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CBSE Class 12th Physics Notes: Nuclei (Part – I)

Get CBSE Class 12th Physics Notes on Nuclei. These notes are important for coming CBSE class 12th board exam 2017.

Jan 30, 2017 11:50 IST
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Class 12th Physics Chapter Wise notes on Nuclei are available in this article. These notes are based on latest CBSE Class 12 Physics Syllabus 2017 and important for coming CBSE board exam 2017.

The topics covered in these notes are given below

Atomic Masses

Discovery of Neutron

Basic Properties of Neutron

Composition of Nucleus

Size of the Nucleus

Nuclear Density

Mass – Energy Equivalence

Size of the Nucleus

Isotopes

Isobars

Isotones

Energy Equivalence of One Atomic Mass Unit

Nuclear binding energy

Mass Defect

Binding Energy

Binding Energy per Nucleon

Binding Energy Curve and its Features

Nuclear Force

The notes of the chapter are given below

Atomic Masses

The mass of an atom is extremely small. It means the mass of a carbon atom 12C is about 1.99 × 10‒26 kg. So, kilogram is not a convenient unit to measure such small mass. A different mass unit (atomic mass unit) is used for expressing atomic masses this is known as atomic mass unit.

This unit is the atomic mass unit (u), defined as 1/12th of the mass of carbon (12C) atom.

1 a.m.u. = 1.66 × 10‒27 kg

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Discovery of Neutron

In 1932 by James Chadwick observed emission of neutral radiation when beryllium nuclei were bombarded with alpha-particles (or helium nuclei).

It was found that this neutral radiation could knock out protons from light nuclei such as those of helium, carbon and nitrogen. The only neutral radiation known at that time was photons (electromagnetic radiation).

Application of the principles of conservation of energy and momentum showed that if the neutral radiation consisted of photons, the energy of photons would have to be much higher than is available from the bombardment of beryllium nuclei with α-particles.

This phenomenon can be explained by assuming that the neutral radiation consists of a new type of neutral particles called neutrons.

Basic Properties of Neutron

mn = 1.00866 u = 1.6749 × 10‒27 kg

• A free neutron, unlike a free proton, is unstable.

• It decays into a proton, an electron and a antineutrino (another elementary particle), and has a mean life of about 1000s. It is, however, stable inside the nucleus.

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Composition of Nucleus

The composition of a nucleus can now be described using the following terms and symbols:

Z - atomic number = number of protons

N - neutron number = number of neutrons

A - mass number = Z + N = total number of protons and neutrons

One also uses the term nucleon for a proton or a neutron.

Number of nucleons in an atom is its mass number A.

Nuclear species or nuclides are shown by the notation where X is the chemical symbol of the species.

For example, the nucleus of gold is denoted by  It contains 197 nucleons, of which 79 are protons and the rest 118 are neutrons.

Size of the Nucleus

It has been found that a nucleus of mass number A has a radius R = Ro A1/3

Where, Ro = 1.2 × 10‒15 m.

This means the volume of the nucleus, which is proportional to R3 is proportional to A.

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Nuclear Density

The density of nucleus is a constant, independent of A, for all nuclei. The density of nuclear matter is approximately 2.3 × 1017 kg m–3.

Mass – Energy Equivalence

Einstein showed from his theory of special relativity that it is necessary to treat mass as another form of energy.

Einstein gave the famous mass-energy equivalence relation E = m c2.

Here the energy equivalent of mass m is related by the above equation and c is the velocity of light in vacuum and is approximately equal to 3×108 m s–1.

Size of the Nucleus

By performing scattering experiments in which fast electrons, instead of α-particles, are projectiles that bombard targets made up of various elements, the sizes of nuclei of various elements have been accurately measured.

It has been found that a nucleus of mass number A has a radius then, R = Ro A1/3

Where Ro = 1.2 × 10–15 m

This means the volume of the nucleus (which is proportional to R3) is proportional to A. So the density of nucleus is a constant and independent of A.

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Isotopes

The nuclei of isotopes of a given element contain the same number of protons, but differ from each other in their number of neutrons.

Isobars

All nuclides with same mass number are called isobars.

Isotones

Nuclei of different atom containing same number of neutrons are called isotones.

Energy Equivalence of One Atomic Mass Unit

1 a.m.u. represents the average mass of a nucleon and 1 a.m.u. = 931.25 eV.

Nuclear binding energy

The nucleus is made up of neutrons and protons so, it may be expected that the mass of the nucleus is equal to the total mass of its individual protons and neutrons. However, the nuclear mass is found to be always less than this.

For example, the nucleus of an oxygen atom (16O8) has 8 neutrons and 8 protons

So,

Mass of 8 neutrons = 8 × 1.00866 u,

Mass of 8 protons = 8 × 1.00727 u,

Mass of 8 electrons = 8 × 0.00055 u

Therefore the expected mass of 16O8 nucleus is 8 × 2.01593 u = 16.12744 u

But, the atomic mass of 16O8 found from mass spectroscopy experiments is seen to be 15.99493 u.

Mass Defect

It is the difference between the sum of the masses of protons and neutrons forming a nucleus and actual mass of the nucleus.

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Binding Energy

As, some mass disappears in the formation of a nucleus in the form of mass defect. This loss in mass reappears in the form of energy called binding energy.

In other words, binding energy is the energy which should be supplied to the nucleus in order to break it up into its constituent particles.

Formulas for Binding Energy

Binding Energy per Nucleon

It is the ratio of the binding energy of a nucleus to the number of the nucleons.

Binding energy per nucleon = (Total binding energy)/(Number of nucleon)

Binding Energy Curve and its Features

Binding energy per nucleon as the average energy per nucleon needed to separate a nucleus into its individual nucleons.

Binding energy curve is a plot of the binding energy per nucleon versus the mass number for large nuclei.

Binding Energy Curve

The main features of his curve are give below:

(i) The binding energy per nucleon (Ebn) is practically constant, i.e. practically independent of the atomic number for nuclei of middle mass number ( 30 < A < 170). The curve has a maximum of about 8.75 MeV for A = 56 and has a value of 7.6 MeV for A = 238.

(ii) Binding energy per nucleon is lower for both light nuclei (A<30) and heavy nuclei (A>170).

From above two observations we can draw the conclusions given below:

(a) The force is attractive and sufficiently strong to produce a binding energy of a few MeV per nucleon.

(b) The constancy of the binding energy in the range 30 < A < 170 is a consequence of the fact that the nuclear force is short-ranged.

(c)A very heavy nucleus, say A = 240, has lower binding energy per nucleon compared to that of a nucleus with A = 120. Thus if a nucleus A = 240 breaks into two A = 120 nuclei, nucleons get more tightly bound. This implies energy would be released in the process.

(d) Consider two very light nuclei (A ≤ 10) joining to form a heavier nucleus. The binding energy per nucleon of the fused heavier nuclei is more than the binding energy per nucleon of the lighter nuclei. This means that the final system is more tightly bound than the initial system. Again energy would be released in such a process of fusion. This is the energy source of the sun.

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Nuclear Force

Previously, we have studied that for average mass nuclei the binding energy per nucleon is approximately 8 MeV, which is much larger than the binding energy in atoms.

Therefore, to bind a nucleus together there must be a strong attractive force of a totally different kind.

This force is nuclear force (strongest force in nature). It is strong enough to overcome the repulsion between the (positively charged) protons and to bind both protons and neutrons into the tiny nuclear volume.

Some important features of the nuclear binding force are given below:

(i) The nuclear force is much stronger than the Coulomb force acting between charges or the gravitational forces between masses. The nuclear binding force has to dominate over the Coulomb repulsive force between protons inside the nucleus. This happens only because the nuclear force is much stronger than the coulomb force. The gravitational force is much weaker than even Coulomb force.

(ii) The nuclear force between two nucleons falls rapidly to zero as their distance is more than a few femtometres. This leads to saturation of forces in a medium or a large-sized nucleus, which is the reason for the constancy of the binding energy per nucleon. A rough plot of the potential energy between two nucleons as a function of distance is shown in the figure given below. The potential energy is a minimum at a distance r of about 0.8 fm. This means that the force is attractive for distances larger than 0.8 fm and repulsive if they are separated by distances less than 0.8 fm.

Potential Energy of a Pair of Nucleon as a Function of their Separation

(iii) The nuclear force between neutron-neutron, proton-neutron and proton-proton is approximately the same. The nuclear force does not depend on the electric charge.

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