Answer:
[tex]\text{(a) }8.187 \times 10^{-14}\text{ J}; \text{(b) 49 300 kJ/mol; (c) } 5.110 \times 10^{5}\text{ eV}[/tex]
Explanation:
This question involves the conversion of mass into energy: E = mc².
e + p ⟶ γ + γ
Each particle has the same mass so, in terms of mass, we can write
2e ⟶ 2γ or
 e ⟶ γ
Thus, we can just convert the mass of an electron to its energy equivalent.
(a) Energy in joules
[tex]E= 9.109 \times 10^{-28}\text{ kg} \times \left (2.998 \times 10^{8}\text{ m$\cdot$s}^{-1}\right )^{2} = \mathbf{8.187 \times 10^{-14}}\textbf{ J}[/tex]
(b) Energy in kilojoules per mole
[tex]E =8.187 \times 10^{-14}\text{ J } \times \dfrac{\text{ 1 k}}{\text{1000 J}} \,\times \,\dfrac{6.022 \times 10^{23}}{\text{1 mol}} = 4.930 \times 10^{7}\text{ J/mol}= \textbf{49 300 kJ/mol}[/tex]
(c) Energy in electron volts
[tex]E = 8.187 \times 10^{-14}\text{ J}\times \dfrac{6.242 \times 10^{18}\text{ eV}}{\text{1 J}} = \mathbf{5.110 \times 10^{5}}\textbf{ eV}[/tex]
