Answer: The energy released for 1 mole of hydrogen formed is [tex]3.597\times 10^{-13}J[/tex]
Explanation:
First we have to calculate the mass defect [tex](\Delta m)[/tex].
The equation for the fusion of two carbon-12 nuclei follows:
[tex]_{6}^{12}\textrm{C}+_{6}^{12}\textrm{C}\rightarrow _{11}^{23}\textrm{Na}+_1^{1}\textrm{H}[/tex]
To calculate the mass defect, we use the equation:
Mass defect = Sum of mass of reactant - Sum of mass of product
[tex]\Delta m=(2m_C)-(m_{Na}+m_{H})[/tex]
[tex]\Delta m=(2\times 12.0000)-(22.989767+1.007825)=2.408\times 10^{-3}amu=3.997\times 10^{-30}kg[/tex]
(Conversion factor: [tex]1amu=1.66\times 10^{-27}kg[/tex] )
To calculate the energy released, we use Einstein equation, which is:
[tex]E=\Delta mc^2[/tex]
[tex]E=(3.997\times 10^{-30}kg)\times (3\times 10^8m/s)^2[/tex]
[tex]E=3.597\times 10^{-13}J[/tex]
Hence, the energy released for 1 mole of hydrogen formed is [tex]3.597\times 10^{-13}J[/tex]
