Energy in the Nucleus of the Atom

binding-energy2 — If you pull apart an atom, the individual parts will weigh more than the atom you started with. The extra mass is the binding energy, which is released when the nucleus of atoms break apart (nuclear fission).

If you pull apart the nucleus of an atom, you’ll find that the mass of its parts is greater than the mass of the original nucleus. That extra mass is where nuclear energy comes from; it’s called the binding energy.

How so?

alpha-particle — An alpha particle is the nucleus of a helium atom.

Take a helium atom for example. Its nucleus typically has two protons and two neutrons*, which in nuclear physics is usually called an alpha particle (α).

While we usually say that the mass of a proton is 1 atomic mass unit (u), its actually a little heavier. The mass of a proton is 1.00728 atomic mass units (u), while neutrons weigh 1.00866 u.

binding-energy — The alpha particle (helium nucleus) has less mass than sum of the masses of the individual particles that make it up.

The combined mass of the two protons and two neutrons in the helium nucleus is 0.03035 atomic mass units more than the mass of a helium nucleus made up of the very same particles.

Why?

The one equation that everyone remembers from Einstein (perhaps from all the t-shirts) is:

$! E = mc^2$

Energy (E) is equal to mass (m) times some constant (c is the speed of light) squared. What it means is that mass is energy, and vice-versa.

When the four nucleons combine, the extra mass is transformed into the energy that holds them together in the nucleus of the atom. The mass can be directly converted to energy, the binding energy of the atom.

How much energy is released?

Somewhere around 10,000 times more energy is released from a single nuclear reaction compared to a single chemical reaction (like the combustion of TNT).

issue5fusion3_large — Binding energy per neuleon for the naturally occuring elements. (image from Science in School).

Footnotes

* Helium with two neutrons would be written $^4_2{He}$ , where the bottom number is the number of protons and the upper number is the atomic mass, which is the sum of the number of protons and the number of neutrons.

Radiation dosages

xkcd has published an excellent graph showing where different dosages of radiation come from and how they affect health. It’s a complex figure, but it’s worth taking the time to look through. I find it easiest to interpret going backward from the bottom right corner that show the dosages that are clearly fatal.

One red square of 100 red blocks is equal to one seivert, which is the radiation dosage that will kill you if you receive it all at once. Note:

If you were next to the reactor core during the Chernobyl nuclear accident, you would have gotten blasted by 50 Sv.
8 Sv will kill you, even with treatment.
Getting 0.1 Sv over a year is clearly linked to cancer.
One hour on the grounds of the Chernobyl nuclear plant (in 2010) would give you 0.006 Sv.
Your normal, yearly dose is about 0.004 Sv, just about how much was measured over a day at two sites near Fukushima.
Eating a banana will give you 0.000001 Sv.

While I did not find equivalent exposure levels, the nuclear bombs dropped on Hiroshima and Nagasaki lead to many deaths and sickness from radiation created by the explosions. Within four months, there were 140,000 fatalities in Hiroshima, and 70,000 in Nagasaki (Nave, 2010). The Manhattan Engineer District, 1946 report describes the radiation effects over the first month:

Rad-injuries — Radiation effects for the month following the dropping of the nuclear bombs on Nagasaki and Hiroshima. (Table from The Manhattan Engineer District (1946) via atomicarchive.com).

The effects were not limited to the explosion itself, though. There is one estimate, that 260,000 people were indirectly affected:

Radiation dose in a zone 2 kilometers from the hypocenter of the atomic bomb was the largest. Also, those who entered the city of Hiroshima or Nagasaki soon after the atomic bomb detonation and people in the black rain areas were exposed to radiation. … some people were exposed to radiation from black rain containing nuclear fission products (“ashes of death”), and others to radiation induced by neutrons absorbed by the soil upon entering these cities soon after the atomic bomb detonation.

— Hiroshima International Council for Health Care for the Radiation Exposed (HICARE): Global Radiation Exposures.

HICARE also has a good summary of what happened at Chernobyl, where 31 people died at the time of the accident, about 400,000 were evacuated, and anywhere between 1.6 and 9 million people were exposed to radiation. Modern pictures of the desolation of Chernobyl are here. The Wikipedia article has before and after pictures of Hiroshima and Nagasaki.

Nuclear Meltdown in Japan

CNN has an informative interview on the explosion at the Fukushima nuclear plant in Japan after the earthquake and tsunami.

Footage of the explosion from the BBC:

Nuclear disasters are so rare that they’re easy to forget about when we’re talking about the right mix of alternative (non-carbon based) energy sources for the future.

Right after the accidents at Three Mile Island in 1979 and Chernobyl in 1986, awareness of the dangers lead to a de facto moratorium on nuclear power plants in the U.S.. This was good in that people were now treating nuclear power much more respectfully, and incorporating the costs of potential accidents into their calculations. However, it also reduced the interest and effort of developing newer and safer types of nuclear plants.

We’ll have this discussion next year when we focus more on the physical sciences.

UPDATE:

1. More details on how nuclear plants work can be found in Maggie Koerth-Baker’s post, Nuclear energy 101: Inside the “black box” of power plants.

guardian-reactor-status — Fukushima reactor status as of March 16th, 5:00 pm GMT from the Guardian live blog.

2. The Guardian’s live blog has good, up-to-date information on the status of the nuclear reactors at Fukushima.