Summary, Concept Map

SUMMARY

• A device used to study the conduction of electricity through gases 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

• The minimum distance between alpha particle and centre of the nucleus just before it gets reflected back by 180º is defined as distance of closest approach r0

• The impact parameter (b) (see Figure 8.12) 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_n = a₀ n²/Z

• The radius of first orbit is a₀ = ε₀h² / πme² = 0.529 Å also known as Bohr radius

• The velocity of electron in nth orbit is υ_n = 

• The fine structure constant is α = 1/137 which is a dimensionless constant

• The total energy of electron in the n^th orbit is E_n = 

• 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 which is in ground state is known as 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 ^A_ZX

• The radius of nucleus (Z > 10) of mass number A is given by R = R₀A^1/3 where R₀ = 1.2 F

• The density of nucleus ρ = 2.3×10¹⁷ kg m⁻³

• If M, m_p and m_n are masses of a nucleus ( ^A_ZX ), proton and neutron respectively , then the mass defect is ∆m = (Zm_p + Nm_n ) - M

• The binding energy of nucleus B.E = (Zm_p + Nm_n - M )c²

• The binding energy per nucleon is maximum for iron which is 8.8 MeV.

• Law of radioactive decay: N = N₀ e^-λt

• In general, after n half lives, the number of nuclei undecayed is N = ( 1/2)ⁿ N₀

• The relation between half-life and decay constant T_1/2 = ln2 / λ

• If a heavier nucleus decays into lighter nuclei, it is called nuclear fission

• If two lighter nuclei fuse to heavier nuclei, it is called nuclear fusion

• In nuclear reactors, the nuclear chain reaction is controlled. In stars, the energy generation is through nuclear fusion. 

CONCEPT MAP