Atomic and Nuclear physics

Objectives

---

• electric discharge through the gases • determination of specific charge of by an electron J.J. Thomson experiment • determination of electronic charge by Millikan’s oil drop experiment • atom models – J.J. Thomson and Rutherford • Bohr atom model and hydrogen atom • atomic spectrum and hydrogen spectrum • structure and properties of nucleus • various classification of nuclei based on atomic number and mass number • mass defect and binding energy • relation between stability and binding energy curve • alpha decay, beta decay and gamma emission • law of radioactive decay • nuclear fission and fusion • elementary ideas of nuclear reactors • qualitative idea of elementary particles

Summary

---

„ A device used to study the conduction of electricity through partical gases at low pressure is known as gas discharge tube „ Charge per unit mass is known as specific charge or normalized charge, and it is independent of gas used and also nature of electrodes used in the experiment. „ The minimum distance between alpha particle and centre of the nucleus just before it gets reflected back by 180° is defined as distance of closest approach r0 . „ The impact parameter (b) (see Figure 9.12) is defined as the perpendicular distance between the centre of the gold nucleus and the direction of velocity vector of alpha particle when it is at a large distance. „ According to Bohr atom model, angular momentum is quantized. „ The radius of the orbit in Bohr atom model is r a n Z n = 0 2 „ The radius of first orbit hydrogen atom is a h me 0 0 2 2 = =0 529 ε π . Å and it is also known as Bohr radius „ The velocity of electron in nth orbit is υ π n h ma Z n = 2 0 ms–1. „ The fine structure constant is α = 1 137 which is a dimensionless constant „ The total energy of electron in the nth orbit is E me h Z n Z n n =− =− eV 4 0 2 2 2 2 2 2 8 13 6 ε . . „ The energy required to excite an electron from the lower energy state to any higher energy state is known as excitation energy and corresponding potential supplied is known as excitation potential. „ The minimum energy required to remove an electron from an atom in the ground state is known as binding energy or ionization energy. „ The potential difference through which an electron should be accelerated to get ionization energy is known as ionization potential. „ The wavelength of spectral lines of Lyman series lies in ultra-violet region „ The wavelength of spectral lines of Balmer series lies in visible region while those of Paschen and Brackett series lie in infra-red region „ The nucleus of element X having atomic number Z and mass number A is represented by Z A X . „ The emprical relation connecting radius of nucleus (Z > 10) R and mass number A is given by R R = 0A1 3/ where R F 0 = 1 2. „ The density of nucleus ρ= × − 2 3 1017 3 . kg m , and the nuclear matter in a highly compressed state. „ If M, mp and mn are masses of a nucleus ( Z A X ), proton and neutron respectively , then the mass defect is ∆m Z = + ( ) m N p n m M „ The average binding energy of nucleus B E Zm Nm M c p n . = + ( ) − 2 „ The binding energy per nucleon is maximum for iron which is 8.8 MeV. „ Alpha decay: Z A Z A X Y → + He − − 2 4 2 4 „ β- decay: Z A Z A X Y → + + e +− 1 ν „ β+ decay: Z A Z A X Y → + − e ++ 1 ν „ Gamma emission: Z A Z A X X * → + γ „ Law of radioactive decay: N N e t = − 0 λ „ In general, after n half lives, the number of nuclei left undecayed is N N n =       1 2 0 „ The relation between half-life and decay constant is T1 2 2 0 6931 / ln . = = λ λ . „ Mean lite τ λ = 1 ; T1 2 0 6931 0 6931 / . = = . λ τ . „ If a heavier nucleus decays into lighter nuclei, it is called nuclear fission „ If two lighter nuclei fuse to form heavier nucleus, it is called nuclear fusion „ In nuclear reactors, the nuclear chain reaction is controlled. In stars, the energy generation is through nuclear fusion.