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Alpha particle is a helium (He’) nucleus which contains two positively charged protons and two neutrons. Because of the higher positive charge, when an alpha particle is headed directly towards the nucleus of an atom it does not make physical contact with the nucleus. This is due to the fact that the nucleus of an atom contains positively charged protons and alpha-particle is also positively charge. So there is a strong Coulomb’s repulsive force between alpha particle and nucleus of the atom, which prevent their physical contact.
The stability of an atom depends on both the number of protons and the number of neutrons. The light nuclides have almost equal number of protons and neutrons and are stable. But heavier nuclides require more neutrons than protons, and the heaviest contain 50 per cent more neutrons than protons. Most nuclides have both an even number protons and an even number of neutrons, such as O, Si, Fe etc.
The implication is that two protons and two neutrons (He) from a particularly stable combination. The reason is that the strong nuclear force occurs due to the exchange of mesons between the nucleons. The interaction between proton-proton or neutron-neutron occurs due to exchange of neutral (Tº) Pi mesons while between proton-neutron by charge (TT) meson. Thus the heavy nuclei require more neutrons in order to provide strong nuclear force for their stability.
Alpha-particle is a helium (H’e) nucleus which has 4amu mass and 2e positive charge while Beta-particle is relatively light and negatively charged, bearing charge e. Due to the heavy mass alpha-particle is deflected less than the beta- particle, when they are both introduced in an electric field between the two Oppositely charged plates. oppositely charged plates.
- Alpha-Particle: The electric force experienced by alpha-particle in the electric field E is given by
for alpha particle q = 2eE so we have
F = 2eE
2 Beta-Particle: The electric force experienced by Beta-particle is given by
Since M>>m so α2>> α1, hence alpha-particle is less deflected than Beta-Particle in an electric field.
The stoms of an element which have the same atomic or change number z but different mass number A are known as isotopes. Isotopes are the nucleides of the same element x which has the same number of protons but different number of neutrons.
- In Common: 1. The isotopes of an element x have the same number of protons and electrons in atoms.
(2) The chemical properties of all the isotopes of an element x are alike.
(3) They have the same place in periodic table.
- Difference: (1) The isotopes of an element x have different number of neutrons in the nuclei of their atoms.
- The isotopes of an element have different physical properties. For example Hydrogen has three isotopes, namely, (1) Protium H’ (2) Deuterium H (3) Tritium H’, which have different physical properties.
The number of electrons and protons in a neutral atom is the same. Now 86Rn222 is symbol of Radan whose mass number A = 222 and charge number z = 86. Thus we can write
Mass number = A = 222
Charge number = z = 86
- So the number of protons = 86
- Number of neutrons = A – Z=222 – 86 = 136
- Number of electrons in neutral atom = 86
The element Radium 88Ra226 has half-life of 1600 years and in 4800 years we have 3 half-lives.
(a) Let N, be the original number of radium atoms which are undecayed at any instant.
The number of atoms decayed after 1″‘ half-life = T1/2 = 1/2N
The number of atoms decayed after 2nd half life = 2 T1/2 =1/2XN/2 = 1/4XN
The number of atoms decayed after 3rd half life = 1/2X1/4XN = 1/8N
The total number of atoms decayed after 3 half = 1/2N + 1/4XN + 1/8N = 7/8N
Fraction of radium decayed = 7/8N/Nx100/100= 7/8X100/100=87.50%
The remaining sample left undecayed=100 -87.5 = 12.5%
(b) Since 1 half-life = 1600 years. So 6 half-lives = 9600 years. Thus in 9600 years there are 6 half lives.
At the time when the earth was formed, all the elements, stable and unstable were formed in varying amounts. From decay law we have.
N = N̥e-λt
This equation implies that a given radioactive sample will take an infinite time to decay completely. Individual radioactive atoms may have life times between zero & infinity. Now we are given that half-life of Radium is
T = 1600 = 1.6×103 years
Age of the Earth = 5 billion years.
Now an infinite time is required for all atoms of a radioactive element radium to decay completely. But Earth’s life is not infinite; it is still 5 billion years. So we can still find the existence of radium 88Ra256 element in nature.
Nuclear reactor is a nuclear power plant which plays the same role as a furnace in a thermal power station. In nuclear power plant control fission chain reaction produces heat. A fission reaction produces energy at the rate of 200MeV/ nuclei in the form of kinetic energy of fission fragments. This K.E is converted into heart through collision between fission fragments and the Uranium atoms. The heat so produce is used to generate steam which rotates the turbine. The turbine rotates the generator to produce electrical energy.
There are two main factors which make a fusion reaction difficult to achieve a. High temperature: The fusions of two nuclei in fusion reaction is only possible if they overcome their mutual electrostatic repulsion. This may be happen if they collide at very high speed that is, they are raised to a very high temperature. Therefore, temperature between 108K to 109K is required in the thermonuclear reaction. Such high temperature is obtained only by using fission reaction (explosion of atomic bomb) to trigger off the fusion reaction. Hence this high temperature makes a fusion reaction difficult to achieve.
- How to keep hot plasma: The second factor which makes the fusion reaction difficult is the containment of the hot reacting gas, called plasma, from touching the vessel holding it. Because at temperature. 10K, any material used for a container vaporizes, and the plasma disperses. Alternatively instead of putting Plasma in a container, it has been tried to confine it at the center of a large diameter tube by means of external magnetic field. Extensive research work is in progress for producing a controlled fusion reaction.
- Fission and fusion are both nuclear reactions which have in common is that both produces energy.
- In both the processes the decrease in the rest mass appears as energy, satisfying the result of special theory of relativity. E =(Δm) C2
- In both the processes the nuclei produced, have a greater binding energy per nucleon.
Differences: Following are the differences between fission and fusion reaction.
Fission: The process in which heavy nucleus is broken in to two intermediate nuclei with the release of energy is called fission reaction. In fission reaction energy is produced at a rate of 200MeV per nuclei. Fission reaction occurs when a slow neutron strikes a u235 nuclei.
Fusion: The process in which two light nuclei are fused to form a relatively heavy nucleus with the release of energy is called fusion reaction. During fusion reaction the energy is liberated at a rate of 3MeV par fusion. For fusion of the two light nuclei high temperature such as 108k is needed.
Similarity: The time constant RC is similar to decay constant λ and half-life T on the following grounds:
- The decay of charge on a capacitor is given by:
q = q̥e-t/RC
While the decay of radioactive nuclei in a radioactive sample is
N = N̥e-λt
Hence both the quantities exponentially changes.
- The decay curve of charge against time has the same shape as the decay curve of N, number of nuclei against time t.
- The decay curve shows that it decreases by the same fraction in successive equal time intervals. If the charge falls from q to q/2 in time T1/2, it will also fall from q/2 to q/4 in the next interval of time T1/2. The time T1/2 is therefore known as half-life.
(a) The time constant is the duration of time after which 37% charge remaining on the capacitor, while decay constant λ is the rate of disintegration per nuclei.
(b) The unit of time constant Rc is second (se) while that of decay constant λ is 1/second = Se-1
When a nucleus emits a y-radiation, then neither its charge number z changes is not its mass number A changes. This is due to the fact that a Gamma-radiation is simply a photon which has neither any charge nor any rest mass. After the emission of α particle or β-particle, the daughter nucleus is in the excited state. This excited state is unstable, so the nucleus comes to a stable state by emission of one or more y-rays photons. So their emissions do not make any change in charge number z or mass number A. The y-decay process is written as
zXA à α zX*A à zXA + y-ray
Here X represents an excited daughter nucleus.
The neutron activated nuclei tends to emit electron. Because the emission of electron from the nucleus can takes place, when neutron emitting electron and converts to proton.
n1 à P1+B1 – particle
n1 à P1+e’
This means that the B-particle is formed at the time of emission. That is why at the time of emission of B-particle the charge number z of the nucleus increases by one unit but not by one unit but no change in its mass number A. Because the mass of electron is very small. It should be noted that during neutron activation, neutrons are added the nuclei, which increases the neutron to proton ratio (n/p). So the nuclei tends to decay by electron emission.
For example thorium 90Th22 is transformed, into protactinium 9Pa252 after emission of B-particle (electron).
90Th232 à 91Pa232 +β’
The heavy nuclei are unstable because their binding energy per nucleon is less than the lighter nuclei or those which are lying in the middle portion of the periodic table. Moreover, nucleons are not rigidly bounded with each other in heavy nuclei. The low value of binding energy for the nuclei with large mass number A is due to coulomb’s repulsive force. The protons inside the nucleus repel each other according to Coulomb’s law that decreasing the binding energy. As the mass number A, increases, the magnitude of strong attractive nuclear forces among the nucleons decreases, so the binding energy decreases. This decrease in binding energy makes the heavy nuclei unstable. Hence less energy is required to break the heavy nuclei.
- Emission of electron: The emission of electron from radioactive nuclei takes place by the conversion of neutron to proton.
n1 à P1+B1
The emission of electron increases the charge number z of the nuclei by 1 unit but no change in its mass number A, as the mass of electron is very small. For example 90Th232 transforms to 91Pa232 by emitting electron.
90Th232 à 91Pa232 +β’
(2) By capture of electron: When an electron is slowed or captured by the electric field of a nuclei, electromagnetic waves (x-rays) are emitted which never change the charge number z and mass number A.
(3) Emission of α-particle: By the emission of a particle the mother nucleus drops down by two units in charge number z and four units in mass number A. Because alpha-particle has two protons and two neutrons. For example 92u235 transforms to 90Th232 by alpha emission.
9 92u235 à 90Th232 + α-particle
When 90Th298 transforms to 82Pb212, then the emission of four α-decay takes place, the series is given below.
90Th298 à 88Rn294 + α-particle
88Rn294 à 86Rn290 + α-particle
86Rn290 à 84Ra286 + α-particle
84Ra286 à 82Pb282 + α-particle
Thus a-particle emission occurs when 90Th298 converts to 82Pb282.
A strong force which keeps the quarks pack inside the nucleus is known as colour force. Colour force is a type of strong force like strong nuclear force that keeps the nucleus together inside a nucleus. Similarly colour forces bind the most basic particles together in a nucleus. It is different from all the other force there. Because as the distance between the individual quarks increases, the colour fosrces increases exponentially. So as the quarks drift further from each other, they are pulled back, keeping the bond between them fully intact. In fact this attraction is so strong that individual quarks have never been observed.