A penny has a mass of 30 g Calculate the energy that would b

A penny has a mass of 3.0 g. Calculate the energy that would be required to separate all the neutrons and protons in this coin from one another. For simplicity, assume that the penny is made entirely of 63 Cu atoms (of mass 62.929 60 u).The masses of the proton-plus-electron and the neutron are 1.007 83 u and 1.008 66 u. respectively.

Solution

mass of penny m = 3 g

molar mass of cu is M = 63 g

Number of moles n = m/M

                            = 3/63

                            = 47.61 x10 ^-3 mol

Number of atoms in 1 mole = 6.023 x10 ²³

Number of atoms in n moles is N = nx(6.023 x10 ²³)

                                                 = 2.868x10 ²²

Number of protons(or electrons) in Cu = 29

Number of neutrons in Cu = 63 -29

                                     = 34

Mass defect dm = 29(mass of proton plus electron) + 34 (mass of neutron) - mass of ⁶³ Cu

                       = 29(1.00783 u) +34(1.00866 u) -62.92960 u

                       = 0.59191 u

We know 1 u = 931.5 MeV

energy required to separate protons and neutrons from one Cu atom E = dm x931.5 MeV

E = 0.59191 x931.5 MeV

    = 551.36 MeV

Energy required to separate protons and neutrons in this coin from one another

    E \' = NE

         = ( 2.868x10 ²²)(551.36 MeV)

         = 1.581 x10 ²⁵ MeV

        = 1.581 x10 ²⁵ x 1.6x10 ^-13 J

        = 2.53 x10 ¹² J