Energy production that converts Hydrogen to Iron?

[Devin-M]

releases 84.33 Terajoules of energy.

According to my calculator, 8 grams works out to about 719TJ per kilo of Deuterium.

 

[Devin-M]

It makes me wonder whether it would be better to accelerate all the iron, or simply dump some overboard and accelerate the rest to a higher velocity.

 

[usernamess]

(Edited to fix typos) I'm definitely no expert but here's my crack at it.

Deuteron = 1875.61 MeV
per nucleon= 937.8

Iron 56 has roughly 7.5Mev more binding energy per nucleon than a deuteron or 930.3MeV per nucleon.

930.3/937.8 = 0.992002

In other words a kilo of deuteron to iron-56 fusion releases 8 grams worth of energy.

Nuclear physics is not my area of expertise: It's possible I'm calculating incorrectly. Could you walk me through your process? This is the process I took:

I used the isotopic mass of protium and deuterium from this table, and converted them to grams using Google's built in unit conversion tool.

 

[Devin-M]

Could you walk me through your process?

I found the ratio of the mass per nucleon of Iron / Deuterium = 0.992, so I reasoned 1 kg of Deuterium produces 992 grams of Iron-56.

Deuterium mass per nucleon= 937.8 MeV/c^2

Iron 56 has 7.5MeV more binding energy per nucleon

Deuterium mass per nucleon 937.8 MeV/c^2 - Binding Energy 7.5MeV/c^2 = 930.3Mev/c^2 Mass Per Nucleon Iron 56

Ratio: 930.3Mev/c^2 / 937.8 MeV/c^2 = 0.992

Therefore 1 kg Deuterium Converts to 0.992 kg Iron-56 with an 8 gram energy yield.

 

[usernamess]

I found the ratio of the mass per nucleon of Iron / Deuterium = 0.992, so I reasoned 1 kg of Deuterium produces 992 grams of Iron-56.

Deuterium mass per nucleon= 937.8 MeV/c^2

Iron 56 has 7.5MeV more binding energy per nucleon

Deuterium mass per nucleon 937.8 MeV/c^2 - Binding Energy 7.5MeV/c^2 = 930.3Mev/c^2 Mass Per Nucleon Iron 56

Ratio: 930.3Mev/c^2 / 937.8 MeV/c^2 = 0.992

Therefore 1 kg Deuterium Converts to 0.992 kg Iron-56 with an 8 gram energy yield.

Thank you. I had fat fingered an extra '4' in the conversion from MeV to Joules. Our numbers still disagree by a lot; I'm double checking all my other values now to see if I can find another error. In the meantime, your fusion rocket just jumped from .0433c to .1375c now that I'm converting the energy properly.

 

[usernamess]

I had fat fingered an extra '4' into the conversion from MeV to J in my original calculations, as highlighted in the screenshot of my calculations below:

Correcting that mistake yields the following:

Since I used Joules to calculate both mass lost and the velocity, the conversion error had a profound impact on the final numbers I generated. As I stated, nuclear physics isn't my forte: I've been unable to find another source of error in my math, however I have no formal education in the subject and am not confident none exist. I would appreciate anyone deeply knowledgeable in the subject reviewing the math and identifying any further errors made.

Deuterium mass per nucleon= 937.8 MeV/c^2

Iron 56 has 7.5MeV more binding energy per nucleon

Deuterium mass per nucleon 937.8 MeV/c^2 - Binding Energy 7.5MeV/c^2 = 930.3Mev/c^2 Mass Per Nucleon Iron 56

I greatly appreciate you walking me through your process. Converting your units to mine identified the constant I had mistyped. However, I am unsure if your formula is accurate. By my understanding, the binding energy is an energy, in units MeV/nucleon. In your equation you seem to be subtracting it from a mass (units MeV/c^2) without first converting it. Am I misunderstanding your work?