Revision: Atoms and Nuclei >> Nuclei Physics (Theory) ISC (Science) ISC Class 12 CISCE

Ionization potential is defined as ionization energy per unit charge.

The minimum energy required to remove an electron from an atom in the ground state is known as binding energy or ionization energy.

One atomic mass unit (u) is defined as the 1/12^th of the mass of the isotope of carbon \[\ce{^12_6C}\].

The nuclear force is the strong attractive force between nucleons (protons and neutrons) that binds them together inside the nucleus.

A different mass unit used for expressing atomic masses is the atomic mass unit (u), defined as one-twelfth of the mass of a carbon-12 atom, called atomic mass unit.

Mathematically: 1 u = \[\frac{\text{mass of one }^{12}\mathrm{C~atom}}{12}\] = 1.660539 × 10⁻²⁷ kg

Atomic species of the same element differing in mass are called isotopes.

The nucleus of the lightest atom of hydrogen, which has a relative abundance of 99.985%, is called the proton.

A new type of neutral particle whose mass is very nearly the same as that of a proton is called neutron.

A proton or a neutron is called a nucleon.

All nuclides with the same mass number are called isobars.

Nuclides with the same neutron number but different atomic number are called isotones.

The atoms of the same element, having same atomic number Z, but different mass number A, are called isotopes.

OR

Atoms having the same atomic number (Z) but different mass numbers (A).

The atoms of different elements which have the same mass number A, but different atomic number Z, are called isobars.

The atoms having different number of protons but same number of neutrons i.e., different Z and A, but same (A-Z), are called isotones. They have different number of electrons.

A nuclear reaction is a process in which atoms collide with other atoms and lose some of their original mass.

Nuclear fission is a neutron-induced nuclear reaction in which a heavy nucleus, such as uranium-235, breaks into two intermediate-mass nuclear fragments.

Nuclear fusion is the process in which light nuclei combine to form a more tightly bound heavier nucleus, and energy is released during the process.

Because both nuclei carry a positive charge, they repel each other through electrostatic force. This repulsion is called the Coulomb barrier in the context of fusion.

Thermonuclear fusion is fusion initiated by extremely high temperature, which gives nuclei enough kinetic energy to approach one another closely.

One grey corresponds to one joule of energy absorbed per kilogram of target material. 

The difference between the sum of the masses of the nucleons constituting a nucleus and the rest-mass of the nucleus is called ‘mass defect'.

The binding energy (BE) of a nucleus is defined as the minimum energy required to separate its nucleons and place them at rest at infinite distance apart.

Binding energy per nucleon is defined as the average energy required to remove a nucleon from the nucleus to infinite distance. Higher the binding energy per nucleon, greater is the stability of the nucleus.

Stellar energy is the energy obtained continuously from the sun and the stars.

When two or more very light nuclei moving at very high speeds are fused together to form a single nucleus, then the process is known as ‘nuclear fusion’.

OR

When two or more light nuclei combine to form a heavier stable nuclide, part of the mass disappears and is converted into energy. This phenomenon is called nuclear fusion. 

An uncontrolled chain reaction is a chain reaction in which more than one neutron from each fission causes further fissions, leading to a rapid increase in reactions and a violent release of energy (as in a nuclear bomb).

A chain reaction once started in a fissionable material, will remain steady, decreases or increases, depends on a parameter known as multiplication or reproduction factor (K).

“Nuclear holocaust means large-scale destruction and devastation that would result by the use of nuclear weapons.”

A controlled chain reaction is a chain reaction in which, on average, only one neutron from each fission causes further fission, so the reaction proceeds at a steady rate (as in a nuclear reactor).

A nuclear reactor is a device in which a self-sustaining controlled chain reaction is produced in a fissionable material.

OR

Nuclear reactor is a device which works on the principle of nuclear fission by sustained chain reaction, to release nuclear energy at a constant rate.

Whenever an electron and a positron come very close to each other, they annihilate each other by combining together and two y photons (energy) are produced. This phenomenon, in which mass is converted into energy, is called 'pair-annihilation'.

The nuclei having equal number of neutrons are called ‘isotones’.

OR

Atoms having equal number of neutrons (N) and called isotones.

The atoms of an element whose nuclei have the same number of protons but different number of neutrons are called the 'isotopes' of that element.

OR

Atoms having the same atomic number but different mass numbers are called isotopes. 

Radioactivity can be induced in elements, by bombarding them with a-particles, ne1,1trons, protons etc. and is called artificial radioactivity

Decay constant of a radioactive substance is defined as the ratio of its instantaneous rate of disintegration to the number of atoms present at that time. N = N₀ e^-λt.

The method of determining the age of organic materials by measuring the amount of radioactive carbon-14 present in them.

One curie is defined as the quantity of any radioactive substance which undergoes 3. 7 × 10¹⁰ disintegrations per second.

A nuclear chain reaction is a process in which neutrons produced in one fission reaction cause further fissions, leading to a self sustaining series of nuclear reactions.

When an energetic γ-ray photon falls on a heavy substance, it is absorbed by some nucleus of the substance and its energy gives rise to the production of an electron and a positron. This phenomenon, in which energy is converted into mass, is called 'pair-production'.

Nuclear fission is a process in which a heavy nucleus, after capturing a thermal neutron (having energy 0.027 eV), splits up into two lighter nuclei of comparable masses.

OR

Nuclear fission is a disinteg.ration process, in which a heavier nucleus gets split up into two lighter nuclei, with the release of a large amount of energy.

Since very high temperatures are needed for the fusion of nuclei, the process is called a 'thermonuclear reaction', and the energy released is called as 'thermonuclear energy'.

Conversion of nucleus of one element into nucleus,of another element is called transmutation.

The nuclear transmutations represented by means of equations similar to chemical reactions are called nuclear reactions.

The nuclei which have the same number of nucleons, but different number of protons and different number of neutrons are called ‘isobars’.

OR

Elements with the same mass number (A) but with different atomic n.umbers (Z) are called isobars.

The spontaneous emission of highly penetrating radiations (a particle, f3-particle, and y-rays) from heavy elements, of atomic  weight greater than 206 is called "natural radioactivity".

The unit for measuring activity is Curie (Ci).

“The energy that is absorbed or released in a nuclear reaction is called the disintegration energy or the Q-value of the reaction.”

Exposure is defined as the amount of ionisation produced in a unit mass of dry. air at standard pressure (STP). The S.I unit of radiation dosage is called gray (Gy).

A = Z + N

Where:

• Z = atomic number = number of protons.
• N = neutron number = number of neutrons.
• A = mass number = total number of protons and neutrons.

m_p ​= 1.00727 u = 1.67262 × 10⁻²⁷ kg

m_n​ = 1.00866 u = 1.6749 × 10⁻²⁷ kg

Einstein gave the famous mass-energy equivalence relation:

Where: 

• E = energy equivalent of mass mm 
• m = mass 
• c = velocity of light in vacuum 
• c ≈ 3 × 10⁸ m s⁻¹

R = R₀​A^1/3

\[E=mc^2\]

\[\rho=\frac{3m}{4\pi R_0^3}\] (constant for all nuclei)

V ∝ A

K = \[\frac{\text{Number of neutrons present at the begining of present generation}}{\text{Number of neutrons in the begining of previous generation}}\]

\[E_{b}=\left[Zm_{\mathrm{H}}+(A-Z)m_{n}-m(_{Z}X^{A})\right]c^{2}\]

Isotopes are atoms of the same element that have the same atomic number but different mass numbers (different number of neutrons).

Same in isotopes:

• Atomic number (Z)
• Number of protons and electrons
• Electronic configuration
• Position in periodic table
• Chemical properties (nearly identical)

Different in isotopes:

• Mass number (A)
• Number of neutrons
• Physical properties

Examples: \[_1H^1and_1H^2\]

Isobars are atoms of different elements that have the same mass number but different atomic numbers.

Same in isobars:

• Mass number (A)
• Number of nucleons

Different in isobars:

• Atomic number (Z)
• Number of protons, electrons, and neutrons
• Electronic configuration
• Position in periodic table
• Chemical properties

Examples: \[_{18}Ar^{40}\mathrm{and}_{19}K^{40}\]

Isotones are atoms of different elements that have the same number of neutrons but different atomic and mass numbers.

Same in isotones:

• Number of neutrons

Different in isotones:

• Atomic number and mass number
• Number of protons and electrons
• Electronic configuration
• Position in periodic table

Examples: \[_1\mathrm{H}^3\mathrm{~and~}_2\mathrm{H}\mathrm{e}^4\]

• A nuclear reaction involves atoms colliding with other atoms and losing some of their original mass.
• Lost mass is converted into energy as per \[E=mc^2\].
• The two types of nuclear reactions used to produce energy are fission and fusion.

• Atomic mass refers to the mass of a neutral atom and includes the mass of the nucleus, orbital electrons, and their binding energies.
• The unified atomic mass unit (u) is \[\frac {1}{12}\] of the mass of one ¹²C₆ atom; the mass of a carbon-12 atom is exactly 12 u.
• The value of 1 u in kilogram is
  1 u = 1.6605 × 10⁻²⁷ kg.
• Masses of fundamental particles are expressed in u; for example: proton ≈ 1.0073 u, neutron ≈ 1.0087 u, electron ≈ 0.0005486 u.
• The energy equivalent of 1 u (using E = mc²) is
  1 u = 931.5 MeV,
  which is widely used in nuclear physics.

• Biological dose is measured in rem (roentgen equivalent man) and is equal to:
  rem = rad × RBE factor; 1 millirem = one thousandth of a rem.
• Radiation effects increase with dose: below 25 rem, no visible effects, but doses above 500 rem can cause death within a week.

• The binding energy curve is a plot of average binding energy per nucleon versus mass number (A).
• The curve has a maximum around A = 50 to 80 (about 8.5 MeV per nucleon); hence, nuclei like Fe⁵⁶ are the most stable.
• For very heavy nuclei (A > 80), the binding energy per nucleon decreases, so such nuclei, such as uranium, are less stable and may be radioactive.
• For very light nuclei (A < 20), the binding energy per nucleon is also low, so they are comparatively less stable.
• Energy is released when heavy nuclei split (nuclear fission) or when light nuclei combine (nuclear fusion) because the binding energy per nucleon increases in both cases.

• The radius of a nucleus is of the order of 10⁻¹⁵ m and is given by
  R = R₀A^1/3
  where R₀ = 1.2 × 10⁻¹⁵ m and A is the mass number.
• The nuclear radius increases with mass number, so heavier nuclei have larger radii.
• Nuclei are generally spherical in shape, with only small deviations (about 10%).
• The density of a nucleus is independent of mass number and is nearly the same for all nuclei.
• The average nuclear density is about 2 × 10¹⁷ kg m⁻³, showing that the nucleus is extremely dense.

• U²³⁵ undergoes fission by slow neutrons, forming an unstable U²³⁶ nucleus which splits into two lighter nuclei, releasing 2–3 neutrons and large energy (~200 MeV).
• The energy released per fission is about 200 MeV, due to the increase in binding energy per nucleon of the fission fragments.
• Fission of 1 g of U²³⁵ releases about 8.2 × 10¹⁰ J, which is equivalent to the explosion of about 20 tons of TNT.

• A nuclear reaction is a process in which a nucleus interacts with a particle, forming a new nucleus and one or more new particles, and is written as
  X + a → Y + b or X(a, b) Y.
• Nuclear reactions may involve emission or absorption of energy, called reaction energy or disintegration energy.
• In every nuclear reaction, charge, total number of nucleons (mass number), and total mass plus energy are conserved.

• Fast neutrons produced in fission are mostly absorbed by U²³⁸, so moderators like graphite or heavy water are used to slow them down and help continue the reaction.
• The uranium must have a minimum size (critical mass); otherwise, neutrons escape and the chain reaction stops.

• Rutherford showed that the nucleus is very small (≈10⁻¹⁵ m) and contains almost all the mass and positive charge of the atom.
• The proton–electron hypothesis suggested that the nucleus is made of protons and electrons.
• This hypothesis failed because electrons cannot exist inside the nucleus due to energy and magnetic moment problems.
• After the discovery of the neutron (1932), it was accepted that the nucleus contains protons and neutrons.
• Atomic number (Z) = number of protons, mass number (A) = protons + neutrons, and neutrons = A − Z.