Nuclear Physics, portons and neutrons

[aimslin22]

Homework Statement

You have 10 protons and 10 neutrons to paly with (mass of oxygen = 15.994915)

a. What is the mass of an oxygen nucleus that you build with equal numbers of protons and neutrons?

b. What is the binding energy of this nucleus?

Homework Equations

E=mc^2

The Attempt at a Solution

for a.

There are 8 protons in an oxygen, so 8 neutrons as well. Thus...
16(1.67x10^-27)=2.672...x10^-27
in us its about 16.096u...isn't suppose to be exactly 16, or is it close enough?

for b.

E=mc^2- except m is the change in m, so would it be 16.096-15.994915?

 

[wavingerwin]

You are right!

minor things:
mass of neutron at rest and proton at rest are not exactly the same.
However, In three significant figures, it is 1.67 E-27 kg, so you are right.

for b,
E='delta'mc²
delta mass means change in mass, change is always calculated as final minus initial
so its mass final minus mass initial
hence change in mass is actually 15.994915 - 16.096 = -0.101085 u
and binding energy is -0.101085*c²

Binding energy is minus, because the question is done in terms of energy loss
due to mass loss of the nucleons.

If the question is asking "how much energy is needed to break the nucleons in an oxygen nucleus apart", hence the mass final (when the nucleons are free) will be bigger than initial (when the nucleons are bonded together). And in this case energy will be positive (as energy input, not loss).

 

[aimslin22]

Thanks so much!