Calculate the nuclear binding energy of Mn(A=55, z=25) in joules. The atomic mass of 5525Mn is 54.938 amu The speed of light is c=3.00×108 ms The mass of a proton is 1.0073 amu The mass of a neutron is 1.0087 amu The mass of an electron is 5.4858×10−4 aμ 1 kg=6.022×1026 aμ 1 J=1 kg⋅m2s2 1 MeV=1.602×10−13 J

Question

Calculate the nuclear binding energy of Mn(A=55, z=25) in joules.  The atomic mass of 5525Mn is 54.938 amu  The speed of light is c=3.00×108 ms  The mass of a proton is 1.0073 amu  The mass of a neutron is 1.0087 amu  The mass of an electron is 5.4858×10−4 aμ  1 kg=6.022×1026 aμ  1 J=1 kg⋅m2s2  1 MeV=1.602×10−13 J

Carl Swisher · Accepted Answer

The number of the neutrons of the substance is  N=A−Z  =55−25  =30  The expression for the final mass of the substance is  mf=Z(mp)+N(mn)  =25(1.0073 aμ)+30(1.0087 aμ)  =55.4435  The difference in mass is  △m=mf−mi  =55.4435 aμ−54.938 aμ  =0.5055aμ(1.66×10−27kg1aμ)  =8.39×10−28kg  The binding energy is  BE=△mc2  =(8.39×10−28kg)(3×108ms)2  =7.55×10−11J

Calculate the nuclear binding energy of M_n(A=55,\ z=25) in joul

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