Question

Find the binding energy per nucleon for the plutonium isotope 239Pu. The mass of the neutral atom is 239.05216 u.

Answer 1

The answer is "
`\bold{7.56 \ Me\ V}`".

Step-by-step explanation:

calculating the binding energy on per nucleon:

calculating number of proton and neutrons:

proton
`P_u=94`

neutron
`= 239-94=145`

calculating mass:

proton mass
`\ m_P=1.007825 \ amu\\\\`

neutron mass
`\ m_n=1.008665 \ amu\\\\`

neutral atom mass
`m = 239.05216 \ amu\\\\`

mass of prtons
`= 94 * 1.007825 = 94.73555 \ amu\\\\`

mass of neutrons
`= 145 * 1.008665= 146.256425 \ amu\\\\`

Total nucleons mass formula:

`\to m_n = (P+n)`

`= 94.73555+ 146.256425\\\\= 240.991975 \ amu`

calculating the mass of defect:

`\to \Delta m= m_n-m\\\\`

`= 240.991975 - 239.05216\\\\= 1.939815 \ amu\\\\`

calculating the total of the binding energy:

`\to BE=\Delta m* 931.5 \ mev`

`= 1.939815 * 931.5\\\\=1806.938 \ Me \ V\\\\`

BE in per nucleon
`=(BE)/(239)= 7.56 \ Me\ V`