(1)

here is constant known as disintegration constant or decay constant of the radioactive element. It is defined as the ratio of the substance which disintegrates in a unit time to the amount of substance present

Equation (1) can be written as

Integrating we get

(2) here C is constant of integration

Let be number of radioactive atoms present initially.

Then when ,

Therefore,

Substituting for C in (2) we get

(3)

This equation shows that number of atoms on taken radioactive element decreases exponentially with time. Theoretically, infinite time is required for radioactivity to disappear completely and this is same for all elements. Hence to compare two element’s radioactive properties, a quantity called half-life period is used.

Half life period: The half life period of a radioactive substance is defined as the time required for one half of the radioactive substance to disintegrate. For any given radioactive element, at the end of time only 50% of the radioactive atoms remain unchanged and at the end of only 25% remain and at the end of 12.5% remain and after 6.25% remain and so on.

Value of half-life period

We have the relation

If be the half life period, then at and

Thus we can conclude that half life is inversely proportional to disintegration constant lambda. Half life is different for different radioactive substances. Uranium has a half life period of and Radium has a half life of 1622 years while element Radon has half life of 3.8 days.

Rutherford showed later that the emanations given off by uranium sulfate were capable of ionizing the air in the space between two oppositely charged metallic plate (an ionization chamber). The current registered by a galvanometer in series with the circuit was taken to be a measure of activity in the compound.

A systematic study of the activity of various elements and compounds led Mme. Curie to the conclusion that this activity was an atomic phenomena and by the methods of chemical analysis, she and her husband Pierre Curie found that “ionizing ability” or “activity” was associated not only with uranium but with two other elements that they discovered, radium and polonium. The activity of radium was found to be more than a million times that of uranium. Since the pioneer days of the Curies, many more radioactive substances have been discovered.

The activity of radioactive material may be easily shown to be the result of three different kinds of emanations. In earlier experiments, a small piece of radioactive material is placed at the bottom of a long groove in a lead block. Some distance above the lead block a photographic plate is placed, and the whole apparatus is highly evacuated. A strong magnetic field is applied at right angles. After developing the plate, three distinct spots are found, one in the direct line of the groove in the lead block, one deflected to one side and one deflected to the other side. From the knowledge of the direction of the magnetic field, it is concluded that one of the emanations is positively charged (alpha particle), one is negatively charged (beta particle) and other is neutral (gamma rays).

Further investigation showed that not all three emanations are emitted simultaneously by all radioactive substances. Some elements emit alpha particles, others emit beta particles, while gamma rays sometimes accompany one and sometimes the other. Furthermore, no simple macroscopic physical or chemical process such as raising or lowering the temperature, chemical combination with other non radioactive substance etc, could change or affect in any way the activity of a given sample. As a result, it was suspected from the beginning that radioactivity is a nuclear process and that the emission of a charged particle from the nucleus of an atom results in leaving behind a different atom, occupying a different place in the periodic table. In other words, radioactivity involves the transmutation of elements. The first measurement of the charge of the alpha particle used a device called a Geiger counter, still an important instrument of modern physics.

Interaction	Particles affected	Range	Relative strength	Particles exchanged
Strong	Hadrons		1	Mesons
Electro	Charged particles			Photons
Weak	Hadrons and leptons			Intermediate bosons
Gravitational	All			Gravitons

1. Strong interaction: Strong interaction is responsible for holding the nucleons together in atomic nucleus and is independent of electric charge. This interaction works within a distance of  and time for interaction is 

2. Electromagnetic interaction: It works on all charged particles and are charge dependent resulting in attractive as well as repulsive force. Its range is infinite and this interaction happens through photon.

3. Weak interaction: Weak interaction is responsible for decay of strange and non strange particles and for non leptonic decays of strange particles. The weak interaction is responsible for the radioactive decay of subatomic particles, and it plays an essential role in nuclear fission.

4. Gravitational interaction: It is the weakest among the four and has infinite range. This interaction is clearly visible on larger scale but in atomic scale its effect can be easily neglected. This interaction is explained in terms of ‘Gravitons’ with mass zero and travel with the speed of light. Gravitons are yet to be detected in lab.

It should be noted that gravitational force is universal as it effects all known particles.On the contrary, weak force affects all particles except photon. Electromagnetic force happens between charged particles.

Proton and antiproton: The antiproton was first discovered in 1955 and is a particle identical to the proton except for a negative charge and was produced by bombarding protons in a target with 6GeV protons thereby initiating the reaction . The KE of the bombarding proton is converted to a proton antiproton pair plus the KE of the four residual particles. Antiproton interact with proton and produces five pions and their KE like

Neutron and antineutron: Antineutron was discovered in 1956 by Cork, Lamberton and Wenzel. Both neutron and antineutron have zero charge and same mass. Antineutron are annihilated by proton or neutron with production of pions. If antineutron is not annihilated by a nucleon, it decays by the reaction

Neutrino and antineutrino: The antiparticle of neutrino is antineutrino. The spin of neutrino is opposite in direction to the direction of its motion; viewed from behind, the neutrino spins counterclockwise. But the spin of the antineutrino is in the same direction as its direction of motion; viewed from behind, it spins clockwise. The neutrion moves through space in the manner of a left handed screw while the antineutrino does so in the manner of a right handed screw. Thus neutrino possesses a “left handed” helicity; the antineutrino possesses a “right handed” helicity that is a neutrino and antineutrino differ only in the sense of their helicity. Particle accompanied by positron is neutrino () and particle accompanied by an electron is antineutrino ().  Because of the lack of charge and magnetic moment of neutrino, they hardly interact with matter except in reaction leading to inverse beta decay. The interaction is extremely week and the cross section for this process is only . Hence matter is almost totally transparent to neutrinos.

Antimatter: Antimatter is a matter formed by the combination of antiparticles. For example, positron and antiproton can form an atom of antihydrogen. With a collection of positron, antiproton and antineutron, a world of antimatter can be created and it will be indistinguishable for ours as long as it is made of antiparticle. Antimatter will however annihilate with matter and release tremendous amount of energy when they come in contact with each other.

1. Baryons: Baryons are also known as heavy particles and they comprise of proton and other heavier particles. Proton and neutron of this group are called nucleons and the other are termed as hyperons. All baryons has anti-particle. We assign a number +1 for baryon and -1 for antibaryon. So, in any closed system, the baryon number is conserved in interaction or decay. This is called as the law of conservation of baryons.

Hyperons are very special and are known by a time decay of the order of seconds and mass between that of neutron and deuteron. Their decay time is greater than the time of formation . It is this unsolved problem that these particles along with K-mesons are called strange particles. There are four kinds of hyperons: Lambda, Sigma, Xi and Omega.

2. Leptons: This group contains electron, photon, neutrino and muon.

Mesons: The rest mass of these particle lie between 250me and 1000 me. It acts as an agent for interaction between particles inside the nucleus. Baryons and mesons are combinely called as hadrons and are particle of strong interaction.

Leptons	Name	Symbol
	Photon
	Neutrion
	Electron
	Muon
Mesons	Pion
	Kaon
	Eta
Baryons	Proton
	Neutron
	Lambda
	Sigma
	Xi
	Omega

Whereas Democritus’s atomism had been purely theoretical, Dalton showed that common substances always broke down into the same elements in the same proportions. He concluded that the various compounds were combinations of atoms of different elements, each of a particular size and mass that could neither be created nor destroyed. Atomic theory was now accepted by the scientific community, but the next major advancement would not come until nearly a century later with the physicist J.J. Thompson’s 1897 discovery of the electron. He showed atoms as uniformly packed spheres of positive charge matter filled with negatively charged electrons.

Thompson won a Nobel Prize in 1906 for his electron discovery, but his model of the atom didn’t stick around long. Ernest Rutherford, also known as the father of the nuclear age while studying the effects of X-rays on gases, decided to investigate atoms more closely by shooting small, positively charged alpha particles at a sheet of gold foil. Under Thompson’s model, the atom’s thinly dispersed positive charge would not be enough to deflect the particles in any one place. The effect would have been like a bunch of tennis balls punching through a thin paper screen. But while most of the particles did pass through, some bounced right back, suggesting that the foil was more like a thick net with a very large mesh. Rutherford concluded that atoms consisted largely of empty space with just a few electrons, while most of the mass was concentrated in the center, which he termed the nucleus. The alpha particles passed through the gaps but bounced back from the dense, positively charged nucleus.

But the atomic theory wasn’t complete just yet. In 1913, another of Thompson’s students by the name of Niels Bohr expanded on Rutherford’s nuclear model. Drawing on earlier work by Max Planck and Albert Einstein he stipulated that electrons orbit the nucleus at fixed energies and distances, able to jump from one level to another, but not to exist in the space between. Bohr’s planetary model took center stage, but soon, it too encountered some complications. Experiments had shown that rather than simply being discrete particles, electrons simultaneously behaved like waves, not being confined to a particular point in space.

And in formulating his famous uncertainty principle, Werner Heisenberg showed it was impossible to determine both the exact position and speed of electrons as they moved around an atom. The idea that electrons cannot be pinpointed but exist within a range of possible locations gave rise to the current quantum model of the atom, a fascinating theory with a whole new set of complexities whose implications have yet to be fully grasped. Even though our understanding of atoms keeps changing, the basic fact of atoms remains.

Mass of 2 protons + 2 neutrons =

= 4.031882

Mass of particle = 4.001506

Mass defect =

B.E. =

B.E. =

Binding energy per nucleon =

The binding energy per nucleon and the mass number is plotted in the figure. We can see that the curve rises steeply initially and then gradually reaches maximum of 8.79 MeV at A=56. This number A=56 corresponds to Iron . The curve now drops very slowly to somewhere around 7.6 MeV at the highest known mass number. From this graph we can say that nuclei of intermediate mass are more stable since high amount of energy is required to separate these nucleons. This also means that a large amount of energy will be liberated if heavier nuclei can be divided into lighter ones in nuclear fission.

Packing fraction: The ratio between mass defect and the mass number is called the packing fraction. Packing fraction means mass defect per nucleon. Packing fraction is used to measure the comparative stability of the atom.

Packing fraction can be positive or negative. If packing fraction is negative, the isotopic mass is less than the mass number and in that case the mass gets transformed into energy in the formation of that nucleus according to the formula . This nuclei is more stable.

A positive packing fraction would mean a tendency towards instability. This is not essentially correct for atoms will lower atomic mass though. It should be noted that the element with mass numbers more than 230 are radioactive and goes through spontaneous disintegration.

Nuclear stability

The stability of nuclei are classified according to even and odd number of protons and neutrons

For stable nuclei, we can see that nature prefers even number of protons and an even number of neutrons. The odd odd combination of proton and neutron in the nucleus are very less and are found only in lighter elements. For elements with large number of proton in the nucleus, the coulomb electrostatic force of repulsion becomes significant and the number of neutrons must be greater to compensate this repulsion effect.

Without the Higgs, we do not exist. It should be noted that when we study the smallest components of matter, we address the biggest questions of the universe and the Higgs boson will tell us how the fundamental particles acquire their mass. This, in turn, allows the existence of complex things – such as atoms, molecules and human beings.

What Is a Boson?

 Fermions and bosons are the two division types of subatomic particles. Fermions are responsible for making up matter and bosons are responsible for interaction and carrying forces. Example of fermions includes electrons, protons and neutrons while bosons are photon, the gluon, the W and Z bosons – responsible respectively for electromagnetic forces, strong nuclear and weak nuclear force.

What is the Higgs boson?

Higgs boson is a type of elementary particle responsible for giving mass in the Universe. Higgs particle were confirmed by Large Hadron Collider (LHC). LHC is a place to smash atoms together as it is one of the most powerful particle accelerator in the world located at Franco-Swiss border near Geneva and run by CERN.

Importance of Higgs Particle?

Higgs particle was the only particle remained to be discovered. It was an integral part of Standard Model of particle physics. As of now standard model is able to describe perfectly the elementary particles and their interactions but particle giving mass i.e. Higgs remained to be discovered in this model. Higgs particle play an important role in the universe because it gives mass to fermions. Without this, the matter wouldn’t be able to come together to form more complex things.

To explain the working of this, Peter Higgs introduced the mechanism of Higgs field. Electromagnetic field and light has photon as the fundamental components and similarly, Higgs field needs to have a quantized carrier particle called Higgs boson. It is the process that causes every particle to interact with the field and this interaction results as a mass.

Working of Higgs Mechanism?

The Higgs field is defined to be a continuum that extends throughout space, consisting of countless Higgs bosons similar to electromagnetic field consisting countless photons. The mass of the particles would be caused by interaction of these particles with the Higgs field as they pass through this ever pervasive field, so that the particles that have a greater interaction with the field have a larger mass.

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