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### Atomic Structure - Important Points for competetive exams

1. Distance of closest approach: It is the distance from which the nucleus of an atom, the alpha particle comes to rest and its kinetic energy is totally converted  into electrostatic potential energy. It is denoted by ro.

ro = (1/4πεₒ)*[(2ze²)/(1/2)*(V²m)]

2. Diameter of atom: 10⁻¹⁰ meter

3. Diameter of Nucleus: 10⁻¹⁴ meter

4. Impact Parameter(b):  (1/4πεₒ)*[(ze²tan𝜃)/(1/2)*(U²m)]; U is velocity of alpha particle

5. Impact Parameter(b) is inversely proportional to the angle of scattering(𝜃).

6. The equation mvr =n*(h/2π) is called "Bohrs quantisation condition".

7. The equation h𝝂=Ei-Ef is called "Bohr's Frequency condition".

8. Bohr's Radius r = (n²h²εₒ)/πme²

9. Velocity of electron (V) = e²/2nhεₒ

10. If 'C' is velocity of light; V = [(1/4πεₒ)*(2πe²/Ch)]*(C/n)

11. The factor [(1/4πεₒ)*(2πe²/Ch)] is called fine structure constant. It is denoted by '𝛼'

12. The value of 𝛼=1/137; V = (1/137)*(C/n)

13. Energy of electron En = -(1/4πεₒ)²*(2π²me⁴/n²h²)

14. An electron can have only some definite values of energy while revolving in the orbits n=1,2,3,..... It is called energy quantization.

15. Energy Quantization:

E1 = -(1/4πεₒ)²*(2π²me⁴/n²h²) ;
E2 = (1/4)*E1
E3 = (1/9)*E1   ............................E = 0

E = -13.6/n²

16. Rydberg's constant for Hydrogen (RH) is (1/4πεₒ)²*(2π²me⁴/ch³). Its value is 1.09678 x 10⁷m⁻¹

17. Value of (1/4πεₒ) is 9x10⁹ C²N⁻¹m⁻².

18. The charge 'e' of the electron is measured by Millikan's Oil drop method.

19. The ratio of charge to mass(e/m) for an electron is measured by "Thomson".

20. Mass of electron(m) = 9.1 x 10⁻³¹ Kg

21. Mass of Proton is 1835 times that of mass of electron.

22. Canal Rays or Positive Rays are discovered by "E. Goldstein". Wien observed that these rays can be deflected in magnetic field and hence they are called Positive Rays.

23. Rest mass energy of electron is 931 MeV

24. Orbital frequency of electron is (1/T) = (V/2πr)

25. Ionization energy of a Hydrogen atom is 13.6 eV

26. The excitation energy required by the electron to excite from state n1 to state n2 is En₂-En

Spectral series of Hydrogen atom

27. Lyman series lie in Ultravoilet region.

28. Balmer series lie in near UV region and visible region.

29. Paschen series lie in infrared region.

30. Brackett series also lie in infrared region.

31. Pfund series also lie in far infrared region.

(1/) = R[(1/nf²)-(1/ni²)]

In addition to the above, nf=6, Humprey series results.

32. Velocity of an electron is independent of its mass.

33. Velocity of an electron is inversely proportional to the orbit.

34. The electron in the inner most orbit has highest velocity.

35. Velocity of a electron is independent of its mass.

36. Orbital frequency is inversely proportional to the cube of 'n' i.e. 𝜈∝(1/n³).

37. If Ep & Ek represents Potential & Kinetic energies of the orbital electron, then Ek = -Ep/2.

38. When a Hydrogen atom is raised from the ground state to an excited state both kinetic energy and potential energy decrease.E∝(1/n²).

39. The energy difference between two consecutive energy levels decreases as the quantum number 'n' increases.

40. Bohr used conservation of angular momentum to explain his theory.

41. The velocity of an electron in the ground state is e²/2hεₒ = 2 x 10⁶ m/sec

42. The ground state energy of Hydrogen atom is -13.6 eV. The energy needed to ionise the Hydrogen atom from its second excited state is 1.51 eV.

43. According to Bohr's principle, the relation between principle quantum number(n) and radius of orbit is  r ∝ n²