Atomic Models

1. Atomic Models • Scientist studying the atom quickly determined that protons and neutrons are found in the nucleus of an atom. • The location and arrangement of the electrons was more elusive. • Understanding the arrangement of the electrons in an atom is important because the electrons are involved in the formation of ions and compounds.

2. Atomic Models • Elements in the same group exhibit similar chemical and physical properties. • Alkali Metals: • Very reactive • Form cations with +1 charge • Halogens: • Form anions with -1 charge • Noble Gases • Inert (unreactive) • Do not form ions • Why?

3. Atomic Models • The properties and reactivity of an element depends on its electronic structure. • The arrangement of electrons in an atom • Number of electrons • Distribution of electrons around the atom • Energies of the electrons • Much of our knowledge of electronic structure came from studying the way atoms absorb or emit light.

4. Atomic Models • Light is a type ofelectromagnetic radiation • a form of energy with both electrical and magnetic components Wavelength(l) the distance between successive peaks Frequency (u) the number of complete wavelengths that pass a given point in 1 sec

5. Atomic Models • The wavelength and frequency of electromagnetic radiation are inversely proportional:

6. Atomic Models • The energy of light is directly proportional to its frequency: E = h u where h = Planck’s constant = 6.626 x 10-34 J.s • and inversely proportional to its wavelength: E = hc l

7. Atomic Models The electromagnetic spectrum: Low E High E

8. Bohr Model • Two models are used to explain the arrangement of the electrons in atoms. • Bohr model • Nice “picture” but incorrect! • Explains only 1 electron systems • Quantum mechanical model • Hard to visualize but the best model we have!

9. High voltage H2 Bohr Model • When an electrical current is passed thru a sample of H2 (g), light with certain specific wavelengths is emitted (instead of a continuous “rainbow” of colors). Atomic line spectrum

10. Bohr Model • Niels Bohr developed a model that explained the line spectrum formed by hydrogen. • Observations: • Only certain wavelengths of light are emitted. • Since E = hc/l, only light with certain specific energy is emitted.

11. Bohr Model • Bohr explained the line spectrum of hydrogen by assuming that the energy of an electron is quantized. • Restricted to certain values

12. Bohr Model • According to Bohr: • Electrons are confined to specific energy states called orbits. • Only orbits of specific radii are allowed. • An electron in an allowed orbit has a very specific energy.

13. Bohr Model • An electron in the ground state (the lowest energy state) can move to a higher energy orbit by absorbing energy. • An electron in the excited state (a higher energy state) emits energy as a photon (a packet of light) when it falls back to a lower energy level. • The light emitted has a wavelength that corresponds to the energy difference between the two orbits.

14. Bohr Model • The Bohr model effectively explains the line spectra of atoms and ions with a single electron • H, He+, Li2+ • Another model is needed to explain the reactivity and behavior of more complex atoms or ions • Quantum mechanical model

15. Quantum Mechanical Model • In 1924 Louis de Broglie suggested that matter has a dual nature. • Matter (including an electron) has wave-like properties in addition to the expected particle-like properties. • Since matter has wave-like properties, each electron has an associated wavelength: l = h mv where h = Planck’s constant m = mass v = velocity mv = momentum

16. QM Model • Waves don’t have a discrete position! • Spread out through space • Cannot pinpoint one specific location • Since electrons have wave-like properties, determining the location of an electron is difficult. • Heisenberg Uncertainty Principle:The exact momentum (mass x velocity) and exact location of an object cannot be known simultaneously. • You cannot know both the exact energy and exact location of an electron.

17. QM Model • In 1926 Schroedinger developed an equation that incorporates both the particle-like and wave-like behavior of electrons. • Solving the Schroedinger wave equation leads to a series of mathematical functions calledwave functions (y) • Wave function (y): • a mathematical description of an allowed energy state (orbital) for an electron

18. QM Model • Each wave function (y) has a precisely known energy, but the exact location of the electron cannot be determined. • y 2 is used to obtain a map of electron density • the probability of finding an electron in a particular region of space. • high electron density  high probability of finding the electron

19. Quantum Mechanical Model • Complete solution of the Schroedinger equation gives a set of wave functions called orbitals. • Orbital:An allowed energy state of an electron in the quantum mechanical model of the atom • Each orbital has a specific energy, but the exact location of the electron in that atom is not known for certain.

20. Quantum Mechanical Model • An orbital: • describes a specific distribution of electron density in space • has a characteristic energy • has a characteristic shape • is described by three quantum numbers: n, l, ml • can hold a maximum of 2 electrons • Note:A fourth quantum number (ms) is needed to describe each electron in an orbital

21. Quantum Mechanical Model • Principal quantum number (n): • Allowed values: n = 1, 2, 3, 4, etc • describes the energy of the electron • as n increases, the energy of the electron increases • as n increases, the electron is more loosely bound to the atom • indicates the average distance of the electron from the nucleus • as n increases, the average distance from the nucleus increases

22. Quantum Mechanical Model • Azimuthal quantum number (l): • also known as the angular momentum quantum number • Allowed values:l= 0, 1, 2,….(n-1) • Example: If n=2, then l = 0 or 1 • defines the shape of the orbital

23. Quantum Mechanical Model • The value of l for a particular orbital is usually designated by the letters s, p, d, f, and g: • An orbital with quantum numbers of n = 3andl = 2 would be a 3d orbital • A 4p orbital would have the quantum numbers n = 4 and l = 1. 01 2 3 4 s p d f g Value of l Letter used

24. Quantum Mechanical Model • s-orbital: • spherical probability region • found in all shells of an atom • the size of the s-orbital increases with increasing n • as n increases an electron has a greater probability of being found farther from the nucleus 1s 2s 3s

25. Quantum Mechanical Model • p-orbital • Three p orbitals in all shells whenn > 2 • Figure 8 or dumbbell shaped • All p orbitals in the same shell aredegenerate • Have the same energy • The three p orbitals have different spatial orientation.

26. Quantum Mechanical Model • d-orbitals • five d orbitals are present in each shell whenn > 3 • degeneratewithin the same shell • different shapes • different orientation in space

27. Quantum Mechanical Model • f-orbitals • When n > 4, there are seven f orbitals in each shell. • Degenerate (within the same shell) • Complicated shapes

28. Quantum Mechanical Model • Magnetic quantum number (ml): • Allowed values: integers from l to –l • If l = 1, then ml = 1, 0, -1 • describes the orientation in space of the orbital ml = -1 ml = 0 ml = 1

29. Quantum Mechanical Model • The first three quantum numbers (n, l, ml) describe an individual orbital. • A fourth quantum number is used to describe each electron found in an orbital. • Electron spin quantum number (ms) • Allowed values: • ms = + 1/2 ( ) • ms = -1/2 ( )

30. Quantum Mechanical Model • Electron spin:a property of electrons that make it behave as if it were a tiny magnet spinning on its axis