Calculating Energy Released in Fusion Reactions and Comparing to Gasoline

[NDiggity]

Homework Statement

Two deuterium nuclei (deuterium= 2.014102u) combine thru fusion to form a tritium nucleus (mass 3.016050u) and a proton.

2. Attempt at solution
Two parts to this problem:
a) Calculate the energy released in one fusion reaction (in MeV).

So for this I went [(initial masses)-(final masses)]c^2.
So [(2x2.014102u)-(3.016050u + 1.007276u)]931.5 MeV/u (we are given c^2=931.5MeV/u)

So I get 4.54 MeV. The answer is supposed to be 4.03 MeV. What am I doing wrong?b)Calculate the ratio of energy released from 1.00x10^22 deuterium nuclei to 1kg of gasoline (5.00x10^7 J).

Using the correct answer from part a, I go:

4.03 Mev x 1.00x10^22 / ((5.00x10^7 J x 1 eV/1.60x10^-19 J) x 1MeV / 10^6 eV) and i get 128.96. The correct answer is 64.6. Again, what am I doing wrong :p.

Thanks for the help in advance!

 

[dynamicsolo]

What is the source of your deuteron and triton masses? When I use the ones you state, I get your answer of 4.54 MeV. When I use the masses provided at the NIST website [2006 physical constants: deuteron mass: 2.013553 u, triton mass: 3.015501 u], I get 4.03 MeV.

For the second part, the energy release is 4.03 MeV per reaction and two deuterium nuclei go into each reaction. Your answer is off by a factor of 2...

 

[alphysicist]

Hi NDiggity,

Homework Statement

Two deuterium nuclei (deuterium= 2.014102u) combine thru fusion to form a tritium nucleus (mass 3.016050u) and a proton.

2. Attempt at solution
Two parts to this problem:
a) Calculate the energy released in one fusion reaction (in MeV).

So for this I went [(initial masses)-(final masses)]c^2.
So [(2x2.014102u)-(3.016050u + 1.007276u)]931.5 MeV/u (we are given c^2=931.5MeV/u)

So I get 4.54 MeV. The answer is supposed to be 4.03 MeV. What am I doing wrong?

It looks to me like you are using the masses of the deuterium and tritium atom, instead of just the mass of the nuclei. The electron has a mass of 0.000549u, and including that is enough to give the wrong answer. The nucleus of the deuterium and tritium have masses:

dueterium nucleus: 2.013553 u
tritium nucleus: 3.015501 u

b)Calculate the ratio of energy released from 1.00x10^22 deuterium nuclei to 1kg of gasoline (5.00x10^7 J).

Using the correct answer from part a, I go:

4.03 Mev x 1.00x10^22 / ((5.00x10^7 J x 1 eV/1.60x10^-19 J) x 1MeV / 10^6 eV) and i get 128.96. The correct answer is 64.6. Again, what am I doing wrong :p.

Thanks for the help in advance!

Each reaction releases 4.03 MeV. How many reactions occur from 1 x 10^22 deuterium nuclei?

 

[NDiggity]

Ahhhhhhhhhh, thank you so much both of you!