Calculate the binding energy per nucleon for a 157N715N nucleus. The mass of the neutral atom of 157N715N is 15.000109 uu, the mass of the neutral atom of 11H11H is 1.007825 uu and the mass of neutron is 1.008665

The binding energy per nucleon for a nucleus is 7.7 MeV. It was calculated with the mass of the neutral atom (15.000109 u), the mass of proton ¹H (1.007825 u), and the mass of neutron (1.008665 u).  

We can calculate the binding energy per nucleon with the following equation:

Where:

c: is the speed of light

A: is the number of nucleons in the nucleus of = 15

We know that 1 u = 931.5 MeV/c², so the binding energy is:

(1)

Where:

p: is the number of protons = 7

n: is the number of neutrons = A - p = 15 - 7 = 8

: is the proton's mass = 1.007825 u                

: is the neutron's mass = 1.008665 u      

= 15.000109 u  

By entering the above values into equation (1), we have:

Therefore, the binding energy per nucleon is 7.7 MeV.

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Explanation:

The binding energy of a nucleus is given by

(1)

where

is the speed of light

is the mass defect, which is the difference between the sum of the masses of the individual nucleons and the total mass of the nucleus.

Here the mass of the nucleus is

While the mass of the nucleons is:

(mass of the proton)

(mass of the neutron)

The nucleus containes 7 protons (atomic number) and 15 nucleons (mass number), which means that the number of neutrons is

So the mass defect is:

1 atomic mass unit is

So the mass defect in kilograms is

Finally, we can use eq(1) to find the binding energy: