Express to 6 sig figs ADetermine the total binding energy of

Express to 6 sig figs.

A.)Determine the total binding energy of radium-226 (^226_88Ra).

B.)Determine and add together the binding energies of a radon-222 (^222_86Rn) and an alpha particle.

C.) Determine the difference of these numbers, which equals the energy released during alpha decay of (^226Ra).

Solution

a) Mass of radium = 226u
Mass of proton = 1.007316u
Mass of neutron = 1.008664 u
Protons in radium = 88
Neutrons = 226-88 = 138
mass deficit = [88*1.007316 + 138*1.008664 - 226]u = 1.83944u
Binding Energy = Energy due to mass deficit = mass deficit * c^2 (e = mc^2)
E = 1.83944u*c^2 = 1.83944*1.66054e-27 *c^2 = 2.74524e-10 J
b) Alpha particle = 2 protons + 2 neutrons
Binding energy = (2*1.007316u + 2*1.008664 u - 4u)c^2 = 0.03196u*c^2 = 4.769e-12 J
c) Energy diff = 2.6975e-10 J