By going through these CBSE Class 12 Physics Notes Chapter 13 Nuclei, students can recall all the concepts quickly.

## Nuclei Notes Class 12 Physics Chapter 13

→ Masses of all nuclei are integral multiples of hydrogen mass which suggests that all nuclei are made of hydrogen nuclei.

→ Nuclear mass is different from the mass number.

→ The mass number is the integer closest to the nuclear mass.

→ The packing fraction of a nucleus is closely related to its binding energy per nucleon.

→ Electrons and protons have an almost infinite lifetime.

→ ^{56}_{26}Fe nucleus is the most stable.

→ Neutrino is a particle that has zero charges and zero rest mass.

→ Half-life is different for different substances.

→ 3 stable isotopes of Neon are ^{20}_{10}Ne, ^{21}_{10}Ne, ^{22}_{10}Ne.

→ 1 year = 31.6 × 10^{7} s.

→ Becquerel is the S.I. unit of activity.

→ Radioactivity is independent of temperature and pressure.

→ The velocity of u-particles is less than that of P-particles, so a- particles have more ionizing power than P-particles.

→ B.E./nucleon for light nuclei is much smaller (~ 1 MeV for ^{2}_{1}H.)

→ Nuclei with A > 120 are less stable as their B.E./nucleon decreases with increasing A. So such nuclei disintegrate to produce more stable nuclei.

→ The sun radiates 3.92 × 10^{26} J of energy per second.

→ Cadmium rods are very good absorbers of neutrons.

→ Light nuclei have an equal or nearly equal number of protons and neutrons while in heavy nuclei the number of neutrons is greater than the number of protons.

→ Nuclear fusion is an uncontrolled process while nuclear fission can be controlled as in nuclear reactors.

→ Heavy water is the best moderator among heavy water, graphite, beryllium oxide, etc. commonly used as moderators.

→ The density of matter in the nucleus is 10^{14} times that of the ordinary matter,

→ The nuclear density is independent of the size of the nucleus,

→ The whole mass and charge of the atom are concentrated in a tiny nucleus.

→ The nuclear force is the fundamental force of nature and it keeps the nucleons together in spite of the repulsive forces among the protons,

→ The typical nuclear binding energy is 8 MeV per nucleon and it is about a million times larger than typical atomic binding energies.

→ Electron and positron are particle-antiparticle pairs.

→ The annihilation of an electron and a positron gives energy in the form of γ-ray. photons.

→ Electron and positron are identical in mass and have equal and opposite charges.

→ A free neutron is unstable but free proton decay is not possible.

→ Inside the nucleus, the proton and neutron are part of the nucleus and share, energy and momentum.

→ γ decay generally follows α or β emission as the nucleus is in the excited state after each α or β decay.

→ The excited nucleus comes to the ground state after γ-decay.

→ Radioactivity is a measure of the instability of the nuclei.

→ Stability requires the ratio of neutrons to protons to be around 1: 1 for light nuclei.

→ β-particles have a continuous energy spectrum while α-particles and γ-rays have a line energy spectrum.

→ The neutron to proton ratio increases to about 3: 2 for heavy nuclei.

→ In β^{–} -decay antineutrino (v^{–}) is emitted while in β^{+} decay neutrino (v) is emitted.

→ Neutrinos interact extremely weakly with matter and it is difficult even to detect them.

→ Mass and energy are interconvertible according to the relation, E = mc^{2}.

→ 1 a.m.u. = 1.66 × 10^{-27} kg = 931 MeV.

→ Chain reactions are of two types:

(a) Controlled chain reaction.

(b) Uncontrolled chain reaction.

→ The atomic bomb is based on an uncontrolled chain reaction.

→ A reactor is based on a controlled chain reaction.

→ The controlled chain reaction is obtained by slowing down the fast neutrons given out in the fission process

→ A moderator should not be gas and have a small mass number.

→ Nuclei having A > 230 undergo nuclear fission by absorbing a slow neutron.

→ 200 MeV energy is liberated due to the fission of one ^{235}_{92}U and is distributed as follows:

(a) 170 MeV as K.E. of fission fragments.

(b) 6 MeV as K.E. of fission neutrons.

(c) 24 MeV as the energy of γ-ray, β-ray, and antineutrinos.

→ The rate of disintegration is independent of temperature, pressure, electric and magnetic field.

→ The energy released in the fusion of ^{4}_{2}He atom is much less than that in the fission of one atom of ^{235}_{92}U but the energy released per nucleon in nuclear fusion is much greater than the energy released per nucleon in nuclear fission.

→ For the separation of one fermi, the nuclear force is nearly 35 times the electrical repulsion between two protons.

→ The hydrogen bomb is based upon nuclear fusion.

→ Radioactivity was discovered by Henry Becquerel.

→ All elements with atomic no. > 82 are naturally radioactive.

→ Uranium-lead dating is used to know the age of the earth.

→ Carbon dating is used to estimate the time that has elapsed after the death of a once-living organism.

→ The activity of radioactive material has been shown to be the result of three different kinds of emanations called α, β, and γ-radiations or rays.

→ Radioactivity is one kind of manifestation of instability.

→ Nuclear forces are the strongest attractive force between nucleons.

→ B.E./nucleon is maximum for ^{56}_{26}F and is 8.8 MeV.

→ Radioactivity: It is the spontaneous disintegration of the atoms of heavy elements with the emission of α, β, particles, and γ-rays.

→ Half-Life period: It is defined as the time after which the number of atoms of the radioactive sample left is one-half of that at the start.

→ Mean life: It is the ratio of the sum of life limes of all atoms to the total number of atoms

Or

It is the time after which the no. of nuclei fall to \(\frac{1}{e}\) (= 37 %) times the initial value.

→ The activity of radioactive material: It is defined as the rate of disintegration per second.

i.e., A or R = – \(\frac{\mathrm{dN}}{\mathrm{dt}}\) = λ.N.

→ 1 Curie in the older SI unit and = 3.7 × 10^{10} disintegrations per second (dps)

→ 1 becquerel = 1 DPS.

→ Isotopes: They are the atoms of an element whose nuclei have the same Z but different A.

→ Isobars: They are atoms of different elements having the same A but different Z.

→ Isotones: The atoms of different elements having the same number of neutrons are called isotones.

→ Isomers: They are identical atoms whose nucleons are in different energy states.

→ B.E./nucleon: It is the amount of energy required to extract one nucleon from the nucleus.

→ Radioisotope: It is an element that is made radioactive artificially.

→ 1 a.m.u.: It is defined as \(\frac{1}{12}\)th of the mass of one ^{12}_{6}C atom.

∴ 1 a.m. u. = 1.66 × 10^{-27}kg.

→ Moderators: They are the materials used for slowing down the last neutrons.

→ Thermal neutrons: They are the neutrons having energy 0.025 eV.

→ Stellar Energy: It is defined as the energy obtained continuously from the sun and the star.

→ Nuclear Holocaust is the name given to the large-scale destruction and devastation that would be caused by the use of nuclear weapons.

→ Radioisotopes of an element: They are the isotopes of an element capable of emitting radiation just as radioactive elements do.

→ Criticize: The ^{235}_{92}U block is said to be of critical size if the rate of loss of neutrons is equal to the rate of production of neutrons per second.

→ Critical Mass: It is defined as the mass of ^{235}_{92}U blocks of critical size.

**Important Formulae**

→ A = Z + n where A = mass number, Z = atomic number, n = number of neutrons.

→ Mass defect is given by

Δm = [Zm_{p} + (A – Z) m_{n} – m_{N} (^{A}_{Z}χ)]

→ m(^{A}_{Z}χ) = m_{n}(^{A}_{Z}χ) + Zm_{N}.

where (^{A}_{Z}χ) is the mass of the atom, mN (^{A}_{Z}χ) is the mass of the nucleus

→ T_{1/2} = \(\frac{0.693}{\lambda}\)

→ T_{a} = \(\frac{1}{λ}\) = \(\frac{\mathrm{T}_{1 / 2}}{0.693}\) = 1.44 T_{1/2}

where λ is the decay constant, T_{a} = average life of the radioactive substance.

→ E = \(\frac{A-4}{A}\)Q, where E is the K.E. of the α-particle.

→ B.E./nucleon = B.E./A

→ Packing fraction = \(\frac{\Delta \mathrm{m}}{\mathrm{A}}\)

→ B.E. = Δm × 931 MeV.

→ \(\frac{\mathrm{N}}{\mathrm{N}_{0}}=\left(\frac{1}{2}\right)^{n}=\left(\frac{1}{2}\right)^{\mathrm{T}_{\frac{1}{2}}}\)

→ Average atomic mass of an atom having isotopes with abundances x1 in and atomic mass y1 is given by

A = \(\frac{\sum_{i=1}^{n} x_{i} \cdot y_{1}}{\sum_{i} x_{i}}=\frac{\sum_{i=1}^{n} x_{i} \cdot y_{i}}{100}\)

→ Nuclear Radius, R = R_{o} A_{1/3} , where R_{0} = 1.1 × 10^{-15} m.

→ Nuclear density = \(\frac{\text { mass of nucleus }}{\text { Volume of nucleus }}\)

i.e., ρ = \(\frac{\mathrm{m}}{\frac{4}{3} \pi \mathrm{R}^{3}}=\frac{\mathrm{m}}{\frac{4}{3} \pi \mathrm{R}_{0}^{3} \mathrm{~A}}\)

→ Q-value of a nuclear reaction is given by

Q = (Σ mass of reactants – Σ mass of products) a.m.u.

= (Σ mass of reactants – Σ mass of products) × 931 MeV

→ P.E. of two charged particles is given by

U = \(\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q_{1} q_{2}}{r}\)

→ Height of Potential barrier = K. E. = U = \(\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q_{1} q_{2}}{r}\)

→ Density of nucleus is, ρ = \(\frac{\text { mass of nucleus }}{\text { Volume of nucleus }}\)

→ Nuclear charge = 2e.

→ α-decay is represented as:

_{Z}^{A}X → _{Z-2}^{A-4}Y+ ^{4}_{2}He + Q

→ β-decay is represented as

_{A}^{Z}X → _{Z+1}^{A}Y + ^{4}_{2}He + v^{–} + Q

→ 1 MeV = 1.6 ×10^{-13} .

→ 1 rd = 10^{6} dps where rd (= rutherford) is the unit of activity

→ The ratio of two nuclear radii of two nuclei having mass numlwrs A_{1} and A_{2} is given by

\(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}=\left(\frac{\mathrm{A}_{1}}{\mathrm{~A}_{2}}\right)^{\frac{1}{3}}\)

→ Activity = A = R = \(\frac{\mathrm{d} \mathrm{N}}{\mathrm{dt}}\) = – λN

or

[A] = λN = \(\frac{0.693}{\mathrm{~T}_{\frac{1}{2}}}\) N

i.e. more is the half life of the radioactive substance, lesser is its activity and vice-versa.

→ Number of fissions taking place in 1 second is given by

n = \(\frac{\text { Power }}{\text { energy per fission }}=\frac{P}{Q}\)

→ m = m_{0} e^{-λt}

→ P = P_{0} e^{-λt}

→ Mass number, no. of atoms and atomic weights of two isotopes are related as:

M_{1} = N_{1}A_{1} and M_{2} = N_{2}A_{2}

∴ \(\frac{\mathrm{M}_{1}}{\mathrm{M}_{2}}=\left(\frac{\mathrm{N}_{1}}{\mathrm{~N}_{2}}\right) \cdot\left(\frac{\mathrm{A}_{1}}{\mathrm{~A}_{2}}\right)\)