Radioactivity and the Nuclear Atom, Physics tutorial

Nuclear Model of the Atom:

The protons and neutron both being components of the nucleus are termed as nucleons and their total number gives what is termed as the mass number A of the atom. The number of protons in the nucleus (as this is equivalent to the number of electrons) provides the atomic number, Z of the atom. Thus, the number of neutrons in the nucleus, N = A - Z, that is, equivalent to the difference between the mass number and the atomic number of the atom. To sum up:

Atomic number of an atom 'Z' = Number of protons or number of electrons in the atom.

Mass number of an atom 'A' = Number of nucleus in the atom (number of protons + neutrons in the nucleus).

Number of neutrons in an atom 'N' = A - Z = mass number minus atomic number.

Nuclei having similar number of protons (that is, having the similar value of Z) or similar number of neutrons (that is, the same value of N) belong to similar species and a nuclear species is termed as a nuclide. The notation zXA, here 'X' stands for the chemical symbol of the atom or the element, the subscript 'A' for the mass number and the subscript 'Z' for the atomic number of the atom.

Nuclides having the same atomic number, 'Z' (that is, having the similar number of protons) are termed as isotopes; those with the similar value of mass number 'A' (that is, having the same  number of nucleus) are termed as isobars and those with the similar value of N = A-Z (that is, having similar number of neutrons) are termed as isotopes.

Up till now, we have given the masses of protons and neutrons in kilogram. This will concern you to learn that the International Union of Pure and Applied Physics (IUPAP) decided in the year 1960 to adopt a new mass scale for the measurement of masses in the nuclear Physics. It is termed as the atomic mass scale and the atomic unit on this scale (written as amu) is 1/12 of the mass of 6C12, the most rich and the most stable isotope of carbon. It is for all time preferable to state the masses of atoms on the atomic mass scale instead of in kilogram, as it is more appropriate for the magnitude of atomic masses and is far more precise, as atomic masses can be find out very precisely relative to the carbon atom 6C12.

Now, as the mass of an atom is equivalent to its atomic weight divided by Avogadro number (6.02 x 1023), we have:

1 amu = (1/12 x 12)/(6.02 x 1023) g = 1.66 x 10-27 kg

that is almost the mass of a hydrogen atom.

In accordance with the Einstein's mass energy equation Eo = MoC2, here Eo is the energy of a resit mass Mo and C being the velocity of light in the free space = 3.0 x 108 ms-1).

Therefore, 1 amu = 1.66 x 10-27 x (3.0 x 108)2 = 1.49 x 10-10J

And as 1.602 x 10-19J = 1 eV, we have

1 amu = (1.49 x 10-10)/(1.602 x 10-19) = 9.31 x 108 eV

1 amu = (9.31 x 108)/(106) = 931 MeV

Therefore, 1 amu = (1/12) 6C12 = 1.66 x 10-27 kg = 1.49 x 10-10 J = 9.31 x 108eV = 931 MeV

The atomic mass scale is as well termed to as the isotropic mass scale and therefore the mass of an atom in amu is its isotropic mass.

Nuclear Binding Energy:

The mass 'M' of an atom can be found out directly by the mass spectrograph.  (In this, 'M' stands for the mass in kg of an individual atom).

The mass which an atom ought to encompass as an assembly of neutrons and protons and electrons can be computed, for there are Z protons (mass Mp), Z electrons (mass Me) and N = (A - Z ) neutrons (mass Mn), providing a total mass of Zmp + Zmc + NMn.

However the measured mass 'M' is less than this through a difference ΔM = (Zmp + Zmc + Nmn - M) that is termed as the mass defect.

The mass defect ΔM shows the energy ΔMc2 which would be discharged if the nucleons and the electrons were bring together, and it is thus the energy that would have to be supplied in order to dismember the atom again. Therefore the greater the value of ΔM, the greater is the stability of the atom against this type of breaking-up. An enhanced stability criterion is the mass deflect per nucleon, ΔM/A that shows the binding energy per nucleon.

Nuclear Forces:

We are familiar that a nucleus comprises of protons carrying +e charges and neutron carrying no charge, the question occurs as to what keeps the nucleus from falling apart in view of the fairly large force of repulsion among the protons. Certainly, the gravitational force of attraction between the nucleus is much too weak to hold them altogether. There should, thus be some other extremely strong force of attraction, binding the protons and neutrons so compactly altogether, quite dissimilar from the forces by which we are well-known in classical physics.

Different experiments on scattering of nuclei by one other, on collision, clearly represent that there are certainly extremely strong attractive forces that are efficient only in a very small range of the order of 10-15m. It is, thus, not a mere coincidence which the radius of a nucleus too is of the similar order (1015m). Such short range forces are termed as nuclear forces and are efficient only if two nuclei just touch one other and fall to zero as soon as they are separated.

The other important point regarding these attractive forces is that they are similar between protons and protons (p-p force), between protons and neutrons (p-n forces) and between the neutrons and neutrons (n-n forces), despite the fact that there is as well a repulsive force between protons and protons. This later force should obviously be negligible as compared to the attractive nuclear force between them. Therefore, so far as nuclear forces are concerned, neutrons and protons are one and the similar thing, the positive charge on the protons being of no effect at all. This fact is termed to as the charge-independence character of the nuclear forces.

Main Types of Radiation:

Alpha Radiation:

This is a particle, consisting of two protons and two neutrons. Therefore it consists of a mass of around 8000 times that of the electron and a charge of +3.2 x 10-19C.

Beta Radiation:

There are in fact, two B particles, the B- and the B+. The B- is the B-particle generally termed to in Nuclear Physics and it is an electron. Electrons don't in fact exist in the nucleus; however the beta particle is made and ejected from the nucleus if a neutron changes into a proton. The B+ particle (a position same mass as electron, same charge as proton) is made and ejected if a proton changes into a neutron.

Gamma Radiation:

It is a photon of electromagnetic radiation at times ejected by nuclei following beta or an alpha emission, if the nucleus adjusts its energy levels. It consists of no mass and no charge.

Radioactive Decay:

If the nucleus of a radioactive atom disintegrates, it might emit an alpha particle or a beta particle. Gamma rays might precede or follow either type of particle. If an alpha particle is emitted, the mass number 'A' reduces by 4 and the atomic number 'Z' by 2, as the positively charged alpha particle carries off two electronic units of charge, leaving the positive nuclear charge less by two electron units (that is, conservation of energy). Emitting a P-particle doesn't modify the mass number; it raises the atomic number by one, as the negatively charged B-particle carries off one electronic unit of charge, leaving the positive nuclear charge more by one electronic unit.

The disintegration of an individual nucleus is the random event. The term decay (or rate of decay) is employed for the rate at which the number 'N' of surviving nuclei in a given sample of a pure Radiative nuclide reduces by time. As the decay is random, this rate is mainly based merely on itself. The rate - dN/dt at any particular time is proportional to the number of surviving nuclei at that time. Therefore -dN/dt = λN, here λ is a constant that mainly based on the nuclide termed as the decay constant.

Integrating gives loge (N/No) = -λt, here N = No at t = 0, in such a way that at time 't':

N = No e-λt

The number of nuclei which have disintegrated at time 't' is represented by:

No - N = No (1- e-λt)

The half-life T1/2, of a radioactive nuclide is stated as the time, from the original observation, for the number of surviving nuclei to be decreased to one-half. Therefore, for N/No = 1/2 = - loge 2 = -λT1/2, and T1/2 = (loge 2)/λ = 0.693/λ

The quantity which is in reality noticed as the 'activity' is a count-rate, or the equivalent of the ionization current that provides the rate of decay - dN/dt at that instant. However dN/dt is proportional to N, therefore:

-dN/dt = - [dN/dt]o e-λt

An activity of 1 disintegration per second is 1 Bq (Becquerel) Half-lives differ from millionths of a second to thousands of millions of years. Radium 226 consists of a half-life of 1622 years, thus beginning by 1 g of pure radium, 1/2 g remains as radium after 1622 years, 1/4 g after 3244 years and so forth. The exponential decay curve, similar to that for the discharge of a capacitor via a high resistor, is used to describe the idea of half-lives.

The very first member of a series decays into a daughter product, however this in turn will probably itself decay till a stable non-decaying isotope is generated. The list of all the members of the family is termed as the radioactive series. Sometime after the production of the original source all the members of the series will be in equilibrium, that is, they will be generated from their parent at similar rate at which they are decaying, that is, N1 λ1 = N2 λ2 = N3 λ3 ........... Here N1, N2 ....are the equilibrium numbers of atoms of each and every member of the series.

Nuclear Stability:

As the chemical properties of the atom are completely regulated by the number of protons in the nucleus (that is, the atomic number Z), the stability of an atom comes out to base on both the number of protons and the number of neutrons.

For stable nuclides the given points emerge:

1) The lightest nuclides encompass nearly equivalent numbers of neutrons and protons.

2) The heavier nuclides need more neutrons than protons, the heaviest having around 50 percent more.

3) Most of the nuclides encompass both an even number of protons and an even number of neutrons. The inference is those two protons and two neutrons that is, an alpha particle, form a specific stable combination and in this connection, it is worth noting that oxygen (168O), silicon (1428Si) and iron (5628Fe) altogether account for over three quarters of the crust of earth.

For unstable nuclides the given points can be made up of:

1) Disintegrations tend to generate new nuclides closer the 'stability' line and carry on till a stable nuclide is made.

2) A nuclide over the line decays so as to give a raise in atomic number, that is, by beta emission (in which a neutron modifies to a proton and an electron). Its neutron-to-proton ratio is thus raised.

3) A nuclide beneath the line disintegrates in such a manner that its atomic number reduces and its neutron-to-proton ratio rises. In heavy nuclides this can take place by means of alpha emission.

Nuclear Fission and Fusion:

When a nucleus of big mass splits (that is, fissions) into two nuclei of smaller mass, then bearing in mind that the net number of nucleus remains constant, the net energy in the nuclei is less and the energy difference is discharged as kinetic energy of the fragment. In 235U, spontaneous fission doesn't take place, however fission can be mainly caused due to bombarding it having thermal (low energy) neutrons.

235U + 1n → X + Y + K 1n

X and Y exhibits the fission fragments whose nucleon and proton numbers are not similar values for each and every fission; 'K' is the number of neutrons discharged in the process, 'K' is not for all time similar, however the total number of protons and nucleons should be similar on both sides of the equation. 'K' is generally 2 or 3 by an average value of 2.47. The phenomenon might be written as:

313_Nuclear Fission and Fusion.jpg

These neutrons can be employed to generate further fissions, therefore producing a chain reaction that will run out of control unless the number of neutrons generated is kept under control. However, the neutrons generated in a fission reaction encompass considerable energies and are termed as the fast neutrons which don't take part in the fission 234U. The neutrons have to be slowed down to thermal energies.

Some of the different nuclei have been recognized as the result of fission, and all that can be stated is that the nucleus divides into parts having masses in the approximate ratio 5:7.

Energy can as well be generated by the fusion of two nuclei of small mass to generate a more massive nucleus example:

21H + 21H → 32He + 10n

This reaction occurs in the sun. The problem occurs in providing the very high temperatures required to give the two positive nuclei adequate kinetic energy to overcome their electrostatic repulsion.

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