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**1. Works Related with Scientists:**

2. \(\frac{\text { massof } \mathrm{e}^{-}}{\text {mass of } \mathrm{H} \text { atom }}=\frac{1}{1837}\)

**(Speed) Anode rays < < cathode rays**

& (deflection) Anode rays < cathode rays

(e/m)_{anode rays} < < (e/m)_{cathode rays} ( due to m_{p} > m_{e})

For neutral atoms

Z = P = e & A = P + n = Z + n = e + n

**3. Some formulas Related with Bohr Model:**

\(\frac{m v^{2}}{r}=\frac{Z e^{2}}{r^{2}}\)

& mvr = \(\frac{\mathrm{nh}}{2 \pi}\) & c = υλ

& \(\bar{υ}\) = \(\frac{1}{\lambda}\) & E = hυ & E = mc^{2}

& υ = c\(\bar{υ}\)

& v = \(\frac{2 \pi \mathrm{Ze}^{2}}{\mathrm{nh}}\) = 2.188 × 10^{8}Z/n cm/sec

& r = \(\frac{n^{2} h^{2}}{4 \pi^{2} M Z e^{2}}\) = 0.529\(\left(\frac{n^{2}}{Z}\right)\)Å

E_{r} = \(\frac{-2 \pi^{2} m Z^{2} e^{4}}{n^{2} h^{2}}\) = -KE = \(\frac{\mathrm{PE}}{2}\)

= \(\frac{-Z e^{2}}{2 r}\) = K.E. + P.E. In SI unit

E_{r} = \(\frac{-2 \pi^{2} m K^{2} Z^{2} e^{4}}{n^{2} h^{2}}\)

I from E | – 21.8 × 10^{-12} Z^{2}/n^{2} erg |

II from E | – 13.6 Z^{2}/n^{2} erg |

III from E | – 313.6 Z^{2}/n^{2} Kcal |

Iv from E | – 109700 Z^{2}/n^{2} cm^{-1} |

\(\frac{E_{A}}{E_{B}}=\frac{Z_{A}^{2}}{Z_{B}^{2}} \frac{n_{B}^{2}}{n_{A}^{2}}\)

E_{1} < E_{2} < E_{3} < ……. < E_{∞} (0), (EP)_{1} < (EP)_{2} < (EP)_{3} < …….

(E_{2} – E_{1}) > (E_{3} – E_{2}) > (E_{4} – E_{3}) > ………, (SE)_{1} > (SE)_{2} > (SE)_{3} ……..

E_{1} = -13.6 eV

& E_{2} = – 3.4 eV

& E_{3} = -1.5 eV

& E_{4} = -0.85 eV

& E_{5} = -0.54 eV

R_{H} = \(\frac{2 \pi^{2} m e^{4}}{c h^{3}}\)

Total no. of spectrum line = \(\frac{n(n-1)}{2}\)

**4. Various Series of spectrum lines of H-Spectrum:**

**5. Order of wave length & Frequency of electromagnetic radiation –**

Visible zone | |

Cosmic | Rays |

γ | Rays |

x | Rays |

UV | Zone |

VR | |

IR | Zone |

Micro | Wave |

Radio | Wave |

λ↑ υ↓ E↓

**6. De Broglie Wave Equation:**

λ = h/mv = h/p

2πr = nλ & \(\frac{1}{2}\) mv^{2} = ev

& λ = \(\frac{h}{\sqrt{2 e m V}}\)

**7. Heisenberg Uncertainty Principle:**

(Δx) (Δp) ≥ h/4π

& (Δx) (Δv) ≥ h/4πm

ΔE. Δt > ≥ \(\frac{h}{4 \pi}\) (For energy & time)

& ΔΦ. Δθ ≥ \(\frac{h}{4 \pi}\) (For angular motions)

Photo electric effect:

hv = w + \(\frac{1}{2}\) mv^{2}

w = hv_{0} work function

**8. In sommer field concept:**

P_{Φ} = n_{Φ}\(\frac{h}{2 \pi}\)

& P_{r} = n_{r}\(\frac{h}{2 \pi}\)

& P = P_{r} + P_{Φ}

or n = n_{Φ} + n_{r}

\(\frac{\text { Semi major axis }}{\text { Semi minor axis }}=\frac{a}{b}=\frac{n}{\ell}\)

**9. Shrodinger wave Equation:**

Δ^{2}ψ + \(\frac{8 \pi^{2} m}{h^{2}}\)(E – V)ψ = 0

**10. In Moseleys’ experiment**

\(\sqrt{v}\) = a (Z – b) & a = \(\sqrt{\frac{3 \mathrm{R}_{\mathrm{C}}}{4}}\)

11. (a) No. of electrons in any subshell = 2(2l + 1)

(b) No. of orbitals in any subshell = (2l + 1)

(c) Orbital angular momentum of e^{–} = \(\sqrt{[}\)l(l + 1)]h/2π

(d) Spin angular momentum of e^{–} = \(\sqrt{[}\)s(s + 1)]h/2π

(e) No. of Max. electrons in any shell = 2n^{2}

(f) Max. no. of orbitals in any shell = n^{2} (valid upto n = 4)

(g) Max. no. of subshell in any shell = n

12. Nodes [(n – 1) = total nodes, t = angular nodes,

(n – L – 1) = Radial nodes, nodel plane = l]

Nodals surfaces [for s-orbitals = n – 1]

**13. Unstable Particle of atom:**

14.

15. M = \(\frac{M_{1} x+M_{2} y+M_{3} z}{x+y+z}\) & (energy) s < p < d < f & Mμ = 200 Me order of filling e^{–} in various orbitals

1s. 2s, 2p, 3s, 3p. 4s, 3d, 4p, 5s ……

16. 3^{rd} excited slate = E_{4}, 4^{th} excited state = E_{5},

3^{rd} excitation potential = E_{4} – E_{1}, 4^{th} excitation potential = E_{5} – E_{1},

3^{rd} ionisation potential = E_{∞} – E_{3}, 4^{th} ionisation potential = E_{∞} – E_{4},

3^{rd} separation energy = E_{∞} – E_{4}, 4^{th} separation energy = E_{∞} – E_{5},

**17. (i) Kernel of an atom:**

Part remained after removing the outer most orbit is known as kernel,

eg. electrons in Kernel of O → 2e^{–}, P → 10e^{–}, Li → 2e^{–}

**(ii) Core charge:**

No. of electrons in outermost orbit

eg. core charge of O → 6, Na 1, N → 5

**18. Paramagnetic Moment** = \(\sqrt{n(n+2)}\) B.M,

1 B.M. = \(\frac{\mathrm{eh}}{4 \pi \mathrm{mc}}\), n = total no. of unpaired electrons.

**19. Importance of (n – 1):**

- Excited state of electrons is always equals to (n – 1)
- According to sommerfield no. of elliptical orbit is equal to (n – 1)
- Nodal Surface = (n – 1)
- Value of l = 0 to (n – 1)
- Penultimate shell = (n – 1)

**20. Exceptions of Aufbau Principle:**

**21. (a) Atomic weight, x specific heat = 6.4\**

(b) Radius of nucleus 10^{-13} cm = 10^{-15} m

or r_{n} = 1.33 × 10^{-13} (A)^{1/3} A → Mass No.

(c) Radius of atom = 10^{-8} cm = 10^{-10} m

**22. (i) Aufbau Principle:**

According to this principle, “In the ground state, the atomic orbitals are filled in order of increasing energies”, i.e. in the ground state the electrons occupy the lowest orbitals available to them.

**(ii) Pauli’s Exclusion Principle:**

According to this principle, “No two electrons in an atom can have all the four quantum numbers n, l, m and s identical”.

**(iii) Hund’s Rule of Maximum Multiplicity:**

According to this rule “Electron filling will not take place in orbitals of same energy untill all the available orbital of a given sub shell contain one contain one electron each with parallel spin”.

**(iv) Isosters:**

Substance which have same number of electron and atoms called Isosters.

eg.

CO_{2} N_{2}O

22 22

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