What is a Nuclear Equation?

A nuclear equation is a symbolic representation of a nuclear reaction using certain symbols. It is studied in nuclear chemistry and nuclear physics. 

Nuclear Reaction 

It is the change of nucleus into a new element by the release of an alpha particle, a beta particle or a gamma particle. In nuclear reactions an unstable nucleus changes into one or more elements nucleus. The identity of elements is changed. 

The particles which are involved in nuclear reaction are used in writing nuclear equation.  

The most common particles are:  

• Proton 
• Neutron 
• Alpha particle 
• Beta particle 
• Positron 
• Gama rays 

Proton- (₁P¹): It is the constituent particles of nucleus. 

It is represented by the symbol: ₁H¹ 

Neutron - (₀n¹): It is the constituent particles of nucleus. 

 Alpha particle- (₂He⁴): Alpha particles are helium nucleus which is emitted by some radioactive substance. 

It is represented by:  ₂α⁴   

Beta particle- (_-1β⁰): Beta particles are electrons moving in high speed as they have high energy. 

It is represented by: (_-1e⁰) 

Positron- (₊₁β⁰): Positron are positively charged electron. 

It is represented by: (₊₁e⁰) 

Gama rays- (γ): It is high-energy electromagnetic radiation. It is produced when the nucleus changes from a higher energy level to a lower energy level. 

Balancing Nuclear Equations 

•  The sum of mass number on both sides must be equal. 
• The sum of atomic number on both sides must be equal. 

Example:   ₉₂U²³⁵ → ₅₅Cs¹³⁸ + ₃₇Rb⁹⁶ + 2 ₀n¹ 

We can see in this example that the sum of atomic number of Cs and Rb, that is, 55 and 37 respectively, on the right side is equal to the atomic number of uranium (92). 

• Normally charges are not included in equation but they are included when one needs to distinguish between the two types of beta particles. 

Example:   ₈₂Pb²¹⁴ → _-1β⁰ + ₈₃Bi²¹⁴ 

In this example, the -1 is used for minus beta particle. 

How to write balanced nuclear equation for beta decay? 

• The emission of beta particles from an atomic nucleus occurs by the decaying of the original nucleus into its isobar. 
• Beta particle does not exist freely. 
• They are produced by the conversion of a neutron to a proton at the time of emission. 

_zX^A → _z+1X^A + _-1β⁰ 

• The beta decay increases the atomic number by 1 and there is no change in atomic mass. 

₉₁Pa²³⁴ → ₉₂U²³⁴ + _-1e⁰ 

In this example, the atomic number of protactinium is increased by 1 and transformed into uranium (92) and the atomic mass remains same and minus beta particle is emitted. 

Writing -β decay equations: 

₅₃I¹²⁹ → ₅₄Xe¹²⁹ + _-1e⁰ 

In this example, the atomic number is increased by 1 and atomic mass is same as of the parent atom and minus beta particle is emitted. 

₁₅P³² → ₁₆S³² + _-1e⁰ 

Similarly, in this example the atomic number is also increased by 1 and atomic mass is also same as of parent atom and minus beta particle is emitted. 

Writing +β decay equations: 

₁₉K³⁷→ ₁₈Ar³⁷ +₊₁e⁰ 

We can see in this example atomic number of potassium (19) is decreased by 1 and it is transformed into argon (18) and atomic mass remained same. Emission of plus beta particle takes place. 

₉₀Th²³²→₈₉Ac²³²+₊₁e⁰ 

Similarly, in this example the atomic number of thorium (90) is decreased by 1 and transformed into actinium (89) and the atomic mass is same as of parent atom and beta particle is emitted. 

₈O¹⁶→₇N¹⁶ +₊₁e⁰ 

In this example also, the atomic number is decreased by 1 and atomic mass is remained unchanged and beta particle is emitted. 

How to write balanced nuclear equation for alpha decay? 

• The emission of alpha particles from atomic nucleus results into the formation of a new atomic nucleus. 
• In this the mass number of the new formed atom is reduced by 4 and the atomic number is reduced by 2. 
• The emission of alpha particle is done by some of the isotope of the heavy elements. 

Example:  

₉₂U²³²   →   ₉₀Th²²⁸ + ₂He⁴ 

 As we can see in this example, the atomic number of uranium (92) is reduced by 2 and atomic mass (232) is reduced by 4 and transformed into thorium (90, 228) along with the emission of an alpha particle. 

₈₆Rn²²² → ₈₄Po²¹⁸ + ₂He⁴ 

₉₄Pu²³⁹ → ₉₂U²³⁹ + ₂He⁴ 

Similarly, in above equations the atomic number of parent atom is reduced by 2 and atomic mass is reduced by 4 along with the emission of alpha particle. 

How to write balanced nuclear equation for gamma decay? 

• In gamma decay the emission of electromagnetic radiation (photon) from the nucleus takes place and the nucleus changes from a higher energy level to a lower energy level. 
• Gamma rays are high energy radiations. 
• Gamma rays are not charged particle like the alpha particle or the beta particle. 
• There is no change in mass or atomic number. 

_zX^A →  _zX^A + γ 

Here, Z = Atomic number 

          A= Atomic mass 

• Usually gamma rays are emitted along with alpha or beta particle. 

Example:   ₅₃I¹²⁵ → ₅₃I¹²⁵ + γ 

We can see in this example, the element in the product is same as that of parent element. Atomic number and atomic mass are unchanged and only a high frequency and high energy electromagnetic radiation is emitted, i.e., the gamma ray. 

Uses of Nuclear Equations 

Nuclear power 

Nuclear reactions are used in nuclear power to produce electricity. 

• It is obtained from nuclear fission and nuclear fusion reactions. 

• Nowadays most of the electricity from nuclear power is produced by nuclear fission of uranium and plutonium in power plants. 

C-N-O cycle (carbon-nitrogen-oxygen cycle) 

• It is also known as Bethe--Weizascker cycle. 
• It is one of the two sets of fusion reaction and with this, stars convert hydrogen into helium; while the other of the two sets is proton-proton chain reactions (p-p cycle). 
• It is speculated that C-N-O cycle is more in stars which are 1.3 times more massive than sun. 

• It is a catalytic cycle. 
• There are so many possible paths and catalysts are involved in these cycles. 
• All these cycles have the same net result. 

4 ₁H¹ + 2e¯→ ₂He⁴+ 2e⁺ + 2e^- + 2V_e +3γ + 24.7 MeV →₂He⁴ +2V_e +7γ + 24.7 MeV 

Nuclear Chain Reactions 

• These reactions are series of nuclear fissions, in which each reaction releases a neutron which causes the other reaction and this process goes on. 
• These reactions release a very large amount of energy. 
• These reactions mostly occur with heavy radioactive elements. 

Example: Uranium-235

Context and Applications 

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for Bachelors and Masters in Chemistry and Physics. 

Related Concepts

• Nuclear power. 
• Atomic chemistry. 
• CNO cycle (Carbon- Nitrogen-Oxygen cycle). 
• Nuclear chain reaction.