The Quantum-Mechanical Model of the Atom

1. The Quantum-Mechanical Model of the Atom

2. Behavior on the Atomic Scale In the early 1900s, scientist tried to apply their understanding of physics to the structure of the atom. An entirely new approach, called the quantum-mechanical model, was developed to explain some of the unusual behavior of electrons within an atom.

3. The Quantum-Mechanical Model In this approach, very small fast-moving particles such as electrons also have wave-like properties associated with them. Likewise, light, which travels as waves, can also exhibit particle-like properties.

4. Electromagnetic Radiation Early atomic scientists studied the interaction of matter with electromagnetic radiation, or light. Electromagnetic radiation, or radiant energy, includes visible light, infrared, micro and radio waves, and X-rays and ultraviolet light.

5. Atomic Spectroscopy The study of the light emitted or absorbed by matter is a branch of chemistry called spectroscopy. Atomic spectroscopy allows scientists to understand the nature of the electrons in atoms. Molecular spectroscopy provides information about the bonds in molecules.

6. Electromagnetic Radiation Light consists of oscillating electric and magnetic fields that travel through space at the rate of 3 x 108m/s. The oscillating fields interact with electrons in the atom.

7. Electromagnetic Radiation This drawing represents a “snapshot” of an electro-magnetic wave at a given instant.

8. Electromagnetic Radiation Electromagnetic radiation travels in waves. The waves of radiant energy have three important characteristics: 1. Wavelength - λ - (lambda) 2. Frequency – ν – (nu) 3. Speed – c – the speed of light

9. Wavelength Wavelength, λ, is the distance between two adjacent peaks or troughs in a wave. The units may range from picometers to kilometers depending upon the energy of the wave.

10. Frequency Frequency, ν, is the number of waves (or cycles) that pass a given point in space per second. The units are cycles/s, s-1 or hertz (Hz).

11. The Speed of Light All electromagnetic radiation travels at the same speed. The speed of light ( c ) is: c = 2.9979 x 108 m/s

12. Wavelength and Frequency Wavelength and frequency are inversely related. That is, waves with a low frequency have a long wavelength. Waves with a high frequency have short wavelengths.

13. Electromagnetic Radiation The relationship between wavelength and frequency is: λν = c

14. Properties of Light - Amplitude

15. Diffraction Waves of electromagnetic radiation are bent or diffracted with they a passed through an obstacle or a slit with a size comparable to their wavelength.

17. Interference Patterns

18. The Failure of Classical Physics Observations of the behavior of sub-atomic particles in the early 1900s could not be predicted or explained using classical physics. Very small particles such as electrons appear to interact with electromagnetic radiation (light) differently than objects we can see and handle.

19. Black Body Radiation Physicists focused on interactions between light (electromagnetic radiation) and matter to try to better understand the nature of the atom. When objects are heated, they emit light in relation to their temperature. Iron rods glow red, and will glow yellow at higher temperatures.

20. Black Body Radiation Classical physics, when applied to black body radiation, predicted that the intensity of the radiation emitted would dramatically increase at shorter and shorter wavelengths. The result was that any hot body should emit intense UV radiation, and even x-rays. Even a human body at 37oC would glow in the dark. This discrepancy between theory and observation is called “The Ultraviolet Catastrophe.”

21. The Ultraviolet Catastrophe The failure of classical physics is seen in the shorter wavelength ultraviolet region

22. Planck & Black Body Radiation Max Planck (1858-1947) studied the radiation emitted by objects heated until they glowed. In order to explain the observations, he proposed (in 1900) that the energy emitted was not continuous, but instead was released in multiples of hν. h is known as Planck’s constant.

23. Planck & Black Body Radiation ∆E = nhν where n=integer ν = frequency h = 6.626 x 10-34 J-s Planck’s work showed that when matter and energy interact, the energy is quantized, and can occur only in discrete units or bundles with energy of hν.

24. Planck & Black Body Radiation ∆E = nhν Each packet or bundle of energy is called a quantum. A fraction of a quantum is never emitted. A quantum is the smallest amount of energy that can be emitted or absorbed in the form of electromagnetic radiation.

25. Planck’s Law Planck’s approach shows good agreement between the observed spectrum (in blue) and the calculated values (in red).

26. Planck’s Law Planck’s law was based on empirical data. He found a mathematical relationship that fits the observations. It is important to note that Planck did not explain the reason for the relationship. The concept of energy being quantized rather than continuous was quite revolutionary.

27. Planck & Black Body Radiation Planck received the Nobel Prize for his work in 1918 (at the age of 42).

28. Einstein – Photoelectric Effect Albert Einstein (1879-1955) won a Nobel Prize for his explanation of the photoelectric effect. When light of sufficient energy strikes the surface of a metal, electrons are emitted from the metal surface. Each metal has a characteristic minimum frequency, νo , called the threshold frequency, needed for electrons to be emitted.

30. The Photoelectric Effect

31. Observations 1. No electrons are emitted if the frequency of light used is less than νo, regardless of the intensity of the light. 2. For light with a frequency≥ νo , electrons are emitted. The number of electrons increases with the intensity of the light. 3. For light with a frequency > νo , the electrons are emitted with greater kinetic energy.

32. Explanation Einstein proposed that light is quantized, consisting of a stream of “particles” called photons. If the photon has sufficient energy, it can “knock off” an electron from the metal surface. If the energy of the photon is greater than that needed to eject an electron, the excess energy is transferred to the electron as kinetic energy.

33. The Photoelectric Effect Ephoton= hν = hc/λ If incident radiation with a frequency νi is used: KEelectron = hνi -hνo = ½ mv2 The kinetic energy of the electron equals the energy of the incident radiation less the minimum energy needed to eject an electron.

34. The Photoelectric Effect The frequency hνo is the minimum energy needed to eject an electron from a specific metal. This energy is called the binding energy of the emitted electron. Binding energy is often expressed in electron volts (eV), with 1 eV = 1.602 x 10–19 J.

35. Particle-Wave Duality Einstein’s work suggested that the incident photon behaved like a particle. If it “hits” the metal surface with sufficient energy (hνi), the excess energy of the photon is transferred to the ejected electron. In the atomic scale, waves of radiant energy have particle-like properties.

36. Particle-Wave Duality Einstein also combined his equations: E=mc2 with Ephoton= hc/λ to obtain the “mass” of a photon: m= m= hc/λ E = c2 c2 h λc

37. Albert Einstein

38. Particle-Wave Duality The apparent mass of radiant energy can be calculated. Although a wave lacks any mass at rest, at times, it behaves as if it has mass. Einstein’s equation was confirmed by experiments done by Arthur Compton in 1922. Collisions between X-rays and electrons confirmed the “mass” of the radiation.

39. Particle-Wave Duality Arthur Compton attempted to study the collision of a light quantum with an electron moving freely through space. However, creating a collision between a beam of light and a beam of electrons isn’t feasible, since it would take an extremely long time for such a collision to occur.

40. Arthur Compton Compton solved this problem by using extremely high energy x-rays to bombard small atoms. Since the energy of the radiation was so high, the electrons in the atoms were viewed as “free” by comparison. Compton viewed the collision as if between two elastic spheres, and perfectly predicted the scattering of the x-rays and the decrease in frequency as a result of the collision.

41. Arthur Compton Compton received the Nobel prize in 1927.

42. Emission Spectrum of Hydrogen When atoms are given extra energy, or excited, they give off the excess energy as light as they return to their original energy, or ground state. H2 Hg He

43. Emission Spectrum of Hydrogen Scientists expected atoms to be able to absorb and emit a continuous range of energies, so that a continuous spectrum of wavelengths would be emitted.

44. Emission Spectrum of Hydrogen A continuous spectrum in the visible range, would look like a rainbow, with all colors visible. Instead, hydrogen, and other excited atoms emit only specific wavelengths of light as they return to the ground state. A line spectrum results.

45. Emission Spectrum of Hydrogen

46. Emission Spectrum of Hydrogen Instead, only a few wavelengths of light are emitted, creating a line spectrum. The spectrum of hydrogen contains four very sharp lines in the visible range.

47. Emission Spectrum of Hydrogen The discrete lines in the spectrum indicate that the energy of the atom is quantized. Only specific energies exist in the excited atom, so only specific wavelengths of radiation are emitted.

48. The Bohr Atomic Model In 1913, Neils Bohr (1885-1962) proposed that the electron of hydrogen circles the nucleus in allowed orbits. That is, the electron is in its ground state in an orbit closest to the nucleus. As the atom becomes excited, the electron is promoted to an orbit further away from the nucleus.

49. The Bohr Atomic Model Classical physics dictates that an electron in a circular orbit must constantly lose energy and emit radiation. Bohr proposed a quantum model, as the spectrum showed that only certain energies are absorbed or emitted.

50. The Bohr Atomic Model Bohr’s model of the hydrogen atom was consistent with the emission spectrum, and explained the distinct lines observed.