Chapter 7 Quantum Theory of Atom BushraJaved
Contents • The Wave Nature of Light • Quantum Effects and Photons • The Bohr Theory of the Hydrogen Atom • Quantum Mechanics 5. Quantum Numbers and Atomic Orbitals 6. Quantum Numbers and Atomic Orbitals
A Theory that Explains Electron Behavior • The quantum-mechanical model explains the manner in which electrons exist and behave in atoms • It helps us understand and predict the properties of atoms that are directly related to the behavior of the electrons
The Nature of Light:Its Wave Nature • Light is a form of electromagnetic radiation • composed of perpendicular oscillating waves, one for the electric field and one for the magnetic field • an electric field is a region where an electrically charged particle experiences a force • a magnetic field is a region where a magnetized particle experiences a force • All electromagnetic waves move through space at the same, constant speed • 3.00 x 108 m/s in a vacuum = the speed of light, c
Electromagnetic Spectrum The range of frequencies and wavelengths of electromagnetic radiation is called the electromagnetic spectrum.
Characterizing Waves • The amplitude is the height of the wave • the distance from node to crest • or node to trough • the amplitude is a measure of how intense the light is – the larger the amplitude, the brighter the light • The wavelength (l) is a measure of the distance covered by the wave • the distance from one crest to the next
Wave Characteristics Tro: Chemistry: A Molecular Approach, 2/e
Characterizing Waves • The frequency (n)is the number of waves that pass a point in a given period of time • the number of waves = number of cycles • units are hertz (Hz) or cycles/s = s−1 • 1 Hz = 1 s−1 • The total energy is proportional to the amplitude of the waves and the frequency • the larger the amplitude, the more force it has
Characterizing Waves • The longer the wavelength of light, the lower the frequency. • The shorter the wavelength of light, the higher the frequency.
Color • The color of light is determined by its wavelength or frequency • White light is a mixture of all the colors of visible light • a spectrum RedOrangeYellowGreenBlueViolet • When an object absorbs some of the wavelengths of white light and reflects others, it appears colored
Wavelength, Frequency & Speed of Light Wavelength and Frequency are related as: λα 1/ v c = λ v Where c is the speed of light • Light waves always move through empty space at the same speed. • Therefore speed of light is a fundamental constant. c = 3.00 x 108 m/s
The Wave Nature of Light Example 1 Which of the following statements is incorrect? a. The product of wavelength and frequency of electromagnetic radiation is a constant. b. As the energy of a photon increases, its frequency decreases. c. As the wavelength of a photon increases, its frequency decreases. d. As the frequency of a photon increases, its wavelength decreases.
Units of Wavelength & Frequency • Units of Wavelength: nanometers, micrometers, meters and Angstrom 1 nm = 10-9m 1A° = 10-10m • Units of Frequency: 1/second (per second) or 1s-1 Hertz = Hz, MHz and GHz 1-1s = 1 Hz
Wavelength & Frequency Example 2 What is the wavelength of blue light with a frequency of 6.4 1014/s? c = nl so l = c/n n = 6.4 1014/s c = 3.00 108 m/s l = 4.7 10−7 m
Wavelength & Frequency Example 3 What is the frequency of light having a wavelength of 681 nm? c = nl so n = c/l l = 681 nm = 6.81 10−7 m c = 3.00 108 m/s l = 4.41 1014 /s
Electromagnetic Spectrum Example 4 Which type of electromagnetic radiation has the highest energy? a. radio waves b. gamma rays c. blue light d. red light
Wave Theory of light One property of waves is that they can be diffracted—that is, they spread out when they encounter an obstacle about the size of their wavelength. In 1801, Thomas Young, a British physicist, showed that light could be diffracted. By the early 1900s, the wave theory of light was well established.
The Wave/Particle Nature of Light • Max Planck worked on the light of various frequencies emitted by the hot solids at different temperatures. • In 1900, Max Planck proposed that radiant energy is not continuous, but is emitted in small bundles. • Planck theorized that the atoms of an heated object vibrate with a definite frequency. • An individual unit of light energy is a photon.
Dual Nature of Light • Einstein expanded on Planck’s work. • Through Photoelectric Effect ,he showed that when light of particular frequency shines on a metal surface it knocks out electrons. • This knocking out of electrons is dependent only on the frequency of the shining light.
Einstein’s Explanation • Einstein proposed that the light energy was delivered to the atoms in packets, called quanta or photons • The energy of a photon of light is directly proportional to its frequency • inversely proportional to its wavelength • the proportionality constant is called Planck’s Constant, (h)and has the value 6.626 x 10−34 J∙s
Einstein’s Explanation Light, therefore, has properties of both waves and matter. Neither understanding is sufficient alone. This is called the particle–wave duality of light.
Ejected Electrons • One photon at the threshold frequency gives the electron just enough energy for it to escape the atom • binding energy, f • When irradiated with a shorter wavelength photon, the electron absorbs more energy than is necessary to escape • This excess energy becomes kinetic energy of the ejected electron Kinetic Energy = Ephoton – Ebinding KE = hn − f
The Photoelectric Effect Example 5: Suppose a metal will eject electrons from its surface when struck by yellow light. What will happen if the surface is struck with ultraviolet light? a. No electrons would be ejected. • Electrons would be ejected, and they would have the same kinetic energy as those ejected by yellow light. c. Electrons would be ejected, and they would have greater kinetic energy than those ejected by yellow light. d. Electrons would be ejected, and they would have lower kinetic energy than those ejected by yellow light.
Photoelectric Effect Example 6 The blue–green line of the hydrogen atom spectrum has a wavelength of 486 nm.Whatis the energy of a photon of this light? E = hnand c = nl so E = hc/l l = 486 nm = 4.86 10−7 m c = 3.00 108 m/s h = 6.63 10−34 J s E= 4.09 10−19 J
Problems with Rutherford’s Nuclear Model of the Atom • Electrons are moving charged particles • According to classical physics, moving charged particles give off energy • Therefore electrons should constantly be giving off energy • The electrons should lose energy, crash into the nucleus, and the atom should collapse!! • but it doesn’t
Continuous Vs Line Spectra In addition, this understanding could not explain the observation of line spectra of atoms. A continuous spectrum contains all wavelengths of light. A line spectrum shows only certain colors or specific wavelengths of light. When atoms are heated, they emit light. This process produces a line spectrum that is specific to that atom.
Spectra • When atoms or molecules absorb energy, that energy is often released as light energy • fireworks, neon lights, etc. • When that emitted light is passed through a prism, a pattern of particular wavelengths of light is seen that is unique to that type of atom or molecule – the pattern is called an emission spectrum • non-continuous • can be used to identify the material • flame tests
Na K Li Ba Identifying Elements with Flame Tests
Emission Line Spectra • When an electrical voltage is passed across a gas in a sealed tube, a series of narrow lines is seen. • These lines are the emission line spectrum. The emission line spectrum for hydrogen gas shows three lines: 434 nm, 486 nm, and 656 nm.
The Bohr Model of the Atom • The nuclear model of the atom does not explain what structural changes occur when the atom gains or loses energy • Bohr developed a model of the atom to explain how the structure of the atom changes when it undergoes energy transitions • Bohr’s major idea was that the energy of the atom was quantized, and that the amount of energy in the atom was related to the electron’s position in the atom • quantized means that the atom could only have very specific amounts of energy
Bohr’s Model • The electrons travel in orbits that are at a fixed distance from the nucleus • Energy Levels • therefore the energy of the electron was proportional to the distance the orbit was from the nucleus • Electrons emit radiation when they “jump” from an orbit with higher energy down to an orbit with lower energy • the emitted radiation was a photon of light • the distance between the orbits determined the energy of the photon of light produced
Bohr’s Model of Atom Example 7 Which of the following energy level changes in a hydrogen atom produces a visible spectral line? a. 3 → 1 b. 4 → 2 c. 5 → 3 d. all of the above
Rydberg’s Spectrum Analysis • Rydberg analyzed the spectrum of hydrogen and found that it could be described with an equation that involved an inverse square of integers
Bohr’s Model of Atom Energy-Level Postulate An electron can have only certain energy values, called energy levels. Energy levels are quantized. For an electron in a hydrogen atom, the energy is given by the following equation: RH = 2.179 10−18 J n = principal quantum number
Bohr’s Model of Atom The energy of the emitted or absorbed photon is related to DE: We can now combine these two equations:
Bohr’s Model of Atom Light is absorbed by an atom when the electron transition is from lower n to higher n (nf > ni). In this case, DE will be positive. Light is emitted from an atom when the electron transition is from higher n to lower n (nf< ni). In this case, DE will be negative. An electron is ejected when nf = ∞.
Example 8. What is the wavelength of the light emitted when the electron in a hydrogen atom undergoes a transition from n = 6 to n = 3? ni = 6 nf = 3 RH = 2.179 10−18 J = −1.816 10−19 J 1.094 10−6 m
Bohr’s Model of Atom Example 9 What is the frequency (in kHz ) of light emitted when the electron in a hydrogen atom undergoes a transition from level n = 6 to level n = 2? h = 6.63 × 10-34 J . s), RH = 2.179 × 10-18 J) a. 5.49 × 105 kHz b. 7. 31× 1011 kHz c. 7. 31 × 1014 kHz d. 3.64 × 10–28 kHz
Wave properties of Matter In 1923, Louis de Broglie, a French physicist, reasoned that particles (matter) might also have wave properties. The wavelength of a particle of mass, m (kg), and velocity, v (m/s), is given by the de Broglie relation:
Wave properties of Matter Example 10 Compare the wavelengths of (a) an electron traveling at a speed that is one-hundredth the speed of light and (b) a baseball of mass 0.145 kg having a speed of 26.8 m/s (60 mph). Baseball m = 0.145 kg v = 26.8 m/s Electron me = 9.11 10−31 kg v = 3.00 106 m/s
Electron me = 9.11 10−31 kg v = 3.00 106 m/s 2.43 10−10 m Baseball m = 0.145 kg v = 26.8 m/s 1.71 10−34 m
Quantum (or Wave) mechanics Building on de Broglie’s work, Erwin Schrodinger devised a theory that could be used to explain the wave properties of electrons in atoms and molecules. The branch of physics that mathematically describes the wave properties of submicroscopic particles is called or wave mechanics.