# Mass deflect and binding energy

1. Dec 10, 2009

### Nope

1. The problem statement, all variables and given/known data
Energy is required to separate a nucleus into its constituent nucleons. this energy is the total binding energy of the nucleus. for example, separating nitrogen-14 into nitrogen-13 and a neutron takes an energy equal to the binding energy of the neutron.
use the following data for this question
nitrogen-14=14.003074u
nitrogen-13=13.005738u
carbon-13=13.003355u
a) find the energy that binds the neutron to the nitrogen-14 nucleus.
b) similarly, one can speak of the energy that binds a single proton to the nitrogen-14 nucleus . Determine the energy that binds a proton to that nucleus.
c) which is greater? why do you think this is so?

I don't understand a and b..I know how to calculate the mass deflect, but i not sure if it is nitrogen-15 or nitrogen-13
Ty
2. Relevant equations

3. The attempt at a solution

Last edited: Dec 10, 2009
2. Dec 11, 2009

### ehild

What is the mass defect in these processes?

a. N13 + neutron ---> N14?
b. C13 + proton ----> N14?

ehild

3. Dec 11, 2009

### Nope

For a) Is it
m=7(mass of proton)+7(mass of neutron)-14.003074u=mass deflect of nitrogen-14 or (nitrogen-13 and a neutron binding energy)?
I don't know how to do b. i think i did wrong in a?

4. Dec 11, 2009

### ehild

One N13 and one neutron makes a N14 atom. The mass of N13 + mass of free neutron is more than the mass of the N14 atom. The difference is the binding energy of the neutron to the N13 nucleus.

ehild

5. Dec 11, 2009

### Nope

13.005738u+1(1.008665u)=14.014403
and then use mass deflect
m=7(mass of proton)+7(mass of neutron)-14.014403u=
then E=mc^2? to find the binding energy...
Thanks !
btw can you explain why is The mass of N13 + mass of free neutron is more than the mass of the N14 atom? I thought it would be same..
I am confused of "The difference is the binding energy of the neutron to the N13 nucleus."
do you mean 14.014403u-14.003074u?

6. Dec 11, 2009

### ehild

Yes, that will be the binding energy of the neutron if you convert atomic unit of mass to kg and multiply it by c^2.

Everything in the nature tends to have lower energy. It is well known in Chemistry, that bringing together hydrogen and oxygen, the mixture will explode to produce water, as water has lower energy than the sum of the energies of hydrogen and oxygen separately. If you bring N13 and a neutron together, so that they can interact, they will join to make N14, as it is more favourable for both particles than to exist separately.
The product has less energy than the constituents, and the energy released in the process is the binding energy. Since Einstein, we know that the mass is equivalent to energy, every mass m correspond to mc2energy. If the separated N13 and proton together have more energy than if they are united, it is equivalent that the sum of their mass is more than the mass of the N14 atom.

All elements in the Periodic System have less atomic mass than the sum of the masses of their constituent protons and neutrons.

ehild

7. Dec 11, 2009

### Nope

I understand now ,ty
but
is this right for a)?
13.005738u+1(1.008665u)=14.014403
and then use mass deflect
m=7(mass of proton)+7(mass of neutron)-14.014403u=
then E=mc^2? to find the binding energy...
ty!

8. Dec 11, 2009

### ehild

NO, it is not right. Wgat do you want with the 7 protons and seven neutrons?

You need the mass defect with respect to N14. Its mass is given: 14.00307.

ehild

9. Dec 12, 2009

### Nope

I still don't get it... If you can teach me step by step..
m=7(mass of proton)+7(mass of neutron)-14.003074u=mass deflect
I don't know what to do next
actually, i don't understand the formula at all,
m=m(nucleon)-m(nucleus)
How is the mass of nucleon larger than the nucleus, if nucleon is part of nucleus constituents?

10. Dec 13, 2009

### ehild

Processes in nature tend to minimize energy. If two particles unite it is because the energy of the new particle is lower than the sum of the individual energies.

Since Einstein we know that the m mass of a particle is equivalent to E=mc2 energy. It is difficult to digest, but all observations prove that it is valid. The mass is not constant. It depends on velocity, and part of it can be transformed into the energy of a photon.

When two particles, A and B produce a new particle AB, the energy difference

$$E_A+E_B-E_{AB}=E_{binding}$$

is the binding energy. It is released (as some kind of radiation) when the two particles unite, and so much energy is needed to separate them again.

Divide the equation with c2. As E/c2 is mass, the energy equation transforms into a relation among masses.

$$E_A/c^2+E_B/c^2-E_{AB}/c^2=E_{binding}/c^2 \rightarrow m_A+m_B-m_{AB}=E_{binding}/c^2$$

The mass defect is defined as

$$\Delta m= m_A+m_B-m_{AB}$$

Comparing with the previous equitation

$$\Delta m *c^2= E_{binding}$$.

Now you have N13 nucleus as particle A and a neutron as particle B. They unite and a N14 nucleus is produced. You can determine the mass defect in this process and multiplying by c2, you get the binding energy of the neutron in the N14 nucleus. So much energy is needed to kick out the neutron from N14. Such process can happen when a very fast particle collides with N14.

If you calculate the mass defect as dm=7(mass of proton)+7(mass of neutron)-14.003074u, and multiply it by c2, it is the binding energy of the whole N14 nucleus with respect to its constituents. So much energy would be needed to take apart N14 into 7 neutrons and 7 protons. It is an impossible huge energy.

So what is you have to calculate:

N14 (particle A) and a neutron (particle B) produce a N14 nucleus (particle AB).

The masses:
nitrogen-14: 14.003074 u
nitrogen-13: 13.005738 u
neutron: 1.008665 u

$\Delta m = 13.005738+1.008665-14.003074=0.011329 u$.

1 atomic unit =1.660539 x 10-27 kg

The mass defect in kg-s: 1.88112x 10-29 kg.

Multiply it by c2, the speed of light is 2.99792458 x 108 m/s

The binding energy of the neutron is 1.6906x 10-12 Joule.

ehild

11. Dec 13, 2009

### Nope

I think i figure it out. The concept of mass defect confused me a bit, but it make sense that the neutron+nitrogen-13=released energy+nitrogen-14
Tyvm

12. Dec 13, 2009

### ehild

Well done! Now you need to calculate the released energy in both processes

neutron+nitrogen-13=released energy+nitrogen-14 and

proton+carbon-13=released energy+nitrogen-14.

ehild