Nuclear Energy

Article Summary & FAQs

What is nuclear energy?

Nuclear energy comes either from spontaneous nuclei conversions or induced nuclei conversions. It is associated with nuclear binding power. When nuclear energy is generated (splitting atoms, nuclear fusion), a small amount of mass (saved in the nuclear binding energy) transforms into pure energy (such as kinetic energy, thermal energy, or radiant energy).

  • In general, nuclear fission and nuclear fusion result in the release of enormous quantities of nuclear energy because the binding energy stored in atomic nuclei is very high.
  • The amount of nuclear energy released is so high that you can measure a decrease in the mass of products.
  • One of the striking results of Einstein’s theory of relativity is that mass and energy are equivalent and convertible, one into the other. E = mc2
  • In 2011 nuclear power provided 10% of the world’s electricity. In 2007, the IAEA reported 439 nuclear power reactors operating globally, operating in 31 countries.
What are sources of nuclear energy?
What are sources of nuclear energy?

An atomic nucleus must change into a state with higher binding energy to generate nuclear energy. That means light nuclei have to fuse, while heavy nuclei have to split.

How is nuclear energy produced?
How is nuclear energy produced?

In general, nuclear energy is produced or consumed in nuclear reactions. The most common nuclear reactions are nuclear fission, nuclear fusion, and nuclear decay. But there are much more types of nuclear reactions.

What are units of nuclear energy?
What are units of nuclear energy?

Standard units of nuclear energy are megaelectronvolts (MeV). In nuclear and particle physics, the energetics of nuclear reactions are determined by the reaction’s Q-value. The Q-value of the reaction is defined as the difference between the sum of the masses of the initial reactants and the sum of the masses of the final products in energy units (usually in MeV). Electronvolts are a traditional unit of energy, particularly in atomic and nuclear physics. An electronvolt is equal to the energy gained by a single electron when accelerated through 1 volt of electric potential difference. For example, the total energy released in a reactor is about 210 MeV per 235U fission.

What is Nuclear Energy

Nuclear energy comes either from spontaneous nuclei conversions or induced nuclei conversions. Among these conversions (nuclear reactions) are nuclear fission, nuclear decay, and nuclear fusion. Conversions are associated with mass and energy changes. One of the striking results of Einstein’s theory of relativity is that mass and energy are equivalent and convertible, one into the other. Einstein’s famous formula describes equivalence of the mass and energy:

E=MC2 - Nuclear energy
This formula describes the equivalence of mass and energy.

Where M is the small amount of mass and C is the speed of light.

What does that mean? If nuclear energy is generated (splitting atoms, nuclear fusion), a small amount of mass (saved in the nuclear binding energy) transforms into pure energy (such as kinetic energy, thermal energy, or radiant energy).

Example:

The energy equivalent of one gram (1/1000 of a kilogram) of mass is equivalent to:

  • 89.9 terajoules
  • 25.0 million kilowatt-hours (≈ 25 GW·h)
  • 21.5 billion kilocalories (≈ 21 Kcal)
  • 85.2 billion BTUs

or to the energy released by combustion of the following:

  • 21.5 kilotons of TNT-equivalent energy (≈ 21 kt)
  • 568,000 US gallons of automotive gasoline

Whenever energy is generated, the process can be evaluated in terms of E = mc2.

Nuclear Binding Energy – Mass Defect

 
Conservation of Mass-Energy
At the beginning of the 20th century, the notion of mass underwent a radical revision. The mass lost its absoluteness. One of the striking results of Einstein’s theory of relativity is that mass and energy are equivalent and convertible one into the other. Equivalence of the mass and energy is described by Einstein’s famous formula E = mc2. In other words, energy equals mass multiplied by the speed of light squared. Because the speed of light is a vast number, the formula implies that any small amount of matter contains a huge amount of energy. The mass of an object was seen as equivalent to energy, interconvertible with energy, and increasing significantly at exceedingly high speeds near that of light. The total energy was understood to comprise its rest mass and its increase of mass caused by increased kinetic energy.

In the particular theory of relativity, certain types of matter may be created or destroyed. Still, the mass and energy associated with such matter remain unchanged in quantity in all of these processes. Mass was no longer considered unchangeable in the closed system. It was found the rest mass of an atomic nucleus is measurably more minor than the sum of the rest masses of its constituent protons, neutrons, and electrons. The difference is a measure of the nuclear binding energy which holds the nucleus together. According to the Einstein relationship (E = mc2), this binding energy is proportional to this mass difference, known as the mass defect.

E=mc2 represents the new conservation principle – the conservation of mass-energy.

Nuclear Binding Curve
Nuclear binding energy curve.
Nuclear binding energy curve.
Source: hyperphysics.phy-astr.gsu.edu

If the splitting releases energy and the fusion release the energy, so where is the breaking point? For understanding this issue, it is better to relate the binding energy to one nucleon to obtain a nuclear binding curve. The binding energy per one nucleon is not linear. There is a peak in the binding energy curve in the region of stability near iron. Either the breakup of heavier nuclei than iron or lighter nuclei than iron will yield energy.

The reason the trend reverses after the iron peak is the growing positive charge of the nuclei. The electric force has a more extended range than the strong nuclear force. While the strong nuclear force binds only close neighbors, the electric force of each proton repels the other protons.

“Example:
Calculate the mass defect of a 63Cu nucleus if the actual mass of 63Cu in its nuclear ground state is 62.91367 u.

63Cu nucleus has 29 protons and also has (63 – 29) 34 neutrons.

The mass of a proton is 1.00728 u, and a neutron is 1.00867 u.

The combined mass is: 29 protons x (1.00728 u/proton) + 34 neutrons x (1.00867 u/neutron) = 63.50590 u

The mass defect is Δm = 63.50590 u – 62.91367 u =  0.59223 u

Convert the mass defect into energy (nuclear binding energy).

(0.59223 u/nucleus) x (1.6606 x 10-27 kg/u) = 9.8346 x 10-28 kg/nucleus

ΔE = Δmc2

ΔE = (9.8346 x 10-28 kg/nucleus) x (2.9979 x 108 m/s)2 = 8.8387 x 10-11 J/nucleus

The energy calculated in the previous example is nuclear binding energy.  However, the nuclear binding energy may be expressed as kJ/mol (for better understanding).

Calculate the nuclear binding energy of 1 mole of 63Cu:

(8.8387 x 10-11 J/nucleus) x (1 kJ/1000 J) x (6.022 x 1023 nuclei/mol) = 5.3227 x 1010 kJ/mol of nuclei.

One mole of 63Cu (~63 grams) is bound by the nuclear binding energy (5.3227 x 1010 kJ/mol), which is equivalent to:

  • 14.8 million kilowatt-hours (≈ 15 GW·h)
  • 336,100 US gallons of automotive gasoline
“Example:
Calculate the mass defect of the 3000MWth reactor core after one year of operation.

It is known as the average recoverable energy for fission is about 200 MeV, which is the total energy minus the energy of the antineutrinos that are radiated away.

The reaction rate per entire 3000MWth reactor core is about  9.33×1019 fissions/second.

The overall energy release in the units of joules is:

200×106 (eV) x 1.602×10-19 (J/eV) x 9.33×1019 (s-1) x 31.5×106 (seconds in year) = 9.4×1016 J/year

The mass defect is calculated as:

Δm = ΔE/c2

Δm = 9.4×1016 / (2.9979 x 108)2 = 1.046 kg

That means in a typical 3000MWth reactor core, about 1 kilogram of the matter is converted into pure energy.

Note that a typical annual uranium load for a 3000MWth reactor core is about 20 tons of enriched uranium (i.e., about 22.7 tons of UO2). The entire reactor core may contain about 80 tonnes of enriched uranium.

Mass defect directly from E=mc2

The mass defect can be calculated directly from the Einstein relationship (E = mc2) as:

Δm = ΔE/c2

Δm = 3000×106 (W = J/s) x 31.5×106 (seconds in year) / (2.9979 x 108)= 1.051 kg

Nuclear Energy and Electricity Production

Today we use nuclear energy to generate proper heat and electricity. This electricity is generated in nuclear power plants. The heat source in the nuclear power plant is a nuclear reactor. As is typical in all conventional thermal power stations, the heat is used to generate steam which drives a steam turbine connected to a generator that produces electricity. In 2011 nuclear power provided 10% of the world’s electricity. In 2007, the IAEA reported 439 nuclear power reactors operating in the world, operating in 31 countries. They produce base-load electricity 24/7 without emitting any pollutants into the atmosphere (this includes CO2).

Energy consumption
Source: https://www.llnl.gov/news/americans-using-more-energy-according-lawrence-livermore-analysis

Nuclear Energy Consumption – Summary

Nuclear Reactor
The pressure vessel of PWR.

Consumption of a 3000MWth (~1000MWe) reactor (12-months fuel cycle)

It is an illustrative example, and the following data do not correspond to any reactor design.

  • A typical reactor may contain about 165 tonnes of fuel (including structural material)
  • A typical reactor may contain about 100 tonnes of enriched uranium (i.e., about 113 tonnes of uranium dioxide).
  • This fuel is loaded, for example, into 157 fuel assemblies composed of more than 45,000 fuel rods.
  • A typical fuel assembly contains energy for approximately four years of operation at full power.
  • Therefore about one-quarter of the core is yearly removed to the spent fuel pool (i.e., about 40 fuel assemblies). At the same time, the remainder is rearranged to a location in the core better suited to its remaining level of enrichment (see Power Distribution).
  • The removed fuel (spent nuclear fuel) still contains about 96% of reusable material (it must be removed due to decreasing kinf of an assembly).
  • This reactor’s annual natural uranium consumption is about 250 tons of natural uranium (to produce about 25 tonnes of enriched uranium).
  • The annual enriched uranium consumption of this reactor is about 25 tonnes of enriched uranium.
  • The annual fissile material consumption of this reactor is about 1 005 kg.
  • The annual matter consumption of this reactor is about 1.051 kg.
  • But it corresponds to about 3 200 000 tons of coal burned in coal-fired power plants per year.

See also: Fuel Consumption

See previous:

Atomic and Nuclear Structure

See above:

Atomic and Nuclear Physics

See next:

Radiation