Matter wave, atomic spectrum and Bohr model.pptx

introduction to matter wave, atomic spectrum and Bohr model

1. 1. Particles behaving as waves

2. Introduction Viruses (shown in blue) have landed on an E . coli bacterium and injected their DNA, converting the bacterium into a virus factory. This false-color image was made by using a beam of electrons rather than a light beam.

3. de Broglie waves In 1924 a French physicist, Louis de Broglie (pronounced “de broy ”), proposed that particles may, in some situations, behave like waves. A free particle with rest mass m , moving with non-relativistic speed v , should have a wavelength related to its momentum: A particle’s frequency is related to its energy in the same way as for a photon:

4. Davisson and Germer experiment Shown is an apparatus used to study electron diffraction .

5. electron diffraction

6. Electron microscopy The wave aspect of electrons means that they can be used to form images, just as light waves can. This is the basic idea of the transmission electron microscope (TEM), shown. The “lenses” are actually coils that use magnetic fields to focus the electrons. The resolution is limited by diffraction effect (depend on wavelength)

7. 2. Spectra lines

8. Atomic line spectra The light emitted by atoms in a sample of heated gas includes only certain discrete wavelengths. Nineteenth-century physics does not explain this.

9. Atomic line spectra Shown are the emission line spectra of several kinds of atoms and molecules. No two are alike. Note that the spectrum of water vapor (H 2 O) is similar to that of hydrogen (H 2 ), but there are important differences that make it straightforward to distinguish these two spectra.

10. Emission and Absorption spectrum A cool gas that’s illuminated by white light to make an absorption line spectrum also produces an emission line spectrum when viewed from the side.

11. Absorption line spectrum If white light pass through the gas and look at the transmitted light with a spectrometer. The dark lines correspond to the wavelengths that have been absorbed by the gas.

12. The Rutherford scattering experiment (1911)

13. The nuclear atom Rutherford probed the structure of the atom by sending alpha particles at a thin gold foil. Some alpha particles were scattering by large angles , leading him to conclude that the atom’s positive charge is concentrated in a nucleus at its center.

14. The Rutherford scattering experiment Refer to tutorial

15. The failure of classical physics ACCORDING TO CLASSICAL PHYSICS: An orbiting electron is accelerating, so it should radiate electromagnetic waves. The electron’s angular speed would increase as its orbit shrank (Kepler's 2 nd law), so the frequency of the radiated waves should increase. The waves would carry away energy, so the electron should lose energy and spiral inward. Thus, classical physics says that atoms should collapse within a fraction of a second and should emit light with a continuous spectrum as they do so.

16. 3. Bohr model

17. The Bohr model of hydrogen Niels Bohr (1885–1962) postulated that each energy level of a hydrogen atom corresponds to a specific stable circular orbit of the electron around the nucleus, where the corresponding energy can have only certain particular values ( energy level ). In the Bohr model, an atom radiates energy only when an electron makes a transition from an orbit of energy E i to a different orbit with lower energy E f , emitting a photon of energy hf = E i − E f in the process. Bohr won the 1922 Nobel Prize in physics for these ideas.

18. Atomic energy levels When an atom makes a transition from one energy level to a lower level, it emits a photon whose energy equals that lost by the atom. An atom can also absorb a photon, provided the photon energy equals the difference between two energy levels. The lowest energy level is called ground state , levels with energies greater than the ground level are called excited levels.

19. Emission spectrum of a hypothetical atom Consider a hypothetical atom that has energy levels at 0.00 eV, 1.00 eV, and 3.00 eV. (a) shows the energy-level diagram for the hypothetical atom. (b) shows the emission spectrum of this hypothetical atom.

20. The Bohr model of hydrogen Bohr found that the magnitude of the electron’s angular momentum is quantized ; that is, this magnitude must be an integral multiple of h /2 π . Let’s number the orbits by the principal quantum number n , where n = 1, 2, 3, …, and call the radius of orbit n, r n , and the speed of the electron in that orbit v n . The magnitude of the angular momentum of an electron of mass m in such an orbit is:

21. The Bohr model of hydrogen Shown is the angular momentum of an electron in a circular orbit around an atomic nucleus.

22. The Bohr model of hydrogen A standing wave on a string transmits no energy, and electrons in Bohr’s orbits radiate no energy. For the wave to “come out even” and join onto itself smoothly, the circumference of this circle must include some whole number of wavelengths.

23. The Bohr model of hydrogen Total mechanical energy of the electron:

24. The Bohr model of hydrogen The orbital speed of the electron in Bohr’s model of a hydrogen atom is: The radius of this orbit is: where the Bohr radius is a = 5.29 × 10 −11 m.

25. The Bohr model of hydrogen The Bohr model predicts the observable energy levels of the hydrogen atom, which give rise to the hydrogen spectrum, below.

26. Hydrogen spectrum in more detail The Balmer series is not the entire spectrum of hydrogen; it’s just the visible-light portion. Hydrogen also has a series of spectral lines in the ultraviolet ( Lymann ), and several series of spectral lines in the infrared.

27. Hydrogen-like atoms The Bohr model can be applied to any atom with a single electron.    

28. 6. Laser

29. Absorption Consider a gas of atoms in a transparent container. Each atom is initially in its ground level of energy E g and also has an excited level of energy E ex . If we shine light of frequency f on the container, an atom can absorb one of the photons provided the photon energy E = hf equals the energy difference E ex − E g between the levels. The figure shows this process, in which three atoms A each absorb a photon and go into the excited level.

30. Spontaneous emission Excited atoms (which we denote as A*) can return to the ground level by each emitting a photon with the same frequency as the one originally absorbed. This process is called spontaneous emission . The direction and phase of each spontaneously emitted photon are random .

31. Absorption and emission of light between atomic levels: The excited atom can SPONTANEOUSLY (randomly) de-excite to a lower level if a vacant site permits. The average length of time an atoms stays in excited state in tens of nanoseconds (        

32. Boltzmann distribution The (thermal equilibrium) population density of atoms, in an excited state , is related to those in a lower energy state by the Boltzmann relationship,   Energy Population      

33. Stimulated emission In stimulated emission , excited atoms can be triggered or simulated in phase by an incoming photon of a specific energy Incident photon must have an energy corresponding to the energy difference between the higher and lower states and the incident photon is not absorbed by the atom. A kind of resonance effect induces each excited atom to emit a second photon with the same frequency, direction, phase, and polarization as the incident photon, which is not changed by the process.

34. Population Inversion It is possible that the rate at which atoms are PUMPD into one of these states exceed the rate at which they leave. A large number of atoms can be excited into, and held in, the higher energy state leaving an almost empty state below them. Atoms can stay in this metastable state without de-exciting while the population is being built up. Energy Population       De-excitation Pumping of energy LASER action Population inversion between and    

35. Population Inversion An improvement on this behavior is obtained with a four-level structure where the laser transition takes place between the third and second excited states we need depopulation of the lower laser level to be rapid to ensure that the upper level is always full and the lower level always empty. Fast relaxation Fast relaxation Laser transition

36. Optical Resonant Cavity In practice, photons need to be confined in the system to allow the number of photons created by simulated emission to exceed all other mechanisms . bounding the laser medium between two mirrors (Optical resonant cavity: one mirror is totally reflecting and the other partially reflecting).

37. Properties of Laser Monochromaticity: laser light is concentrated in a narrow range of wavelengths laser produce the purest (most monochromatic) light available Coherence: All the emitted photons bear a constant phase relationship with each other in both time and space. The light is said to be coherent.

38. Properties of Laser Beam divergence: all photons travel in the same direction the light is contained in a very narrow pencil almost collimated laser light is low divergence High irradiance: Radiance is the amount of power per unit area emitted by a light source for a given solid angle. The lasers have high power outputs for the small solid angle (low divergence), producing a high radiance. The solid angle can be thought of as a cone through which the light passes. Light bulb Power: Power density at 1m:   Laser Power: Power density at 1m:  

39. Practical lasers The name “laser” is an acronym for “light amplification by stimulated emission of radiation.” The basic requirements of any laser are similar, they all comprise of: An active medium with a suitable set of energy levels to support laser action A source of pumping energy in order to establish a population inversion An optical cavity to introduce optical feedback so as to maintain gain of the system above all losses Laser are usually classified in terms of their active medium: Solid state laser Gas laser Semiconductor laser

40. Gas Lasers The Helium-Neon ( HeNe ) LASER The active laser medium is a gaseous mixture of He and Ne atoms (10:1) The gas is enclosed in a cylindrical quartz DISCHARGE tube sealed at each end by a mirror to form the optical cavity Pumping is done via an electrical discharge (A GLOW DISCHARGE) created between the electrodes. A pulse of about 10kV is applied across the electrodes to start the discharge An electric current is induced through the gas; a steady current of 3-10 mA (DC) is sufficient to keep the discharge established.

41. Gas lasers The lighter He atoms are excited by collisions with electrons in the discharge. The He atoms collide with the heavier Ne atoms and transfer their energy to them. Ne atoms are excited by the collisions into their metastable state where population inversion builds up. Laser light: wavelength 633 nm (red) Power 0.5 to 50 mW Beam divergence about rad.  

42. Gas Lasers The Argon-ion Laser Unlike the HeNe laser, the active medium in the argon laser is a plasma of excited ions An electric discharge is created in a narrow tube of gaseous argon. The argon atoms are first ionized and then excited by multiple collisions with electrons into their upper energy levels. Due to the high energy required to ionize and excite the agon atoms, very high current densities are needed (~1 Amm -2 ) Application: holography, eye surgery, spectrochemistry, optical image processing, semiconductor processing, laser light shows Wavelength: 514 nm Power: 1-20 W

43. Gas Lasers The Carbon dioxide laser The important energy levels are provided not by the distribution of electrons but by the wiggling and jiggling of the entire carbon dioxide molecule itself The molecule can be pictured as a linear arrangement of O-C-O atoms which vibrate in relation to each other and several different modes of vibration give rise to a set of energy levels with transitions far into the infra-red ( Power: up to 25 kW To reach the high powers required from these lasers, cavity lengths can stretch to 2-3m Application: materials-processing applications such as cutting, welding and annealing  

44. Solid State Lasers Solid state lasers are characterized by having as their active medium, a solid rod or slab of crystalline insulator doped with a small amount of impurity. To help avoid confusion in terminology with the semiconductor laser, solid state lasers are sometimes referred to as doped insulator lasers It is the impurity constituent which provides the required energy structure to produce laser action

45. Solid State Lasers The Ruby Laser The first working laser to be demonstrated (~1960) The active medium is a cylindrical crystal of synthetic sapphire ( ) doped with roughly 0.05% (by weight) of chromium ions ( ) The ruby is irradiated by a short pulse of light from a xenon-filled flashtube. It absorbs pumping energy in the blue-green region and excites the chromium ions to the upper level of the laser transition. Wavelength 694.3 nm Crystal and flashtube are placed parallel to each other within a polished pumping chamber ensures that as much light as possible is pumped into the rod  

46. Solid State Lasers The Nd-YAG laser Most common doped insulator laser Host material is a crystal of yttrium- aluminium - garnate ( ), YAG doped with 0.7% of neodymium ( ) ions Wavelength (infra-red)  

47. Light Emitting Diodes (LED) In a basic pn junction, free electrons in n-type diffuse into p-type under forward bias. In the p-region they meet a majority of holes and recombine and excess energy emitted as light Typical emission wavelength GaAs: 800nm GaP : 550nm or 700num GaAsP : 580nm or 660nm Si: 1100 nm Ge: 1810nm

48. Semi-conductor Lasers Formed from heavily doped pn -junctions based on modified LED structure To achieve laser action, need to ensure high concentration of e-h pairs available for recombination. Achieved by high doping concentrations across junction Long spontaneous lifetime materials enhance stimulated emission