How Is Binding Energy Calculated in Nuclear Reactions?

[mugen715]

Homework Statement

This is the question:

2H1 + 3H1 ==> 4He2 + 1n0 +Q

Where Q = 17.7 MeV

The binding energy per nucleon are given below:

2H1 = 1.12 MeV
1n0 = Null
4He2 = 7.07 MeV

" Determine the binding energy per nucleon, in MeV, of tritium (3H1)"

Homework Equations

The Attempt at a Solution

This is how i do it,

The B.E for:

2H1 = 2 x 1.12 = 2.24 MeV
4He2 = 7.07 x 4 = 28.28 MeV

From chemical equation shown above, The energy before reaction is equal to energy after reaction. The energy is conversed before and after reaction:

2.24 + 3(X) = 28.28 MeV + 17.7 MeV

X = 14.58 MeV which is the B.E per nucleon for 3H1

But when i check up the answer, it turns out to be 2.78 MeV. What wrong with my method of solving the questions? can anyone explain what my mistake?

 

[gomboc]

You are very close.

The problem is that on the right side of the equation, binding energy and energy released cannot be added. Energy released is energy that is actually "there", where as binding energy represents mass or energy that's missing. So when you're combining binding energy and energy released in your very last calculation, they need different signs. Turn that + into a - and you should be home free!

 

[mugen715]

You are very close.

The problem is that on the right side of the equation, binding energy and energy released cannot be added. Energy released is energy that is actually "there", where as binding energy represents mass or energy that's missing. So when you're combining binding energy and energy released in your very last calculation, they need different signs. Turn that + into a - and you should be home free!

Thank for your reply. Is it true to explain this way, the total energy required to form helium is 28.28MeV meanwhile 17.7mev will be release from the 28.28mev..is this correct?