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# 3 Math Example Related To Binding Energy

### Math Example Related To Binding Energy.

1. The helium nucleus  42He (also called an alpha particle)has a mass of 4.001506u.Determine its binding energy in terms of the atomic mass units and in MeV.

Solution:

Mass of proton=1.007825u
Mass of neutron=1.008665 u
Total mass of proton=2 x 1.007825 u
=2.01565 u

Total mass of proton=2 x 1.008665 u
=2.01733 u

Total mass of constituents=(2.01565 + 2.01733 )u
=4.032980 u

Mass of alpha particle=4.001506 u

Binding energy =(4.032980 - 4.001506)u
=0.030377 u

In terms of MeV:

The binding energy is =0.030377 x 931.5 MeV
=28.296 MeV  (divided  by 4 )
=7.074 MeV per nucleon.


Math Example Related To Binding Energy.

2. An isotope of Uranium  23595U has a nuclear mass of 235.043930u.Determine its binding energy in terms of the atomic mass units and in MeV.

Solution:

Mass of proton=1.007825u
Mass of neutron=1.008665 u
Total mass of proton=92 x 1.007825 u
=92.7199 u

Total mass of proton=(235-92) x 1.008665 u
=144.239095 u

Total mass of constituents=(92.7199 + 144.239095 )u
=236.958995 u

Mass of alpha particle=235.043930u

Binding energy =(236.958995  - 235.043930)u
=1.915065 u

In terms of MeV:

The binding energy is =1.915065 x 931.5 MeV
=1783.883048 MeV  (divided  by 235 )
=7.59 MeV per nucleon.


Math Example Related To Binding Energy.

3. The most abundant isotope of Uranium  23895U has a nuclear mass of 235.050788u. Determine the binding energy per nucleon in MeV.

Solution:

Mass of proton=1.007825u
Mass of neutron=1.008665 u
Total mass of proton=92 x 1.007825 u
=92.7199 u

Total mass of proton=(238-92) x 1.008665 u
=147.26509 u

Total mass of constituents=(92.7199 + 147.26509 )u
=239.98499 u

Mass of alpha particle=235.050788u

Binding energy =(239.98499  - 235.050788)u
=1.934202 u

In terms of MeV:

The binding energy is =1.934202 x 931.5 MeV
=1801.709163 MeV  (divided  by 238 )
=7.57 MeV per nucleon.


## What Are The Factor Which Goes In Favour Of Nuclear Energy?

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