Title 22. Nuclear Physics.pdf ✅

Nuclear Physics 487 22 Nuclear Physics QUICK LOOK Radioactivity refers to the particles which are emitted from nuclei as a result of nuclear instability. Because the nucleus experiences the intense conflict between the two strongest forces in nature, it should not be surprising that there are many nuclear isotopes which are unstable and emit some kind of radiation. The most common types of radiation are called alpha, beta, and gamma radiation, but there are several other varieties of radioactive decay, There are three primary types of radiation: Alpha: the nucleus releases an alpha particle (a helium-4 nucleus) consisting of two neutrons and two protons; these are fast moving helium atoms. They have high energy, typically in the MeV range, but due to their large mass, they are stopped by just a few inches of air, or a piece of paper. Beta: the nucleus ejects an electron (or a positron). Note: this is not the same as an electron being removed from orbital’s around the nucleus; these are fast moving electrons. They typically have energies in the range of a few hundred keV to several MeV. Since electrons are might lighter than helium atoms, they are able to penetrate further, through several feet of air, or several millimeters of plastic or less of very light metals. Gamma: the protons and neutrons within the nucleus rearrange into a more stable form, and energy is emitted as a gamma ray.; these are photons, just like light, except of much higher energy, typically from several keV to several MeV. X-Rays and gamma rays are really the same thing, the difference is how they were produced. Nucleus consists of protons and neutrons. The number of electrons in every nucleus is zero. Proton was discovered by Rutherford and neutron by Chadwick. Nuclear density is nearly 1017 kg/m3 and is independent of mass number of nucleus. Mass number of nucleus A N Z = + where N = neutron number; Z = proton number. Radius of nucleus 1/3 R R A = 0 where 5 0R 1.2 10− = × m = 1.2 Fermi Size of nucleus is of the order of 10–14 m, Nuclear density : E = 1017 kg/m 3 (independent of mass number) 1 amu = 1.66 × 10–27 kg = 931 MeV Mass defect, ( ) ( , ) ∆ = + − − m Zm A Z m M Z A p n Packing fraction mass defect , mass number f = M A f A − = where M = mass of nucleus, A = mass number Binding Energy: Nuclear binding energy is the energy required to break up the nucleus into its separate nucleons OR this can be expressed as the energy released when the nucleus is formed from separate nucleons. Binding energy is equal to the decrease in potential nuclear energy of the nucleons when they come together. Binding energy is the energy associated with the strong force that holds the nucleons together. Figure: 22.3 Magnetic field B Beta emission is referentially in the direction Opposite the Nuclear spin, in Violation of conservation of parity. Wu, 1957 60Co 60 60 Co Ni e ve → + + − I Nuclear spin e – Figure: 22.2 Radioactive Source γ (gamma) α (alpha) β (beta) Figure: 22.1 Electric Nuclear N N α β γ N N N N N N N N

Nuclear Physics 489 Figure 22.7: Schematic of a Nuclear Power Plant Heat Pump Backup cooling water Pressurizing system Control rods Fuel Rods Fuel elements Hot water Containment building primary loop Heat Pump Water Steam Reactor generator vessel Secondary loop Generator Electricity Turbine Cool Pump Pump Cooling towers Pump Condenser Cadmium and boron-steel rods are used as controller in nuclear reactor. Dose: 2 R A k Ck t D d = R k = does rate from diagram C = strength of source d = distance A k = fraction penetrating a radiation shield Laws of Radioactive Disintegration: The no. of atoms present in the radioactive substance depends upon the rate of disintegration. dN N dt − ∝ (– sing is for disintegration) dN N dt = −λ where λ is decay constant 0 log log e e N t N = − + λ 0 loge N t N = −λ 0 N t e N −λ = ⇒ 0 t N N e−λ = Half Life: half life of a radioactive substance is defined as the time period during which half of the no. of atoms of the substance remains un-decayed. If 0 2 N N = and 1/ 2 t t = 0 1/ 2 0 2 N t N e−λ = 1/ 2 2 ; t e λ = 1/ 2 log 2 ; e = λt 1/ 2 0.693 = λt ; 1/ 2 1/ 2 0.693 t T 0.693τ λ = = = 1/ 2 1/ 2 0.693 0 0 0 0 2 t t t T T t N N N N e N e λ τ θ − − − = = = = Mean Lifetime: The decay of particles is commonly expressed in terms of half-life, decay constant or mean lifetime. The probability for decay can be expressed as a distribution function ( ) t decay f t Ne−λ = where λ is called the decay constant. The average survival time is then the mean value of time using this probability function. The integral becomes: can be integrated by parts 0 1 0 x x t xe e dx τ λ ∞ − − ∞ 〈 〉 = = − = −∫ 0 1 1 0 x e λ λ ∞ − = + − =     1 1/ 2 1/ 2 ln 2 0.693 T T τ λ = = ≈ The Mean Life and "probability per second" Figure: 22.8 Amount remaining Probability, or amount of daughter present Time 100 % 100 % T1/ 2 τ 1 τ Time 1/τ
490 Quick Revision NCERT-PHYSICS MULTIPLE CHOICE QUESTIONS Radioactivity 1. In a radioactive substance at t = 0, the number of atoms is 4 8 10 . × Its half life period is 3 years. The number of atoms 4 1 10 × will remain after interval: a. 9 yearss b. 8 years c. 6 years d. 24 years 2. During a negative beta decay: a. An atomic electron is ejected b. An electron which is already present within the nucleus is ejected c. A neutron in the nucleus decays emitting an electron d. A part of the binding energy is converted into electron 3. What percentage of original radioactive atoms is left after five half lives: a. 0.3% b. 1% c. 31% d. 3.125% 4. Half life of 210 Bi is 5 days. If we start with 50,000 atoms of this isotope, the number of atoms left over after 10 days is: a. 5,000 b. 25,000 c. 12,500 d. 20,000 5. The radioactivity of a certain radioactive element drops to 1/64 of its initial value in 30 seconds. Its half life is: a. 2 seconds b. 4 seconds c. 5 seconds d. 6 seconds 6. The average life T and the decay constant λ of a radioactive nucleus are related as: a. Tλ =1 b. 0.693 T λ = c. 1 T λ = d. λ c T = 7. The half life of a radioactive element which has only 1 32 of its original mass left after a lapse of 60 days is: a. 12 days b. 32 days c. 60 days d. 64 days 8. A radioactive nucleus undergoes a series of decay according to the scheme A A A A A 1 2 3 4 → → → → α β α γ If the mass number and atomic number of A are 180 and 72 respectively, then what are these number for A4? a. 172 and 69 b. 174 and 70 c.176 and 69 d.176 and 70 9. The decay constant of radium is 4 4.28 10− × per year. Its half life will be: a. 2000 years b. 1240 years c. 63 years d. 1620 years 10. Atomic mass number of an element thorium is 232 and its atomic number is 90. The end product of this radioactive element is an isotope of lead (atomic mass 208 and atomic number 82). The number of alpha and beta particles emitted is: a. α β = = 3, 3 b. α β = = 6, 4 c. βα == 0,6 d. α β = = 4, 6 11. A radio-isotope has a half- life of 5 years. The fraction of the atoms of this material that would decay in 15 years will be: a. 1/8 b. 2/3 c. 7/8 d. 5/8 12. Three α − particles and one β − particle decaying takes place in series from an isotope 238 88Ra . Finally the isotope obtained will be: a. 220 84 X b. 222 86 X c. 224 83 X d. 215 83 X 13. The half life of polonium is 140 days. After how many days, 16 gm polonium will be reduced to 1 gm (or 15g will decay) a. 700 days b. 280 days c. 560 days d. 420 days 14. A radioactive element emits 200 particles per second. After three hours 25 particles per second are emitted. The half life period of element will be: a. 50 minutes b. 60 minutes c. 70 minutes d. 80 minutes 15. The half life of the isotope 24 11Na is 15 hrs. How much time does it take for 7 8 th of a sample of this isotope to decay? a. 75 hrs b. 65 hrs c. 55 hrs d. 45 hrs 16. If 20 gm of a radioactive substance due to radioactive decay reduces to 10 gm in 4 minutes, then in what time 80 gm of the same substance will reduce to 10 gm? a. In 8 minutes b. In 12 minutes c. In 16 minutes d. In 20 minutes