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How much energy would be required to remove one neutron from nitrogen-14 isotope, given these masses?

a) N-14 isotope 14.0031 u

b) N-13 isotope 13.0057 u

## Homework Equations

Knowns

Electron = 0.000549 u

Proton = 1.007276 u

Neutron = 1.008665 u

## The Attempt at a Solution

Okay so the first step is to determine how many Protons and Neutrons there are: Periodic table says 7. Therefore A = 14, 13 and Z = 7

Second Step Determine what the unified mass of N-14 without its Electrons

m

_{nu1}= m

_{N-14}- 7m

_{e}

m

_{nu1}= 14.0031u - 7(0.000549)

m

_{nu1}= 13.999257 u

Third Step Determine what the unified mass of N-13 by adding its Nucleus components together

m

_{nu2}= 7m

_{p}+ 7m

_{n}

m

_{nu2}= 7(1.007276) + 7(1.008665)

m

_{nu2}= 14.11587 u

Now we need to subtract the two to find the difference in mass

|m

_{nu1}- m

_{nu2}| = |13.999257 u - 14.11587 u| = 0.102607 u

We can now convert this into the total binding energy

0.102607 u (931.5 MeV/c

^{2}/u) = 95.58 MeV/c

^{2}

If we divide this by A we will get our average Binding Energy

6.83 MeV/c

^{2}per Nucleon

When I do the same procedure for N-13 I get an answer of 7.24 Mev/c

^{2}

The back of the book completes the answer a totally separate way.

It takes the unified mass of N-13 and adds a neutron to it. It then takes this value and subtracts the unified mass of N-14 to get a difference of 0.0113 u. They convert this into an average binding value of 10.5 MeV/c

^{2}.

They then go on to say it would require ΔE = Δmc

^{2}= 10.5 MeV/c

^{2}of energy to remove one neutron from the N-14 isotope.

So my questions are as follows;

1. Who is more correct for their average binding value the book or me?

2. Why is my method wrong if the book is right?

3. For either my value or the books value, the final answer would've required me to convert the MeV/c

^{2}value into a kg equivalent, and then plugged it into the E=mc

^{2}equation to get a proper Joules value.

I appreciate any clarification you can offer.