A recent documentary stated that 0.6 gm. of mass was converted to energy in the Hiroshima blast.
How many photons are released per gram in a uranium fission reaction? What is the range of wavelengths? What is the average wavelength?
Peace through Liberty
rwjefferson
There’s a complex question. From what I recall, most photons intially released were very high energy – what you’d call gamma rays and x-rays (the ranges overlap, and the distinction often used that relates to the source doesn’t apply here). But these are so numerous and high energy that a lot of them will interact with the air molecules and ionize the, resulting in transitions that release lower energy photons that will, in turn interact with more matter. I’m told that people looking at the 1950s A-bomb tests saw purple lightning and glowsw in the fireball, some of which were probably transitions in the nitrogen in the air. On the other hand, a lot of gamma rays (and lower energ photons, of couerse) would travel for miles and instantly heat up structures and the ground and people, well before the mechasnical shock wave blew them apart. That’s why in those films you see the houses constructed at the test sites start to smoke before they’re shattered – they’ve been cooked long distance by high-energy photons.
I have no idea what the relative mix of photons is, but it’s undoubtedly a complex mix of photons from the fission itself mixed with a lot of secondary and tertiary processes and, ultimately, blackbody radiation from everything that suddenly got heated to very high temperatures. As a guess, then. I’d say the spectrum looked like a high temperature blackbody curve with a very big high-energy spike.
At this point I wish I’d paid attention during my degree, and not forgotten everything the moment I left. However, the amount of energy per gram is simply E=mc squared, surely? I’m so unsure of my physics now though that I’m not even going to plug in the numbers.
Then, as CalMeacham said, I think it’d be a blackbody curve… one could work out the energies of the photons, and the relative abundancies etc…
I said one could… not I could.
For a crude zeroeth-order estimate: the energy released is E = m c[sup]2[/sup]. The energy per photon is E = h f = h c / λ. So the number of photons released is something like N = m c λ / h. And to guesstimate some values: 6x10[sup]-4[/sup] x 3.00x10[sup]8[/sup] x 1x10[sup]-7[/sup] / 6.63x10[sup]-34[/sup] = 3x10[sup]31[/sup] photons.
I used 100nm photons which is in the UV spectrum.
42
.6 grams converted completely to energy yields 13 kilotons of energy.
http://www.1728.com/einstein.htm
Nobody asked this, but it might come in handy for anyone who wants to do any more photon calculations.
Perhaps the OP actually wants the candlepower generated by the Bomb?
Feh! That’s easy. First get an atomic bomb. Next stand a known distance away with an incident flash meter when it goes off. From there it’s simple calculation to get foot candles and candlepower.
Safety note: do not wear a polyester shirt
RIGHT! That would be a MAJOR conflagration!
Thanks for the answers so far. I was interested in the initial fission only. I realize there would be a cascade as these initial photons interact with surrounding matter.
I would assume that the average photon would be in the very high x-ray energy range, (this is nuclear force after all). I would also guess this initial release would be a spike, or spikes, as opposed to a broad curve. I would expect slightly different spikes for plutonium.
[url= http://www.1728.com/einstein.htm?A=1+gm] wolf-meister’s [\url] site gives the values of 8.9876e+20 ergs or 8.9876e+13 joules per gram.
Pleonast – I suck at the math part. Do you have a calculation for energetic x-rays?
Thanks again for all your help.
rwjefferson.
Why? You think he might be infested with Denevan nerve parasites?
Bryan Ekers
That requires 1 million candle power doesn’t it?
Changing the wavelength is easy. Energetic x-rays? I’ll pull the wavelength 10pm (1x10[sup]-11[/sup]m) out of the air. So that gives us 6x10[sup]-4[/sup] x 3.00x10[sup]8[/sup] x 1x10[sup]-11[/sup] / 6.63x10-34 = 3x10[sup]27[/sup] photons.
Taking the yield at Hiroshima as 12.5 kilotons, the energy released was about 3.2 x 10[sup]29[/sup] MeV. The total energy released in the fission of U235 is, on average, 205 MeV, but about 12 MeV of this is carried off by neutrinos and so we’ll ignore that. That suggests a total of about 1.7 x 10[sup]27[/sup] fissions.
The trickier issue is then estimating the average number of prompt photons per fission. About 6 MeV per fission is released via these, so pretty much any estimate means that we’re talking about gamma rays. This paper (a pdf) suggests that there’s an average of 7 such prompt gamma rays per U235 fission. However, that’s based on a 1971 paper by Peelle and Maienschein that only considers fission induced by thermal neutrons. I’d expect that the number should be different for fast neutrons, but, in the absence of anything better, let’s gratuitously assume that this estimate applies. That gives about 10[sup]28[/sup] gamma ray photons.
In terms of energy, about a third to half the energy released in a fission bomb in the form of photons is as these prompt gamma rays.
It’s always nice when independent estimates come out close.
On reflection, I think I’ve been too cautious here. The neutron, whether fast or thermal, produces an unstable nucleus that then falls apart. Excited fragments then almost immediately radiate the prompt gamma ray photons. But there’s then 200-odd MeV of energy sloshing about and a triggering fast neutron can only contribute an extra couple of MeV. That probably doesn’t make any significant difference - at least for a back-of-an-envelope estimate - to the production of the prompt photons.
My gratuitous assumption may be a really rather good approximation.
Seems to answer this question accurately requires knowing the detailed EM emissions spectrum of the bomb’s explosion over time.
Not given the clarification that rwjefferson added as OP in the 9th post about only being interested in the photons from the fissions (i.e. the prompt ones).
Removing that restriction does massively complicate the issue, because multiple other processes then also come into effect. Though figure 8.14 in Glasstone and Dolan’s The Effects of Nuclear Weapons nicely plots the energy released via gamma rays against time and the same chapter also briefly describes the different mechanisms that are involved, which is at least a start.
Thanks all for your input. Please accept my apologies for my difficulty in asking the proper question. My interest was in the matter that becomes energy, as opposed to the uptake and re-radiation of photons that follows.
I am not sure how to better paraphrase the question: How many photons are released as 1 gm of matter is converted into energy? (…from the 1 gram being converted…?)
I would think the number would be close whether it is limited to 1 gram of the initial mass or 1 gram total: initial plus subsequent disintegration.
I would also assume that a gram converted in fusion would yield fewer, but higher energy photons.
Thanks again for your efforts.
Peace
rwj