Respuesta :
Answer : The energy produced is [tex]3.410\times 10^{10}J[/tex]
Explanation :
First we have to calculate the moles of [tex]^{17}O[/tex].
[tex]\text{Moles of }^{17}O=\frac{\text{Mass of }^{17}O}{\text{Molar mass of }^{17}O}=\frac{5g}{16.99913g/mole}=0.294133moles[/tex]
Now we have to calculate the mass defect.
The balanced reaction is,
[tex]^{14}N+\alpha \rightarrow ^1H+^{17}O[/tex]
Mass defect = Sum of mass of product - sum of mass of reactants
[tex]\Delta m=[(n_{^1H}\times M_{^1H})+(n_{^{17}O}\times M_{^{17}O})]-[(n_{^{14}N}\times M_{^{14}N})+(n_{\alpha}\times M_{\alpha})][/tex]
where,
n = number of moles = 0.294133 moles
M = molar mass
Now put all the given values in the above, we get:
[tex]\Delta m=[(n_{^1H}\times M_{^1H})+(n_{^{17}O}\times M_{^{17}O})]-[(n_{^{14}N}\times M_{^{14}N})+(n_{\alpha}\times M_{\alpha})][/tex]
[tex]\Delta m=[(0.294133mole\times 1.00783g/mole)+(0.294133mole\times 16.99913g/mole)]-[(0.294133mole\times 14.00307g/mole)+(0.294133mole\times 4.0026g/mole)][/tex]
[tex]\Delta m=0.00037943157g=3.7943157\times 10^{-7}kg[/tex]
Now we have to calculate the energy produced.
[tex]Energy=\Delta m\times (c)^2[/tex]
[tex]Energy=(3.7943157\times 10^{-7}kg)\times (299792458m/s)^2[/tex]
[tex]Energy=3.410\times 10^{10}J[/tex]
Therefore, the energy produced is [tex]3.410\times 10^{10}J[/tex]
