Electronic Structure of Atoms

1. Electronic Structure of Atoms Chapter 6 BLB 12th

2. The Periodic Table: the key to electronic structure

3. Expectations • Work with wavelength, frequency, and energy of electromagnetic radiation. • Know the order (energy and wavelength) of the regions in the electromagnetic spectrum. • Interpret line spectra of elements (lab). • Understand electronic structure. • Quantum numbers • Orbitals • Electron configurations

4. 6.1 The Wave Nature of Light • Electromagnetic Radiation • A form of energy • Light, heat, microwaves, radio waves • Speed of light in a vacuum: c = 2.9979 x 108 m/s • Wave characteristics • Wavelength (λ) in m or nm • Frequency (ν) in s-1 or Hz • Velocity (c) in m/s • Amplitude – height of a wave • Node – point where amplitude equals zero

5. Electromagnetic Spectrum

6. Electromagnetic Spectrum

7. Relating Wavelength and Frequency • All light travels at the same velocity: • As λ↑, ν↓. • Electromagnetic spectrum (Fig. 6.4, p. 209) • Arranged by wavelength and frequency • Visible portion: 350 – 760 nm • Know order of spectrum!

8. Calculate the wavelength (in nm) for light with a frequency of 5.50 x 1014 s-1.

9. 6.2 Quantized Energy and Photons • Matter (atoms) and energy (light) were thought to be unrelated until 1900. • Matter – consists of particles with mass and position • Energy (waves) – massless with uncertain position • 3 problems: • Emission of light from hot objects (blackbody radiation) • Emission of electrons from a metal surfaces on which light shines (photoelectric effect) • Emission of light from electronically excited gas atoms (emission spectra)

10. What do these have in common? Color and intensity of light are temperature dependent. Different colors of light are produced by each gaseous element.

11. Quantized Energy • Max Planck (1900) – postulated that energy of matter is quantized, that is, occurs only in certain discrete units of energy • Equantum = hνh = 6.626 x 10-34 J·s (Planck’s constant) • E = nhνn = an integer • Quantized – restricted to certain quantities • Quantum – fixed amount

12. Quantized Energy • Einstein (1905) – explained that electro-magnetic radiation is quantized • Assumed light consists of tiny energy packets called photons that behave like particles!?! • Ephoton = hν • Some types of light have more energy than other types. • Energy ⇐ ? ⇒ Matter

13. Photoelectric Effect

14. Molybdenum requires a photon with a frequency of 4.41 x 1015 s-1 to emit electrons. Calculate (a) the energy of one photon and (b) of one mole of photons.

15. 6.3 Line Spectra and the Bohr Model • Spectrum – radiation separated into different wavelengths • Continuous – light of all wavelengths • Line – contains only specific wavelengths • Different gases produce different line spectra.

16. Continuous Spectrum

17. Atomic Line Spectra

18. Rydberg Equation ↑ RH • niandnf are integers; ni>nf for emission • Used to calculate the wavelengths of the lines in the line spectrum of hydrogen

19. Bohr Model of the Atom Postulates: • Orbits have certain radii, which correspond to certain energy levels. • An electron in an orbit has a specified energy. • Energy is only emitted and absorbed by an electron as it moves from one energy state to another.

20. Energy States of the Hydrogen Atom • Bohr calculated the energy of each orbit. • n is an integer (1…∞); the principal quantum number • Ground state (n = 1) – lowest energy state • Excited state – higher energy state • Energy values are negative, indicating stability from the electron-nucleus attraction.

21. Electronic Transitions • Ultraviolet (Lyman) • ni→ nf = 1 • Visible (Balmer) • ni→ nf = 2 • Infrared (Paschen) • ni→ nf = 3

22. Electronic Transitions:

23. e- transition practice Calculate the wavelength, energy, and frequency for an electron transition from n = 5 to n = 3.

24. Limitations of the Bohr Model • Offered an explanation of the hydrogen atom, but failed for other atoms. • The electron does not orbit about the nucleus. But, • Electrons do exist in energy levels. • Energy is involved in moving an electron between energy levels.

25. 6.4 The Wave Behavior of Matter • Louis de Broglie (1923) – discovered the relationship between a particle’s mass and wavelength • Diffraction of x-rays and electrons • Tiny particles like electrons have wave-like properties!?! • Sample Exercise 6.5: λ = 1.22 x 10-10 m v – velocity (m/s) m – mass (kg)

26. Heisenberg Uncertainty Principle • It is impossible to know both the position and momentum of a particle at a given time. • Heisenberg may have been here! • Enter quantum mechanics, a way to deal with both the wavelike and particle-like behavior of the electron.

27. 6.5 Quantum Mechanics and Atomic Orbitals • Quantum (or wave) mechanics • Schrödinger solved an equation. • Treated electron as wave • Solved for energy of the wave • Mathematical solution gives the size and shape of a wave function or orbital.

28. 6.5 Quantum Mechanics and Atomic Orbitals • Schrödinger solved an equation. • Predicts the probability of finding an electron (electron density) • Node – where probability of finding an electron is zero • Each equation solution uses four variables called quantum numbers.

29. So what are these orbitals anyway? • The Periodic Table gives us the answer. • A rule first: Each orbital can hold only one pair of electrons – with spins of +½ and −½ ↿⇂

30. The Periodic Table: the key to electronic structure

31. The Periodic Table: the key to electronic structure

32. The Periodic Table

34. 6.6 Representations of Orbitals Electron density map

35. Radial Probability Plot

36. The 1s, 2s, and 3s orbitals < <

37. The p orbitals

38. The d orbitals

39. Quantum Numbers (p. 220, 227) Each set of four quantum numbers defines individual electrons.

40. Orbital energy levels in the hydrogen atom n = 4 shell

41. Quantum Numbers

42. Quantum # Practice

43. 6.7 Many-Electron AtomsRules of Orbital Filling • Pauli Exclusion Principle – In a given atom, no two electrons can have the same set of four quantum numbers, i.e. only two electrons per orbital. • Aufbau Principle – Lowest energy orbitals are filled first. • Hund’s Rule – For degenerate orbitals, the lowest energy is attained with maximum number of unpaired electrons.

44. Orbital energy levels in many-electron atoms

45. 6.8 Electron Configurations • Shows the number of electrons and type of orbitals present in an atom or ion • Orbital diagram – use boxes or lines • Spectroscopic notation – 1s2 2s2 2p6 etc. • Core electrons – electrons in filled shells • Valence electrons – electron(s) in unfilled shells

47. 6.9 Electron Configurations and The Periodic Table • Remember: The Periodic Table is the answer. Use it! • Exceptions (p. 237): • 24Cr • 28Cu

48. Valence Electron configurations. p. 236

49. Electron Configurations of Ions (pp. 262-263) • Cations: • Remove electron(s) from the orbital(s) with the highest n and highest l. • For transition metals the s electrons are removed first. • Anions: • Add electron(s) to the empty or partially filled orbitals with the lowest value of n.