or not.