Nuclear Reactions – Definition, Types, Examples

Nuclear responses are processes in which at least one nuclides are created from the crashes between two atomic nuclei or one atomic nucleus and a subatomic particle. The nuclides delivered from nuclear reactions are not quite the same as the reacting nuclei (generally alluded to as the parent nuclei).

Two prominent types of nuclear reactions are nuclear fission reactions and nuclear fusion reactions. The previous includes the retention of neutrons (or other generally light particles) by a heavy nucleus, which makes it split into (at least two) lighter cores. Nuclear fusion reactions are the cycles where two somewhat light nuclei (by means of a crash) manage a single, heavier nucleus.

Nuclear Reactions Releasing Tremendous Amounts of Energy

The mass of an atomic nucleus is less than the amount of the masses of each subatomic particle combined that constitutes it (protons and neutrons). This difference in mass is ascribed to nuclear binding energy (frequently alluded to as a mass defect). Nuclear binding energy can be characterized as the energy needed to hold every one of the protons and neutrons inside the nucleus.

During an nuclear reaction (such as a fission or fusion reaction), the mass represented by the nuclear binding energy is delivered as per the condition e = m × c² (energy = mass occasions the square of the speed of light).

To simplify, the products formed in nuclear fission and nuclear fusion generally have a lower mass than the reactants. This ‘missing’ mass is changed into energy. A one gram of matter can release approximately 90,00,00,00,000 kJ of energy.

Nuclear Fission

It refers to the parting of an atomic nucleus into two or lighter nuclei. This process can happen through a nuclear reaction or through radioactive decay. These reactions regularly discharge a lot of energy, which is accompanied by the emission of neutrons and gamma rays (photons holding enormous measures of energy, enough to take electrons out of atoms).

This reaction was first discovered by the German chemist’s Otto Hahn and  Strassmann in the year 1938. The energy created from fission reactions is changed over into electricity in nuclear power plants. This is finished by utilizing the heat created from the nuclear reaction to change over water into steam. The steam is utilized to pivot turbines in order to generate electricity.

Illustration of Nuclear Fission

A significant illustration of nuclear fission is the parting of the uranium-235 nucleus when it is bombarded with neutrons. Different products can be formed from this nuclear reaction, as depicted in the situations underneath.

U²³⁵ + n¹ → Ba¹⁴¹ + Kr⁹² + 3 n¹
U²³⁵ + n¹ → Xe¹⁴⁴ + Sr⁹⁰ + 2 n¹
U²³⁵ + n¹ → La ¹⁴⁶ + Br⁸⁷+ 3 n¹
U²³⁵ + n ¹→ Te ¹³⁷ + Zr⁹⁷ + 2 n¹
U²³⁵ + n¹ → Cs¹³⁷ + Rb⁹⁶ + 3 n¹
One more significant illustration of nuclear fission is the parting of the plutonium-239 nucleus.

Nuclear Fusion

In nuclear fusion reactions, two or more atomic nuclei combine to form one nucleus. Subatomic particles, for example, neutrons or protons are also formed as products in these nuclear reactions.

Nuclear Fusion Reaction

An example of this reaction is the reaction between deuterium (2H) and tritium (3H) that yields helium (4He) and a neutron (1n). These fusion reactions generally happen at the center of the sun and different stars. The fusion of deuterium and tritium nuclei is accompanied by a loss of approximately 0.0188 amu of mass (which is totally changed over into energy). Approximately 1.69*109 KJ of energy is produced for each mole of helium formed.

Other Important Types of Nuclear Reactions

• Alpha Decay

Nuclei with mass numbers more prominent than 200 will quite often go through alpha decay – a cycle where a 4He nucleus, regularly referred to as an alpha particle (42α) is freed from the parent nucleus.

The condition for alpha decay is: ^AX_Z → ^{A – 4}X’_{Z – 2} + ⁴α₂

Where, A is the mass number and Z is the atomic number. An illustration of alpha decay is given underneath.

²²⁶Ra → 222²²²Rn + ⁴α₂

Here, the radium-226 nucleus decays into a radon-222 nucleus, freeing an alpha particle simultaneously.

• Beta Decay

Beta decay happens when a neutron is changed over into a proton, which is accompanied by the emission of a beta particle (high-energy electron). An illustration of this kind  of nuclear reaction is the beta decay of carbon-14 that affords nitrogen-14:

¹⁴⁶C → ¹⁴⁷N + ⁰β_-1

• Gamma Emission

Gamma discharge happens when an excited nucleus (frequently created from the radioactive decay of another nucleus) gets back to its ground state, which is accompanied by the emission of a high-energy photon.
An illustration of gamma emission is the de-excitation of the excited thallium-234 nucleus (which is delivered from the alpha decay of uranium-238). The condition for this nuclear reaction is:

²³⁴Th* → ²³⁴Th + γ

Sample Problems

Question 1: Complete the following nuclear reactions:

1. ¹n₀ + ⁴⁰Ar₁₈ ⇢ … +α
2. ¹n₀ + ²³⁵U₉₂ ⇢ ⁹⁸Zr₄₀ + …+ 3¹n

Answer:

1. By equating mass number’s:
A = 40 + 1 – 4 = 37,
By equating atomic number’s,
Z = 18 + 0 – 2 = 16,
So the nucleus formed is ³⁷S₁₆

2. By equating mass number’s:
A = 235 + 1 – 98 – 3 = 135
By equating atomic number’s,
Z = 92 + 0 – 40 = 52,
So the nucleus formed is ¹³⁵Te₅₂

Question 2: Consider the reaction  

¹³C₆+¹H₁ ⇢ ⁴He₂+¹⁰B₅

1. Use the masses of the nuclides involved to determine where it is endogenic or exoergic.
2. If it is exoergic, find the amount of energy released, if it is exoergic find the threshold energy.

Request:	Name:	Z:	A:	Mass (Mass Error), u:
Target Nucleus:	C	6	13	13.0033548377
Incident Particle:	proton	1	1	1.00782503207
Outgoing Particle1	He	2	4	4.00260325415
Final Nucleus :	B	5	10	10.01293699

Answer:

Now,
So, according to the Equation for 
Reaction energy:  E react = (M₁ + M₂ – Sum) × c²,
Where,
Variable Sum is the sum of all “Outgoing Particles” masses;
Variable M₁ is the “Target Nucleus” mass,
Variable M₂ is the “Incident Particle” mass.
Which comes negative. So reaction is endogenic.
Now threshold energy =  E_th = [(Sum + M₁ + M₂) × (Sum – M₁ – M₂) / (2 × M₁) ] × c²,
So,
Energy Threshold: 4.37714 MeV

Question 3: Calculate the energy released in the fission reaction:

¹n₀ + ²³⁵U₉₂ ⇢  ⁸⁸Sr₃₈ + ¹³⁶Xe₅₄ + 12n

Request:	Name:	Z	A	Mass (Mass Error), u:
Target Nucleus:	U	92	235	235.0439299
Incident Particle:	neutron	0	1	1.008664923
Selected (by User) Fission Fragment:	Sr	38	88	87.9056121
Defined (by Program) Fission Fragment:	Xe	54	136	135.9072187
Prompt Particle 1, Accompanied Fission:	12_n	0	12	12.10397898888

Answer:

Now,
So, according to the Equation,
Reaction energy: E react = (M₁ + M₂ – SUM) × c₂
Where variable SUM is the sum of all “Outgoing Particles” masses;
Variable M₁ is the “Target Nucleus” mass,
Variable M₂ is the “Incident Particle” mass.
So, Reaction Energy: 126.4828(73) MeV

Question 4: Find the threshold energy for the following reaction:

¹⁶O₈ + ¹n₀  ⇢  ¹³C₆ + ⁴He₂

Request:	Name:	Z	A	Mass (Mass Error), u:
Target Nucleus:	O	8	16	15.9949146195
Incident Particle:	neutron	0	1	1.008664923
Outgoing Particle 1:	He	2	4	4.00260325415
Final Nucleus :	C	6	13	13.0033548377

Answer:

Now,
So, according to the Equation for 
REACTION ENERGY :  E react = ( M1 + M2 – SUM ) * c2,
where variable SUM is the sum of all “Outgoing Particles” masses;
variable M1 is the “Target Nucleus” mass,
variable M2 is the “Incident Particle” mass
Now threshold energy =  Eth = [ ( SUM + M1 + M2 ) * ( SUM – M1 – M2 ) / ( 2 * M1 ) ] * c2,
so,Energy Threshold: 2 MeV.

Question 5: Find the threshold energy for the following reaction:

³He₂ + ¹n₀  ⇢ 2²H₁

Request:	Name:	Z	A	Mass (Mass Error), u:
Target Nucleus:	He	2	3	3.0160293191
Incident Particle:	:neutron	0	1	1.008664923
Outgoing Particle	H	1	2	2.01410177785

Answer:

Now,
So, according to the Equation for 
Reaction energy: E react = (M₁ + M₂ – SUM) × c₂,
Where variable SUM is the sum of all “Outgoing Particles” masses;
Variable M₁ is the “Target Nucleus” mass,
Variable M₂ is the “Incident Particle” mass
Now threshold energy = Eth = [(SUM + M₁ + M₂) × (SUM – M₁ – M₂) / (2 × M₁)] × c₂,
So, Energy Threshold:  4 MeV.