## Article Summary & FAQs

### What is nuclear energy?

By definition, **nuclear energy** refers to the combined potential energy that binds nucleons to form the atomic nucleus. The nuclear particles are bound together by the strong nuclear force. Weak nuclear forces provide the potential energy for certain kinds of radioactive decay.

- Separate nucleons contain a huge amount of nuclear potential energy. In terms of energy, they rather bind together to form compound nuclei, and during their formation, this potential energy is released. That is what we call 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, or nuclear reactions), 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 = mc**^{2} - 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 is Nuclear Energy

By definition, **nuclear energy** refers to the combined potential energy that binds nucleons to form the atomic nucleus. The nuclear particles are bound together by the strong nuclear force. Weak nuclear forces provide the potential energy for certain kinds of radioactive decay.

**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:

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.

## Q-value – Energetics of Nuclear Reactions

In nuclear and particle physics the **energetics of nuclear reactions** is determined by the **Q-value** of that reaction. 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).

For reactions in which there is an increase in the kinetic energy of the products **Q is positive**. The positive Q reactions are said to be **exothermic** (or **exergic**). There is a net release of energy, since the kinetic energy of the final state is greater than the kinetic energy of the initial state.

For reactions in which there is a decrease in the kinetic energy of the products **Q is negative**. The negative Q reactions are said to be **endothermic** (or **endoergic**) and they require a net energy input.

See also: Q-value

## Nuclear Binding Energy – Mass Defect

**In the special 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 = mc ^{2}**), this binding energy is proportional to this mass difference, known as the

**mass defect**.

At the nuclear level, the **nuclear binding energy** is the energy required to **disassemble** (to overcome **the strong nuclear force**) **a nucleus of an atom into its component parts** (protons and neutrons).

During the **nuclear splitting** or nuclear fusion, some of the mass of the nucleus gets **converted** into huge amounts of energy. Thus this mass is removed from the total mass of the original particles, and the mass is missing in the resulting nucleus. **The nuclear binding energies are enormous**. They are on the order of a million times greater than the electron binding energies of atoms.

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: Nuclear Energy Release in Nuclear Fission

From the nuclear binding energy curve and from the table, it can be seen that, in the case of splitting a ^{235}U nucleus into two parts, the binding energy of the fragments (A ≈ 120) together is more significant than that of the original ^{235}U nucleus.

According to the Weizsaecker formula, the total energy released for such a reaction will be approximately **235 x (8.5 – 7.6) ≈ 200 MeV.**

### Example: Mass defect of a 63Cu

Calculate the **mass defect** of a ** ^{63}Cu** nucleus if the actual mass of

^{63}Cu in its

**nuclear ground state is 62.91367 u.**

^{63}Cu 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 = (9.8346 x 10^{-28} kg/nucleus) x (2.9979 x 10^{8} 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 ^{63}Cu:

(8.8387 x 10^{-11} J/nucleus) x (1 kJ/1000 J) x (6.022 x 10^{23} nuclei/mol) = **5.3227 x 10 ^{10} kJ/mol of nuclei.**

One mole of ^{63}Cu (~63 grams) is bound by the nuclear binding energy (5.3227 x 10^{10} kJ/mol), which is equivalent to:

**14.8 million kilowatt-hours (≈ 15 GW·h)****336,100 US gallons of automotive gasoline**

### Example: Mass defect of the reactor core

Calculate the **mass defect** of the **3000MW _{th}** 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 **3000MW _{th}** reactor core is about

**9.33×10**.

^{19}fissions/second**The overall energy release** in the units of joules is:

200×10^{6} (eV) x 1.602×10^{-19} (J/eV) x 9.33×10^{19} (s^{-1}) x 31.5×10^{6} (seconds in year) = **9.4×10 ^{16} J/year**

The mass defect is calculated as:

Δm = ΔE/c^{2}

**Δm** = 9.4×10^{16} / (2.9979 x 10^{8})^{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 UO _{2}**). The entire reactor core may contain about 80 tonnes of enriched uranium.

**Mass defect directly from E=mc ^{2}**

The mass defect can be calculated directly from the Einstein relationship (**E = mc ^{2}**) as:

Δm = ΔE/c^{2}

Δm = 3000×10^{6} (W = J/s) x 31.5×10^{6} (seconds in year) / (2.9979 x 10^{8})^{2 }= **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).

## Nuclear Energy Consumption – Summary

**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**k**of an assembly)._{inf}

**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**per year.**coal-fired power plants**

See also: Fuel Consumption