Lithium can undergo the following proton-induced reaction used in some fusion…

PHYSICS · Multi-part · A Level · Physics · Nuclear physics · Nuclear physics

Problem

Lithium can undergo the following proton-induced reaction used in some fusion schemes:

^{7}_{3}\mathrm{Li}+{}^{1}_{1}\mathrm{H}\;\longrightarrow\;2\,{}^{4}_{2}\mathrm{He}+\gamma

Atomic masses (in u):

^{7}_{3}\mathrm{Li}=7.016004

, proton

=1.007825

^{4}_{2}\mathrm{He}=4.002603

. Assume the energy of the emitted

\gamma

-ray is entirely due to the mass difference. Use

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

and

1\,\text{MeV}=1.6\times10^{-13}\,\text{J}

. Answer the following. (i) Compute the Q-value of the reaction in MeV. (ii) Express the Q-value obtained in part (i) in joules. (iii) Is the

\gamma

-ray photon more energetic or less energetic than a typical visible-light photon of wavelength

550\,\text{nm}

? Substantiate your answer with a numerical comparison of energies.