Question

Nuclear binding energy and fusion a) Using Einstein’s energy-mass equivalence, calculate the energy in MeV corresponding to one atomic mass unit u. b) Now, consider the fusion process of a deuterium nucleus and a proton into a Helium-3 nucleus: 2 1H +1 1 H → 3 2He (i) Given the masses of the nuclei M( 2 1H) = 2.014102 u and M( 3 2He) = 3.016030 u, calculate the mass defects of the 2 1H and 3 2He nuclei in atomic mass units. (ii) Calculate the binding energy per nucleon (B.E./A) in MeV for the 2 1H and 3 2He nuclei. (iii) Calculate the energy (expressed in MeV) released in the fusion process. (iv) How does this energy compare with the typical order of magnitude of energy released in a single chemical reaction of atoms or molecules, e.g. in the combustion of fuel? By how many orders of magnitude is the energy released in the fusion process larger?

Answer 1

(a)Einsteins mass-energy relation .

one atomic mass unit(amu)=1/12th of C-12 atom,atomic mass of C-12=12.

number of atoms in 12gms of carbon=no of atoms in one mole of carbon.

By using avagadros no N=6.023*

mass of 1 atom of C-12=12*/6.023*10kg

1 a.m.u=1.66*kg

velocity of light c=3*m/s

now by using energy in a.m.u=1.66**(3*)*(3*)

=1.66**9*

but one electron volt 1eV=1.6*J

1 a.m.u in eV=1.66**9*/1.6*eV=931*eV=931MeV