Question

In a red giant star, the energy generated through the fusion of helium to carbon is described by the overall reaction 3 4/2 HE ⇒ 12/6 C Assuming that the atomic mass of helium is 4.0026amu, the atomic mass of carbon is 12.000amu and that 1amu = 1.660539 x 10^-27 which of the following is true? a) the mass of the reactants exceeds the mass of the product by about 1.3x10^-29kg per reaction b) The reaction is exothermic and releases 1.17 x 10^-10J per reaction c) The fusion of 3 helium nuclei to carbon releases more energy than the production of the 3 helium nuclei from hydrogen fusion d) The reaction is slow because it invovles neutrinos and therefore proceeds by means of the weak interaction

Answer 1

Total mass of reactants is

$3\times4.0026=16.0104$ amu$=16.0104\times1.660539\times10^{-27}=1.993942020\times10^{-26}$

Mass of product is $1\times12.000=12.000$ amu$=12.000\times1.660539\times10^{-27}=1.9926468\times10^{-26}$

Hence mass of reactants is greater than product. Difference is

$\Delta m=1.9939420204\times10^{-26}-1.992646800000000\times10^{-26}\approx1.3\times10^{-29}$

(b) Since the mass of reactant is greater hence reaction will be exothermic

Energy released = $1.3\times10^{-29}\times(3\times10^8)^2=1.17\times10^{-12}$

hence flase

(c) True