Page 1 : ATOMS & NUCLEI, 1. Rutherford’s Alpha Scattering Experiment, 2. Distance of Closest Approach (Nuclear Size), 3. Impact Parameter, 4. Composition of Nucleus, 5. Atomic Number, Mass Number and Atomic Mass Unit, 6. Radius of the Nucleus and Nuclear Density, 7. Mass Energy Relation and Mass Defect, 8. Binding Energy and Binding Energy per Nucleon, 9. Binding Energy Curve and Inferences, 10. Nuclear Forces and Meson Theory, 11. Radioactivity and Soddy’s Displacement Law, 12. Rutherford and Soddy’s Laws of Radioactive Decay, 13. Radioactive Disintegration Constant and Half-Life Period, 14. Units of Radioactivity, 15. Nuclear Fission and Fusion

Page 3 : Alpha – particle is a nucleus of helium atom carrying a charge of ‘+2e’ and, mass equal to 4 times that of hydrogen atom. It travels with a speed nearly, 104 m/s and is highly penetrating., , Rutherford, Experiment, , Geiger &, Marsden, Experiment, , Source of, α-particle, , Radon, 222, 86Rn, , Bismuth, 214, 83Bi, , Speed of, α-particle, , 104 m/s, , 1.6 x 107 m/s, , Thickness of, Gold foil, , 10-6 m, , 2.1 x 10-7 m

Page 4 : S. No. Observation, , Conclusion, , 1, , Most of the α-particles passed, straight through the gold foil., , It indicates that most of the space, in an atom is empty., , 2, , Some of the α-particles were, scattered by only small angles,, of the order of a few degrees., , α-particles being +vely charged and, heavy compared to electron could, only be deflected by heavy and, positive region in an atom. It, indicates that the positive charges, and the most of the mass of the, atom are concentrated at the centre, called ‘nucleus’., , 3, , A few α-particles (1 in 9000), were deflected through large, angles (even greater than 90°)., , α-particles which travel towards the, nucleus directly get retarded due to, Coulomb’s force of repulsion and, ultimately comes to rest and then, fly off in the opposite direction., , Some of them even retraced, their path. i.e. angle of, deflection was 180°., , N(θ) α, , 1, sin4(θ/2)

Page 5 : Distance of Closest Approach (Nuclear size):, When the distance between α-particle, and the nucleus is equal to the distance, of the closest approach (r0), the α-particle, comes to rest., At this point or distance, the kinetic, energy of α-particle is completely, converted into electric potential energy, of the system., , ½ mu 2 =, , r0 =, , 1, , 2 Ze2, , 4πε0, , r0, , 1, , 2 Ze2, , 4πε0 ½ mu 2, , r0, , +

Page 6 : Impact Parameter (b):, The perpendicular distance of the, velocity vector of the α-particle from, the centre of the nucleus when it is, far away from the nucleus is known, as impact parameter., , u, , θ, , b, r0, , +, , Ze2 cot (θ/2), b=, , 4πε0 (½ mu 2), , i) For large value of b, cot θ/2 is large and θ, the scattering angle is small., i.e. α-particles travelling far away from the nucleus suffer small deflections., ii) For small value of b, cot θ/2 is also small and θ, the scattering angle is large., i.e. α-particles travelling close to the nucleus suffer large deflections., iii) For b = 0 i.e. α-particles directed towards the centre of the nucleus,, cot θ/2 = 0, , or, , θ/2 = 90°, , or, , θ = 180°, , The α-particles retrace their path.

Page 7 : Composition of Nucleus:, Every atomic nucleus except that of Hydrogen has two types of particles –, protons and neutrons. (Nucleus of Hydrogen contains only one proton), Proton is a fundamental particle with positive charge 1.6 x 10-19 C and, mass 1.67 x 10-27 kg (1836 times heavier than an electron)., Neutron is also a fundamental particle with no charge and, mass 1.675 x 10-27 kg (1840 times heavier than an electron)., , Atomic Number (Z):, The number of protons in a nucleus of an atom is called atomic number., , Atomic Mass Number (A):, The sum of number of protons and number of neutrons in a nucleus of an, atom is called atomic mass number., A=Z+N, , Atomic Mass Unit (amu):, Atomic Mass Unit (amu) is (1 / 12)th of mass of 1 atom of carbon., 1 amu =, , 1, 12, , x, , 12, 6.023 x, , g, 1023, , = 1.66 x 10-27 kg

Page 8 : Size of Nucleus:, Nucleus does not have a sharp or well-defined boundary., However, the radius of nucleus can be given by, R = R0 A⅓, , where R0 = 1.2 x 10-5 m is a constant which is the, same for all nuclei and, A is the mass number of the nucleus., , Radius of nucleus ranges from 1 fm to 10 fm., Nuclear Volume, V = (4/3) π R3 = (4/3) π R03 A, VαA, , Nucleus Density:, Mass of nucleus,, Nuclear Volume,, , M = A amu = A x 1.66 x 10-27 kg, V = (4/3) π R3 = (4/3) π R03 A, =, , 4, 3, , x, , 22, , x (1.2 x 10-15)3 A m3, , 7, , = 7.24 x 10-45 A m3, Nucleus Density, ρ = M / V = 2.29 x 1017 kg / m3

Page 9 : Discussion:, 1. The nuclear density does not depend upon mass number. So, all, the nuclei possess nearly the same density., 2. The nuclear density has extremely large value. Such high, densities are found in white dwarf stars which contain mainly, nuclear matter., 3. The nuclear density is not uniform throughout the nucleus. It has, maximum value at the centre and decreases gradually as we move, away from the centre of the nucleus., 4. The nuclear radius is the distance from the centre of the nucleus, at which the density of nuclear matter decreases to one-half of its, maximum value at the centre.

Page 12 : Mass Defect:, It is the difference between the rest mass of the nucleus and the sum of the, masses of the nucleons composing a nucleus is known as mass defect., ∆m = [ Zmp + (A – Z) mn ] - M, Mass defect per nucleon is called packing fraction., , Binding Energy:, It is the energy required to break up a nucleus into its constituent parts and, place them at an infinite distance from one another., , B.E = ∆m c2, Nuclear Forces:, They are the forces between p – p, p – n or n – n in the nucleus. They can be, explained by Meson Theory., There are three kinds of mesons – positive (π+), negative (π-) and neutral (π0)., π+ and π- are 273 times heavier than an electron., π0 is 264 times heavier than an electron., Nucleons (protons and neutrons) are surrounded by mesons.

Page 13 : Main points of Meson Theory:, 1. There is a continuous exchange of a meson between one nucleon and, other. This gives rise to an exchange force between them and keep, them bound., 2. Within the nucleus, a neutron is never permanently a neutron and a, proton is never permanently a proton. They keep on changing into each, other due to exchange of π-mesons., 3. The n – n forces arise due to exchange of π0 – mesons between the, neutrons., n, , → n + π0, , n + π0 → n, , (emission of π0), (absorption of π0), , 4. The p – p forces arise due to exchange of π0 – mesons between the, protons., p, , → p + π0, , p + π0 → p, , (emission of π0), (absorption of π0)

Page 14 : 5. The n – p forces arise due to exchange of π+ and π- mesons between the, nucleons., n, , → p + π-, , n + π+ → p, p, , → n + π+, , p + π- → n, , (emission of π-), (absorption of π+), (emission of π+), (absorption of π-), , 6. The time involved in such an exchange is so small that the free meson, particles cannot be detected as such., , Binding Energy per Nucleon:, It is the binding energy divided by total number of nucleons., It is denoted by B, B = B.E / Nucleon = ∆m c2 / A

Page 16 : Special Features of Binding Energy Curve, 1. Binding energy per nucleon of very light nuclides such as 1H2 is very small., 2. Initially, there is a rapid rise in the value of binding energy per nucleon., 3. Between mass numbers 4 and 20, the curve shows cyclic recurrence of, peaks corresponding to 2He4, 4Be8, 6C12, 8O16 and 10Ne20. This shows that the, B.E. per nucleon of these nuclides is greater than those of their immediate, neighbours. Each of these nuclei can be formed by adding an alpha particle, to the preceding nucleus., 4. After A = 20, there is a gradual increase in B.E. per nucleon. The maximum, value of 8.8 MeV is reached at A = 56. Therefore, Iron nucleus is the most, stable., 5. Binding energy per nucleon of nuclides having mass numbers ranging from, 40 to 120 are close to the maximum value. So, these elements are highly, stable and non-radioactive., 6. Beyond A = 120, the value decreases and falls to 7.6 MeV for Uranium., 7. Beyond A = 128, the value shows a rapid decrease. This makes elements, beyond Uranium (trans – uranium elements) quite unstable and radioactive., 8. The drooping of the curve at high mass number indicates that the nucleons, are more tightly bound and they can undergo fission to become stable., 9. The drooping of the curve at low mass numbers indicates that the nucleons, can undergo fusion to become stable.

Page 17 : Radioactivity:, Radioactivity is the phenomenon of emitting, alpha, beta and gamma radiations, spontaneously., , Soddy’s Displacement Law:, 1., , A, ZY, , 2., , A, ZY, , 3., , A, ZY, , α, β, γ, , Z-2Y, , A-4, , Z+1Y, ZY, , A, , A, , (Lower energy), , +, +, +, +, +, +, +, +, +, +, , γ, β, α, Lead Box Radioactive, substance, , Rutherford and Soddy’s Laws of Radioactive Decay:, 1. The disintegration of radioactive material is purely a random process and, it is merely a matter of chance. Which nucleus will suffer disintegration, or, decay first can not be told., 2. The rate of decay is completely independent of the physical composition, and chemical condition of the material., 3. The rate of decay is directly proportional to the quantity of material, actually present at that instant. As the decay goes on, the original material, goes on decreasing and the rate of decay consequently goes on, decreasing.

Page 19 : Radioactive Disintegration Constant (λ):, According to the laws of radioactive decay,, dN, N, , = - λ dt, , If dt = 1 second, then, dN, N, , =-λ, , Thus, λ may be defined as the relative number of atoms decaying per second., Again, since, , N = N0 e- λ t, N = N0 / e, , And if, t = 1 / λ, then, N, or, , N0, , 1, =, , e, , Thus, λ may also be defined as the reciprocal of the time when N / N0 falls to 1 / e.

Page 20 : Half – Life Period:, Half life period is the time required for the disintegration of half of the amount, of the radioactive substance originally present., If T is the half – life period, then, N, , 1, , N0, , =, , = e -λT, , 2, , (since, , N = N0 / 2), , eλT = 2, λ T = loge 2 = 0.6931, 0.6931, T=, , or, , λ=, , λ, , 0.6931, T, , Time t in which material changes from N0 to N:, t = 3.323 T log10 (N0 / N), , Number of Atoms left behind after n Half – Lives:, N = N0 (1 / 2)n, , or, , N = N0 (1 / 2)t/T

Page 21 : Units of Radioactivity:, 1. The curie (Ci): The activity of a radioactive substance is said to be one, curie if it undergoes 3.7 x 1010 disintegrations per second., 1 curie = 3.7 x 1010 disintegrations / second, 2. The rutherford (Rd): The activity of a radioactive substance is said to be, one rutherford if it undergoes 106 disintegrations per second., 1 rutherford = 106 disintegrations / second, 3. The becquerel (Bq): The activity of a radioactive substance is said to be, one becquerel if it undergoes 1 disintegration per second., 1 becquerel = 1 disintegration / second, 1 curie = 3.7 x 104 rutherford = 3.7 x 1010 becquerel, , Nuclear Fission:, Nuclear fission is defined as a type of nuclear disintegration in which a heavy, nucleus splits up into two nuclei of comparable size accompanied by a, release of a large amount of energy., 1, 0n, , + 92U235 → (92U236) → 56Ba141 + 36Kr92 +30n1 + γ (200 MeV)

Page 22 : Chain Reaction:, , Neutron (thermal) 0n1, Uranium, , 235, 92U, , Barium, , 141, 56Ba, , Krypton, , 92, 36Kr, , n = No. of fission stages, n=1, , n=2, , n=3, , N = No. of Neutrons, , N=1, , N=9, , N = 27, , N = 3n

Page 23 : Chain Reaction:, , Critical Size:, For chain reaction to occur, the, size of the fissionable material, must be above the size called, ‘critical size’., A released neutron must travel, minimum through 10 cm so that it, is properly slowed down (thermal, neutron) to cause further fission., If the size of the material is less, than the critical size, then all the, neutrons are lost., If the size is equal to the critical, size, then the no. of neutrons, produced is equal to the no. of, neutrons lost., , n=1, , n=2, , n=3, , N=1, , N=9, , N = 27, , If the size is greater than the, critical size, then the reproduction, ratio of neutrons is greater than 1, and chain reaction can occur.