Understanding Atomic Spectra and the Bohr Model

1. Electrons in the Atom

2. Electrons in the Atom • Thomson: discovered the electron • Rutherford: electrons like planets around the sun • Experiments: bright – line spectra of the elements

3. Atomic Spectrum The colors tell us about the structure of electrons in atoms

4. Electromagnetic Spectrum • Complete range of wavelengths and frequencies (gamma to radio) • Mostly invisible to human eye • Substances can either absorb or emit different radiations

5. Continuous Spectrum • Display of colors that are merging into each other. Rainbow, visible light, heated gases emit continuous spectrum. • The range of frequencies present in light. • White light has a continuous spectrum. • A rainbow.

6. Prism and White Light • White light is made up of all the colors of the visible spectrum. • Passing it through a prism separates it. Continuous spectrum

7. Line Spectrum (Discontinuous) • Images appear as narrow colored lines separated by dark regions. • Bright Line Spectra: gases at low temperature emit lines of colors. • Each line corresponds to a particular wavelength emitted by the atom.

8. If the Light is not White • By heating a gas with electricity we can get it to give off colors. • Passing this light through a prism produces the bright line spectrum Bright line spectra

9. Atomic Spectrum • Each element gives off its own characteristic colors. • Can be used to identify the atom. • How we know what stars are made of. Atomic fingerprints

10. These are called discontinuous spectra • Or line spectra • Unique to each element. • These are emission spectra • The light is emitted given off.

11. An Explanation of Atomic Spectra NIELS BOHR explained only the Hydrogen Spectra

12. Hydrogen spectrum • Emission spectrum: these are the colors hydrogen emits when excited by energy. • Called a line spectrum. • There are just a few discrete lines showing in the visible spectrum 656 nm 434 nm 410 nm 486 nm

13. What this means • Only certain energies are allowed for the electrons in hydrogen atom. • The atom can absorb or emit only certain energies (packets-photons, quanta). • Use Planck’s: DE = hn = hc / l • Energy in the atom is quantized.

14. Bohr’s Model of the Atom Based on • Spectra of the atoms • Rutherford’s nuclear atom • Classical electrostatics (like charges repulse, unlike charges attract) • Planck’s Quantum Theory

15. Bohr’s Postulates 1. Atoms consist of central nucleus. 2. Only certain circular orbits are allowed. Radius of orbit proportional to 1/n2 3. Electron in an orbit has a definite amount of energy. It is quantized. It is in a stationary state. Its energy is:

16. 4. Energy of the electron at infinity (when it is totally removed from the atom) is equal to zero. 5. Energy is emitted or absorbed when electrons JUMP from orbit to orbit (lower to higher: energy is absorbed; higher to lower: energy is emitted). In- between stages are forbidden • ΔE > 0 , energy is absorbed • ΔE < 0, energy is emitted

17. Bohr’s Model Nucleus Electron Orbit Energy Levels

18. Bohr’s Model } • Further away from the nucleus means more energy. • There is no “in between” energy • Energy Levels Fifth Fourth Third Increasing energy Second First Nucleus

19. Bohr’s Model – Equations • Energy of electron in an orbit: Difference of energy between two levels

20. The Bohr Model • n is the energy level • for each energy level the energy is defined by an equation E = -2.178 x 10-18 J (Z2 / n2 ) • Z is the nuclear charge, which is +1 for hydrogen; Rh is Rydberg constant equal to 2.178 x 10-18 J . • n = 1 is called the ground state • when the electron is removed, n = ¥, and • ΔE = 0 of the electron.

21. Energy for Electron Transitions When the electron moves from one energy level to another, the change in energy is: DE = Efinal - Einitial DE = -2.178 x 10-18 [Z2 (1/ nf2 - 1/ ni2)], Joules, but z =1. Therefore: DE = 2.178 x 10-18 ( 1/ ni2 -1/ nf2 ) Joules

22. Examples • Calculate the energy needed to move an electron from its ground state (n=1) to the third energy level. • Calculate the energy released when an electron moves from n= 5 to n=2 in a hydrogen atom.

24. Changing the energy • Let’s look at a hydrogen atom

25. Changing the energy • Heat or electricity or light can move the electron up energy levels. Energy is being absorbed

26. Changing the energy • As the electron falls back to ground state it gives the energy back as light. Energy is being emitted

27. Changing the energy • May fall down in steps • Each with a different energy

28. Further the electrons fall, more energy, higher frequency. • This is simplified picture • the orbitals also have different energies inside energy levels (more about it later) • All the electrons can move around. Ultraviolet Visible Infrared

29. The Bohr Ring Atom • Could not explain that only certain energies were allowed. • He called these allowed energies energy levels. • Putting Energy into the atom moved the electron away from the nucleus. • From ground state to excited state (energy is absorbed). • When it returns to ground state it gives off light of a certain packet of energy.

30. The Bohr Model • Doesn’t work. • Only works for hydrogen atoms. • Electrons don’t move in circles. • The quantization of energy is right, but not because they are circling like planets.

31. The Quantum Atom

32. The Quantum Mechanical Model of the Atom • A totally new approach. • De Broglie (1892-1987) said: • matter could be like a wave. • Matter waves are standing waves. • The vibrations of the wave are like of a stringed instrument.

33. DeBroglie Waves

34. De Broglie Waves - Simulations • http://www.launc.tased.edu.au/online/sciences/physics/debrhydr.html

35. What’s possible? • You can only have a standing wave if you have complete waves. • There are only certain allowed waves. • In the atom there are certain allowed waves called electrons. • 1925 Erwin Schrödinger described the wave function of the electron. • Much math but what is important are the solutions.

36. The Quantum Mechanical Model • Things that are very small behave differently from things big enough to see. • The quantum mechanical model is a mathematical solution • It is not like anything you can see.

37. The physics of the very small • Quantum mechanics explains how the very small behaves. • Classic physics is what you get when you add up the effects of millions of packages (Newtonian Physics). • Quantum mechanics is based on probability because we cannot see the particles and they are many of them moving randomly.

38. The Quantum Mechanical Model • Has energy levels for electrons. • Orbits are not circular. They are not uniquely defined. There is no definite path for the motion of the electron. • The model predicts the probability of finding an electron a certain distance from the nucleus. The space is defined by the solution of Schrödinger equation. • Orbitals are found in energy levels.

39. The Quantum Mechanical Model • The atom is found inside a blurry “electron cloud” • A area where there is a chance of finding an electron. • Draw a line at 90 % probability

40. Heisenberg Uncertainty Principle • It is impossible to know exactly the speed and velocity of a particle. • The better we know one, the less we know the other. • The act of measuring changes the properties.

41. Heisenberg Uncertainty Principle Introduces the Unknown Factor • To measure where a electron is, we use light. • But the light moves the electron • And hitting the electron changes the frequency of the light. • Therefore we are never sure where the electron is.

42. After Before Photon changes wavelength Photon Electron Changes velocity Moving Electron

43. Duality of Matter and Light • Light behaves as a wave (Young + others) • Light behaves as stream of particles (Einstein) • Matter behaves as a particle (ancients + Newton) • Matter behaves as waves (deBroglie)

44. What is light • Light is a particle - it comes in chunks. • Light is a wave- we can measure its wave length and it behaves as a wave • If we combine E=mc2 , c=ln, E = 1/2 mv2 and E = hn • We can get l = h/mv • The wavelength of a particle.

45. Matter is a Wave • Does not apply to large objects • Things bigger that an atom • A baseball has a wavelength of about 10-32 m when moving 30 m/s. Too small to measure. • An electron at the same speed has a wavelength of 10-3 cm • Big enough to measure.

46. Schrödinger Equation • Treats electrons as waves and particles. • Solution of equation determine the probable energy of the electron (energy level) • Solutions come in form of set of quantum numbers. Each set determines an orbital. • Orbital: the 90% probability space for finding a given electron.

47. Atomic Orbitals • Wave function corresponding to a particular set of three quantum numbers (n, l, and ml) • Within each energy level the complex math of Schrödinger's equation describes several shapes. • Regions where there is a high probability of finding an electron.

48. The Wave Mechanical Model of the Atom The atom has two parts: • A dense nucleus in which most of the mass is concentrated • Energy levels that contain orbitals in which electrons are placed • Each electron is described by four quantum numbers: (n, l, m, s) • The quantum numbers (n, l, m) are solutions of Schrödinger equation • The quantum number (s) added for the spin of the electron.

49. Schrödinger’s Equation

50. Solutions to Schrödinger’s Equation