Showing posts with label Nuclei. Show all posts
Showing posts with label Nuclei. Show all posts

Nuclear Fission and Nuclear Fusion

Nuclear Fission

It is experimentally observed that binding energy per nucleon will be decreasing with atomic number after iron. Uranium is a element which has less stability, it always tries to get the stability. When a slow moving neutron strikes a uranium atom, it splits into barium, krypton and there is some emission of the energy also. Simultaneously in this process there is emission of three more neutrons. These available neutrons can further participate in reactions and break three more uranium nucleus and it can happen continuously. This process is actually called chain reaction.

Nuclear fusion is simply a process of heavy nucleus splitting up into lighter nuclei and the emission of energy. When a uranium atom splits into multiple atoms there is emission of energy that is approximately equal to 200,000,000 electron volt. But for the uranium atom to split it need only a slow moving neutron. The slow moving neutron will give enough time for the nucleus is to absorb the energy therefore it can split up further into different elements. The energy released in the process is in the form of kinetic energy at a major level. The pressure and temperature in this process are going to be very high.

The average number of the neutrons emitted in each step is approximately 2.5. The emitted neutrons can initiate further fission and that leads to chain reaction. In each reaction three neutrons are emitted and hence in each step the number of the neutrons increases in multiples of three. Over the time, because of this release of the energy which is in very high in magnitude that was generated in a small amount of time, there could be explosion. This way of creating the explosion with a high-energy is called nuclear fission bomb or atomic bomb.



For the nuclear chain reaction to happen there shall be minimum mass of the uranium elements and the minimum required mass is called critical mass. There is another condition that has to be satisfied for the chain reaction to continue. That is the numerical value of neutron multiplication factor shall be greater than one. This is also called reproduction factor. Reproduction factor is defined as the ratio of number of the neutrons available in the present generation when compared with the number of the neutrons available in the previous generation of the chain reaction.

When the reproduction factor is less than one, the chain reaction is not going to be sustained. This is called sub critical state. When the reproduction factor is equal to one, it is called just critical state and the chain reaction is going to happen but not with the enormous amount of release of energy. If the reproduction factor is greater than one the chain reaction becomes uncontrolled reaction and it leads to atomic bomb.



Uncontrolled chain reaction leads to emission of high-energy at a very high temperature which leads to disaster situations. If we are able to control the energy that is emitted in a systematic way, we can convert that energy into other formats of energy like electricity and can be used for the real-life requirements. This can be done with the controlled chain reaction. We can achieve controlled chain reaction using some devices like the nuclear reactor. The very purpose of the nuclear reactor is to produce a nuclear reaction in a controlled manner therefore we can use that energy into our requirements.

A nuclear reactor consists of some major parts like a fuel to initiate the process. The fuel could be uranium or thorium.

We need slow-moving neutrons for the nuclear chain reaction to happen. We can use elements called moderators to slow down the fast moving neutrons. Graphite, carbon, water can be used as moderators as per the requirement.

To control the number of the neutrons available so that the chain reaction can be in control, we have a device called control rods. The very purpose of the control rods is to absorb the neutrons so that the number of the neutrons will be in the control. Cadmium or boron can be used for the purpose of the control rods. Whenever it is required this control rods are get into the system therefore they can start absorbing neutrons.

The coolant like water is circulated around the system to control the temperature of the nuclear reactor. A strong shield is also provided around the system to protect the environment from possible radioactive emissions.

By using this kind of nuclear reactor we can get electricity and that kind of energy is called nuclear energy. So by using the nuclear energy in a productive way, we can use the sciences for the development in the comfort of people.

We know that, with each nuclear fission there is energy emission of approximately 200,000,000 electron volts. What is the total power that is available with a nuclear reactor can be calculated as the multiple of number of the Frisians per second the energy per fission. We can solve small problem on this concept as shown below.


Nuclear fusion

The process of the formation of a single stable nucleus by fusing the two or more lighter nuclei is called nuclear fusion.

One of the simple example is the formation of the helium nucleus by fusing four hydrogen nuclei. In this process there is a release of energy. This energy at the outlook appears like a smaller energy than that of fission. But the energy emitted per nucleon is much higher in the case of the fission than that of the fusion. Therefore the energy of the fusion is higher in magnitude. There is a small difference in between the mass of for hydrogen nuclei together when compared with the mass of the helium. This missing mass converts into energy and is released in the process. For the fusion to happen, different nuclei have two combined together. This is possible only when we are able to dominate the force of the repulsion. Hence there is a very high amount of energy is required for the nuclear fusion to happen and it approximately demands 1000000 Kelvin of temperature.

We cannot get this temperature easily and in fact we need to run nuclear fission to get this much of high-temperature. Therefore nuclear fission initiates the process of nuclear fusion. Nuclear fusion can happen in different processes like hydrogen and hydrogen cycle and the carbon and nitrogen cycle. Nuclear fusion is the energy source of the sun and the stars which are emitting huge energy for us. Depending on the temperature of the star it could be any of the cycles therefore energy could be emitted by the stars.

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Nuclei Complete Lesson

Nuclear physics deals with the elements of atom, nuclei and its applications. Here we learn about nuclear forces which are strongest and short range forces exits between nucleons. It deals with mass defect which is the difference in the mass of nucleons when compared with the nucleus. It deals with binding energy and binding energy per nucleon which is a measure of stability of the nucleus.


Here we are also going to deal with the concept of radioactivity. We learn about acquiring the stability of nucleus by emitting some of its elements. We also deal with the concept of nuclear fission and fusion and its applications in the topic. Here all the links are available about the topics.


Radio Activity and Half Life Period

Spontaneous emission of Alpha, beta and gamma radiation from the unstable nuclei is called radioactivity. This generally happens with the heavy nucleus like uranium and thorium. We cannot change the radioactivity by playing high-temperature, high-pressure or electric field. Nuclei can disintegrate immediately or it may take in finite time.

Alpha decay

The Alpha particle is nothing but a helium nucleus. It is a positively charged particle whose charge is equal to two times a charge of the photon. It is deflected both electric and magnetic fields.

With the emission of the Alpha particle, the atomic number of the nucleus is reduced by two and its mass number is reduced by four.

Beta decay

The emission of the fast moving electrons from the nucleus is called beta decay. The neutron inside the nucleus splits up into proton and electron. The electron is rejected out like beta particle. The proton reminds inside the nucleus itself. Because of this the atomic number is increased by one when there is emission of beta particle will. Anyway the mass number of the nuclei is going to remain same as the number of the neutrons decreases by one and the number of the protons increases by one.

As the beta particles are having a charge they are also deflected by electric and magnetic fields. They have ionization power less than that of Alpha particles and penetration power better than that of Alpha particles.


Gamma Decay

Gamma rays are nothing but electromagnetic radiation of short wavelength. There is no effect on atomic number as well as the mass number during this emission. During the emission of Alpha Ray and beta Ray electrons goes to excited states. They cannot stay in the excited state for a long time and they will come back to their earlier states. 

During this process they emit some energy and that energy is observed in the form of this electromagnetic waves. Gamma rays alone cannot be emitted. As a consequence of Alpha Ray or beta Ray, they can be emitted.



Law of radioactivity

Basing on experimental observations and analysis of radioactive material this is formulated. According to this law the rate of radioactive decay at any instant is directly proportional to number of nuclei present at that instant and is independent of physical conditions like temperature, pressure and chemical composition. Radioactive decay is nothing but the number of the nuclei decaying per unit time.

We can derive the relation between number of the nucleons present with respect to the initial number of the nucleons after a specified time as shown below.


Half life period

The time interval during which the number of radioactive nuclei of a sample disintegrates to half of its original number of nuclei is called a half life period.

We can derive the relation between half life period and the decay constant basing on their respective definitions as shown below.



Half life period of a material is its characteristic property and it cannot be changed by any of the known methods. We can express the relation between the initial number of nucleons and the final number of nucleons with respect to number of the half lives as shown below.


It can be mathematically noticed that after half of the half life period 70.7% of the initial number of the nucleons are going to be present. It means approximately 30% of the nucleons were disintegrated in the first half of the half life period. You might notice that it is not 25% but 30% . More disintegration is happened because initially there are more number of nucleons.

Average life

The phenomenon of radioactivity is random and we cannot predict which one of the atoms will decay first and when. Each atom will decay in its one-time and to determine the average of all the decays, we have defined average life. It is defined as the ratio of total lifetime of all the nucleons to the number of nuclei. It can be mathematically proved as the reciprocal of the decay constant. We can derive the relation between half life period and the average life as shown below.



Problem and solution

The half-life period of the Cobalt is 72 years. How much time does it take for three by fourth of its initial mass to disintegrate?

We can solve this problem basing on the Basic derivation is that we have made in the above pages. We can calculate the number of half life period is as shown below.



Problem and solution

A radioactive sample can decay in two different processes simultaneously with a different half life periods. Find the effective half liquidate of the sample?

We can solve this problem basing on the law radioactive decay. According to this law the number of the nucleons disintegrated per second is directly proportional to initial number of nucleons. The same element is going through two different processes and hence the initial number of the nucleons are same. The total rate of disintegration is equal to the sum of rate of disintegration of both the cases. We can solve this problem as shown below.



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Mass Defect and Binding Energy of Nucleus

Mass defect

The mass of the total nucleons is little bit more than the mass of the nucleus. This difference in the mass is called mass effect. Between the protons there is a strong force of the repulsion because of their positive charges. To overcome this repulsion and to keep them together, they need some energy. They cannot get the energy from the outside so a portion of the mass is sacrificed and that mass is converted into energy to keep the nucleons together. This sacrificed the mass could be called as mass defect.

Binding energy

The energy that is corresponding to mass defect is called binding energy. This energy keeps the nucleons together therefore nucleus will be having its stability. If there is no mass defect, then there won’t be any binding energy and hence nucleons cannot be together.

Anyway mass defect is not the exact measure of stability of the nucleus. Similarly even the binding energy is not the exact measure of the stability of a nucleus. It is not the binding energy, but the binding energy per nucleons is a measure of the stability of the nucleus. This binding energy per nucleon is called binding fraction. If binding energy per nucleons is more, then the nucleus will be more stable.

We can write the equations for mass defect, binding energy and the binding energy per nucleon as shown below.



Binding energy curve

We can draw a graph taking the mass number on x-axis and the binding energy per nucleon on y-axis. This graph is drawn for all the existing elements of the periodic table and it is observed that with the increase of the mass member, binding energy per nucleon is also increasing up to some extent. Within this region itself there are specific elements like helium, carbon and oxygen that are having exceptionally highly binding energy per nucleon. It means that there are more stable than the neighboring elements.

It is noticed that up to the iron, with respect to the increase of mass number binding energy per nucleon is also increasing. Beyond iron with the increase of the mass number binding energy per nucleon slowly starts decreasing and by the time uranium is reached, it reaches to its minimum value. It means to say that uranium is the most unstable element because of its less binding energy per nucleon.

In the case of the uranium, there is more number of the protons inside the nucleus and between them there does a strong repulsive force exist. This makes the nucleus unstable and to get the stability, it emits some elements from the nucleus. This kind of emission is called radioactivity.



Problem and solution

The following problem we are expected to calculate mass defect, binding energy and binding energy per nucleon of an Alpha particle? In the problem mass of the proton and neutron are given as shown below.

We know that the mass defect is nothing but the difference in the mass of the total nucleons to the mass of nucleus. It can be identified that an Alpha particle will have two protons and two neutrons. By substituting the appropriate data we can get the answer as shown below.




Nuclear forces

There are three kinds of basic forces in the nature. They are gravitational forces, electromagnetic forces and nuclear forces. Among the existing forces gravitational forces are the weakest forces, electromagnetic forces are much stronger than the gravitational forces and the nuclear forces are the strongest forces.

Both gravitational and electric forces are long-range forces whereas nuclear forces a short-range force. The nuclear force acts only between the nucleons of a given nucleus.
Gravitational forces are always attractive whereas electromagnetic forces either attractive are repulsive. Nuclear forces by default are attractive in nature.

Nuclear forces are charge independent forces. It means the force of attraction between the protons, neutrons and between the proton and neutron is same.

Nuclear forces are spin dependent forces. If two nucleons are having the parallel spin between them, there is a better force of attraction and vice versa.


Nuclear forces are non-central forces and there is no simple mathematical formula to express them.

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Discovery of Neutron,Radius and Density of Nucleus

We know that matter is made up of atoms. We also know that in atom, at the Center, mass is concentrated with the combination of protons and neutrons. That central part of the atom is called nucleus and the elements of the nucleus are called nucleons. We also know that electrons revolve around the nucleus in specified orbits.

The number of the protons inside the nucleus is called atomic number. The total number of the nucleons inside the nucleus is equal to the sum of number of the protons and the number of the neutrons. This total number of the nucleons is called mass number. The number of the nucleons present inside the nucleus is the difference between the mass number and the atomic number. The conversion of one element into the other element by artificial means is called artificial transmutation of element.



Discovering neutrons has taken much longer time than the discovery of electrons and protons. It is simply because they are not having a charge and hence identifying their presence has taken a little bit longer time. A scientist by the name James Chadwick has discovered the neutrons.

When a helium particle is allowed to strike a beryllium atom, carbon atom is farmed which is in unstable state. It further splits into a stable carbon atom and a neutron. The problem with the identification of the neutron is it is not having charge. Therefore it is allowed to pass through paraffin material which is a rich resource of protons. 

Whenever a neutron strikes the paraffin, one proton is released. Identifying the proton is very easy with electronic counter. The number of the neutrons released in this process is nothing but equal to the number of the protons. The experimental arrangement is as shown in the block diagram.



Properties of neutrons

  1. It has no charge.
  2. It is not influenced by electric and magnetic fields as it is not having a charge.
  3. It has a high penetration power so that it can penetrate deep into the materials.
  4. It has low ionization ability.
  5. It is stable inside the nucleus but not stable outside the nucleus. It has average life of thousand seconds outside the nucleus. It means once if it is outside the nucleus it can stay like the neutron only for thousands seconds and within that time it converts into anti-neutrino, electron and proton.
  6. The speed of the neutron can be slowed down by passing it through heavy water.
  7. The mass of the neutron is approximately equal to mass of the proton.


Classification of nuclei

The nuclei having the same atomic number but different mass number are called isotopes. They have same number of protons but different number of neutrons.

The nuclei having the same mass number but different atomic number are called isobars. Here total number of the nucleons is same but the number of the protons and neutrons are different in each case.

The nuclei having the same number of the neutrons are called isotones. They have different mass numbers and different atomic numbers but the difference between mass number and atomic number is same.

In the following attracted paper the examples of this different kinds of nuclei are given.



To measure the mass of fundamental particles like electrons and protons the regular systems like standard international system are not directly useful. As these masses are very small, in accordance to them, small unit of mass is defined and that unit is called atomic mass unit. One atomic mass unit is defined as one by 12th of the mass of the carbon atom.

Nuclear size

Nucleus consists of both protons and neutrons. Neutrons are neutral particles whereas the protons are having positive charge. The total charge of the nucleus is equal to the product of number of the protons and the charge of each proton. In terms of magnitude charge of proton and electron are equal. But the proton has a positive charge whereas the electron has a negative charge.

There is a lot of empty space inside the atom. The size of the nucleus is very small when compared with the size of the atom. The size of the nucleus is directly proportional to number of nucleons. It is simply because the nucleus is nothing but the group of the nucleons.

Therefore we can conclude that the volume of the nucleus is directly proportional to mass number. We can also assume that the nucleus is approximately spherical in shape. Basing on this we can derive the relation between the radius of the nucleus and the mass number as shown below. We can also express this radius in terms of the mass number as shown below.



Application

A stationary nucleus splits into two lighter nuclei. Find the ratio of velocity of the two elements of the nuclei?

As there is no external force acting on the system, the linear momentum of the system is always conserved. Initially the nucleus is being in the state of rest and hence its initial momentum equal to 0. After the explosion both the particles will have same the momentum in the opposite direction. Hence we can express the equation for velocity and kinetic energies as shown below.



We have already explained that the mass of the fundamental particles can be measured with the unit called atomic mass unit. Similarly to measure their corresponding energies we need to use a unit called electron volts. We know according to Einstein’s mass energy relation that each mass will have correspondingly some energy.

In the above diagram the conversion is made and it is proved that one atomic mass unit is having energy equal to 931.5 million electron volt.

Nuclear density

We know that density is defined as mass per unit volume. Density of the nucleus is also defined as the ratio of total mass of the nucleus to its volume. By substituting the expression for the radius in the above equation and by simplifying we can calculate that the density of the nucleus. It is a very high value as shown below. It is also proved that the density of the nucleus is independent of mass number. It means whatever may be the name of the nuclei; the density is going to be the same. The derivation is shown below.




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