Overview: Nuclei

• 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.

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).

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.

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

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'.

• 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.

• 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.

• 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.

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'.

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.

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'.

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 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. 

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).

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

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 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.

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).

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

• 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.

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

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

OR

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

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

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.

• 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.

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).

• 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.

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

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

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.

“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).

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

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. 

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'.

• 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.

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

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