The Quantum Mechanical Model of the Atom

1. The Quantum Mechanical Model of the Atom ELECTRONS

2. Compare and contrast the major models of the atom. Represent an electron’s location in the quantum mechanical model of an atom in terms of the shape of electron cloud (s & p orbitals), relative energies, and the number of electrons possible in the s, p, d, & f orbitals.

3. Review • Dalton – concept of the atom • Thomson – electrons • Used the Cathode Ray Tube • Developed the Plum Pudding Model • Rutherford – dense positive nucleus & atoms is mostly empty space • Used the Gold Foil Experiment • Include Chadwick (neutrons) in his model

4. Thomson’s Plum Pudding Model • Only includes electrons • Which element does it represent?

6. Electrons orbit the nucleus in set circular paths of fixed energy (energy levels). Bohr Model (1913)

7. Bohr’s Atom • Electrons can jump from energy level to energy level by absorbingor emittingenergy. • In other words, electrons absorb or emit lightenergy when they jump from one energy level to another.

8. Quantum • A quantum of energy is the amount of energy required to move an electron from one energy level to another.

9. QuantumThe energy levels are like the rungs of a ladder but are not equally spaced.

10. Excited State & Ground State • Ground state: the lowest possible energy level an electron can occupy. • Excited state: an energy level higher than the ground state. • When electrons absorb a quantum of energy, they can jump to an excited state.

11. Energy of Emitted by a Photon • Energy emitted by the electron as it drops from higher to lower energy level is proportional to the frequency of the light wave produced. Energy of the emitted photon = Difference in energy between two levels • Frequency of the emitted light corresponds to the color of visible light.

12. Bohr & exciting electrons

13. Emission Spectrum • Light emitted when electrons drop from an excited state to ground state produces a unique emission spectrum.

14. Hydrogen Emission Spectrum Violet Blue Red Balmer Series

15. Drawbacks of Bohr Model • explained the emission spectrum of the hydrogen atom but did not always explain those of other elements. • Said electrons travel in set circular paths – not all paths are actually circular • unable to predict the probable location of electrons.

16. Quantum Mechanical Model • Established in the 1920’s • Combined theories of multiple scientists: • Werner Heisenberg • Uncertainty Principle - can’t accurately measure both location & speed of an electron at the same time • Louis de Broglie • electrons have wave like properties • Erwin Schrodinger • Probability clouds of the electrons – location of electrons • quantum numbers – the address of an electron

17. Werner Heisenberg: Uncertainty Principle • We can not know (accurately measure) both the position and momentum (lets just call it speed)of a particle simultaneously • Why? • To accurately measure position, the electrons must be slowed down. • To accurately measure speed, the electrons are moving too fast to measure location.

18. Louis de Broglie: Wave Properties of Electrons • Since light waves have a particle behavior (shown by Einstein - Photoelectric Effect) then particles could have a wave behavior. • Discovered the wave like behavior of electrons. • de Broglie wavelength h=Planck’s Constant m=mass v=velocity

19. Electron Motion Around Atom Shown as a de Broglie Wave

20. Erwin SchrodingerQuantum (wave) Mechanical Model of the Atom 1925 • established the probability cloud of an electron. • Four Quantum Numbers describe the specific location of an electron • When you have all four quantum number of an electron, you can pin point that electron’s location. • Atomic Orbital • Location where there is a 90% probability that an electron will be found

21. Atomic Orbital • A 3D region in space in which there is high probability of finding an electron. • Schrodinger calculated that there is a 90% probability that an electron will be found in its specific atomic orbital • Also called, the probability cloud of the electron. • Each orbital, can contain at most 2 electrons.

22. Quantum Numbers • specify the properties of atomic orbitals and their electrons • Each electron has a unique set of four quantum numbers • If all four numbers of an electron are known, the probable location of the electron is known. • Think of the set of four unique quantum numbers are the “address” of an electron.

23. Four Quantum Numbers • Principal Quantum Number (n) • Energy level • Orbital Quantum Number (ℓ) • Orbital shape • Magnetic Quantum Number (ml) • Specific orbital • Spin Quantum Number (ms or s) • Direction of electron’s spin

24. Principal Quantum Numbern • Indicates energy levels n = 1, 2, 3, 4… • The maximum number of electrons in a principal energy level is given by: • Max # electrons = 2n2 • Where n is the principal quantum number

25. Orbital Quantum Number ℓ • Also called the Angular Momentum Quantum Number • Tells energy sublevel (or sublevel) for an electron • Indicates shape of orbital ℓ sublevel # possible e # orbitals 0 s 2 1 1 p 6 3 2 d 10 5 3 f 14 7 4 g

26. Shape of s & p orbitals • s orbitals are spherically shaped • p orbitals are dumb-bell shaped

27. s orbital 2s

28. 3p orbitals http://www.rmutphysics.com/CHARUD/scibook/crystal-structure/porbital.gif

29. Magnetic Quantum Number ml • Gives the specific orbitalof an electron within an energy sublevel. • Indicates the orientation of the orbitalin space. • Values of ml :integers -l to l • The number of values represents the number of orbitals. • Example: for l= 2 the possible ml = -2, -1, 0, +1, +2Which sublevel does this represent? Answer: d

30. Electron Spin Quantum Number ms or s • Indicates the spin of the electron (clockwise or counterclockwise). • Tells WHICH SPECIFIC electron within an orbital • Values of ms: +1/2 or -1/2

31. Example Problem • List the values of the four quantum numbers for orbitals in the 3d sublevel. • Answer: n=3 l = 2 (because d sublevel) ml = -2,-1, 0, +1, +2 ms = +1/2, -1/2 for each pair of electrons

32. The Electron Cloud • The electron cloud represents positions where there is high probability of finding an electron.

33. The Electron Cloud The higher the electron density, the higher the probability that an electron may be found in that region. http://www.chemeng.uiuc.edu/~alkgrp/mo/gk12/quantum/H_S_orbital.jpg

34. The Electron Cloud for Hydrogen 90% probability of finding the electron within this space

35. Probability Curve for Hydrogen

36. Summary - Quantum Mechanical Model • Electrons are located in specific energy levels, energy sublevels, and orbitals. • Electrons behave like both a particle & a wave • Cannot measure speed & position of an electron at the same time. • The model estimates the probability of finding an electron in a certain position.

37. FYI: Schrodinger’s Equations!!! • y is called the wave function and indicates the probability of where an electron may be found.