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Atomic Physics

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Abraham Sikaffy

on 22 April 2013

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Transcript of Atomic Physics

Explain how Planck resolved the ultraviolet catastrophe in blackbody radiation.

Calculate energy of quanta using Planck’s equation.

Solve problems involving maximum kinetic energy, work function, and threshold frequency in the photoelectric effect. Objectives Chapter 21 Section 1 Quantization of Energy Chapter 21 Section 2 Models of the Atom Emission and Absorption Spectra of Hydrogen Section 1 Quantization of Energy Chapter 21 The Photoelectric Effect Chapter 21 4. What type of spectrum is created by applying a high potential difference to a pure atomic gas?
A. an emission spectrum Chapter 21 1. According to Einstein’s photon theory of light, what does the intensity of light shining on a metal determine?
A. the number of photons hitting the metal in a given time interval Chapter 21 Because the electron’s location cannot be precisely determined, it is useful to discuss the probability of finding the electron at different locations.
The diagram shows the probability per unit distance of finding the electron at various distances from the nucleus in the ground state of hydrogen. Section 3 Quantum Mechanics The Electron Cloud Chapter 21 In 1927, Werner Heisenberg argued that it is fundamentally impossible to make simultaneous measurements of a particle’s position and momentum with infinite accuracy.
In fact, the more we learn about a particle’s momentum, the less we know of its position, and the reverse is also true.
This principle is known as Heisenberg’s uncertainty principle. Section 3 Quantum Mechanics The Uncertainty Principle Chapter 21 Section 3 Quantum Mechanics In 1924, the French physicist Louis de Broglie (1892–1987) extended the wave-particle duality. De Broglie proposed that all forms of matter may have both wave properties and particle properties.

Three years after de Broglie’s proposal, C. J. Davisson and L. Germer, of the United States, discovered that electrons can be diffracted by a single crystal of nickel. This important discovery provided the first experimental confirmation of de Broglie’s theory. Matter Waves Chapter 21 Section 3 Quantum Mechanics As seen earlier, there is considerable evidence for the photon theory of light. In this theory, all electromagnetic waves consist of photons, particle-like pulses that have energy and momentum.
On the other hand, light and other electromagnetic waves exhibit interference and diffraction effects that are considered to be wave behaviors.
So, which model is correct? Chapter 21 Section 3 Quantum Mechanics *Recognize the dual nature of light and matter.

*Calculate the de Broglie wavelength of matter waves.

*Distinguish between classical ideas of measurement
and Heisenberg’s uncertainty principle.

*Describe the quantum-mechanical picture of the atom, including the electron cloud and probability waves. Objectives Chapter 21 4. Evaluate your answer.
Line 3 is in the visible part of the electromagnetic spectrum and appears to be blue. The frequency f = 6.15  1014 Hz lies within the range of the visible spectrum and is toward the violet end, so it is reasonable that light of this frequency would be visible blue light. Section 2 Models of the Atom Sample Problem, continued Chapter 21 Section 2 Models of the Atom Tip: Note that the energies for each energy level are negative. The reason is that the energy of an electron in an atom is defined with respect to the amount of work required to remove the electron from the atom. In some energy-level diagrams, the energy of E1 is defined as zero, and the higher energy levels are positive.

In either case, the difference between a higher energy level and a lower one is always positive, indicating that the electron loses energy when it drops to a lower level. Sample Problem, continued Chapter 21 Section 2 Models of the Atom Find the energy of the photon.
The energy of the photon is equal to the change in the energy of the electron. The electron’s initial energy level was E4, and the electron’s final energy level was E2. Using the values from the energy-level diagram gives the following:

E = Einitial – Efinal = E4 – E2
E = (–0.850 eV) – (–3.40 eV) = 2.55 eV Sample Problem, continued Chapter 21 Section 2 Models of the Atom Rutherford concluded that all of the positive charge in an atom and most of the atom’s mass are found in a region that is small compared to the size of the atom.
He called this region the the nucleus of the atom.
Any electrons in the atom were assumed to be in the relatively large volume outside the nucleus. Early Models of the Atom Chapter 21 *Explain the strengths and weaknesses of Rutherford’s model of the atom.

*Recognize that each element has a unique emission and absorption spectrum.

*Explain atomic spectra using Bohr’s model of the atom.

*Interpret energy-level diagrams. Objectives Section 2 Models of the Atom Section 1 Quantization of Energy Chapter 21 No electrons are emitted if the frequency of the incoming light falls below a certain frequency, called the threshold frequency (ft).

The smallest amount of energy the electron must have to escape the surface of a metal is the work function of the metal.

The work function is equal to hft. The Photoelectric Effect, continued Section 1 Quantization of Energy Chapter 21 The photoelectric effect is the emission of electrons from a material surface that occurs when light of certain frequencies shines on the surface of the material.
Classical physics cannot explain the photoelectric effect.
Einstein assumed that an electromagnetic wave can be viewed as a stream of particles called photons. Photon theory accounts for observations of the photoelectric effect. The Photoelectric Effect Section 1 Quantization of Energy If Planck’s constant is expressed in units of J•s, the equation E = hf gives the energy in joules.
However, in atomic physics, energy is often expressed in units of the electron volt, eV.
An electron volt is defined as the energy that an electron or proton gains when it is accelerated through a potential difference of 1 V.
The relation between the electron volt and the joule is as follows:
1 eV = 1.60  10^–19 J Quantum Energy Chapter 21 Section 1 Quantization of Energy The graph on the left shows the intensity of blackbody radiation at three different temperatures. Classical theory’s prediction for blackbody radiation (the blue curve) did not correspond to the experimental data (the red data points) at all wavelengths, whereas Planck’s theory (the red curve) did. Blackbody Radiation Chapter 21 Section 1 Quantization of Energy Chapter 21 The ultraviolet catastrophe is the failed prediction of classical physics that the energy radiated by a blackbody at extremely short wavelengths is extremely large and that the total energy radiated is infinite.

Max Planck (1858–1947) developed a formula for blackbody radiation that was in complete agreement with experimental data at all wavelengths by assuming that energy comes in discrete units, or is quantized. Blackbody Radiation, continued Chapter 21 Chapter 21 Standardized Test Prep 16. Describe Bohr’s model of the atom. Identify the assumptions that Bohr made that were a departure from those of classical physics. Explain how Bohr’s model accounts for atomic spectra.
Answer: Answers should describe electrons orbiting a nucleus only in discrete energy levels. The model departs from classical physics in that the electrons are only allowed to have certain energies and they do not lose energy simply by moving in an electromagnetic field. Atomic spectra are the result of photons being emitted or absorbed when electrons jump between energy levels. Extended Response Chapter 21 Standardized Test Prep 11. What is the speed of a proton (m = 1.67  10–27 kg) with a de Broglie wavelength of 4.00  10–14 m?
A. 1.59  10–30 m/s
B. 1.01  10–7 m/s
C. 9.93  106 m/s
D. 1.01  107 m/s Multiple Choice, continued Chapter 21 5. What type of spectrum is used to identify elements in the atmospheres of stars?

A. an absorption spectrum 7. What is the frequency of the photon emitted when an electron jumps from E5 to E2?
A. 2.86 eV
B. 6.15  1014 Hz
C. 6.90  1014 Hz
D. 4.31  1033 Hz Chapter 21 Standardized Test Prep Use the energy-level diagram for hydrogen to answer
questions 7–8. Chapter 21 *Quantum mechanics also predicts that the electron can be found in a spherical region surrounding the nucleus.
*This result is often interpreted by viewing the electron as a cloud surrounding the nucleus.
*Analysis of each of the energy levels of hydrogen reveals that the most probable electron location in each case is in agreement with each of the radii predicted by the Bohr theory. Section 3 Quantum Mechanics The Electron Cloud, continued Chapter 21 As seen by this equation, the larger the momentum of an object, the smaller its wavelength. Section 3 Quantum Mechanics The wavelength of a photon is equal to Planck’s constant (h) divided by the photon’s momentum (p). De Broglie speculated that this relationship might also hold for matter waves, as follows: Matter Waves, continued Chapter 21 Section 3 Quantum Mechanics Some experiments can be better explained or only explained by the photon concept, whereas others require a wave model.
Most physicists accept both models and believe that the true nature of light is not describable in terms of a single classical picture.
At one extreme, the electromagnetic wave description suits the overall interference pattern formed by a large number of photons.
At the other extreme, the particle description is more suitable for dealing with highly energetic photons of very short wavelengths. The Dual Nature of Light Chapter 21 The Bohr Model Section 2 Models of the Atom Bohr’s model was not considered to be a complete picture of the structure of the atom.
Bohr assumed that electrons do not radiate energy when they are in a stable orbit, but his model offered no explanation for this.
Another problem with Bohr’s model was that it could not explain why electrons always have certain stable orbits
For these reasons, scientists continued to search for a new model of the atom. Chapter 21 2. Use Planck’s equation to find the frequency. Section 2 Models of the Atom Tip: Note that electron volts were converted to joules so that the units cancel properly. Sample Problem, continued Chapter 21 Section 2 Models of the Atom Interpreting Energy-Level Diagrams
An electron in a hydrogen atom drops from energy level E4 to energy level E2. What is the frequency of the emitted photon, and which line in the emission spectrum corresponds to this event? Sample Problem Chapter 21 When this occurs, an electron jumps from a lower energy state to a higher energy state, which corresponds to an orbit farther from the nucleus.
This is called an excited state. The absorbed photons account for the dark lines in the absorption spectrum. Section 2 Models of the Atom When light of a continuous spectrum shines on the atom, only the photons whose energy (hf ) matches the energy separation between two levels can be absorbed by the atom. The Bohr Model, continued Chapter 21 Section 2 Models of the Atom In 1913, the Danish physicist Niels Bohr (1885–1962) proposed a new model of the hydrogen atom that explained atomic spectra.
In Bohr’s model, only certain orbits are allowed. The electron is never found between these orbits; instead, it is said to “jump” instantly from one orbit to another.
In Bohr’s model, transitions between stable orbits with different energy levels account for the discrete spectral lines. The Bohr Model of the Hydrogen Atom Chapter 21 However, accelerated charges should radiate electromagnetic waves, losing energy. This would lead to a rapid collapse of the atom.
This difficulty led scientists to continue searching for a new model of the atom. Section 2 Models of the Atom To explain why electrons were not pulled into the nucleus, Rutherford viewed the electrons as moving in orbits about the nucleus. Early Models of the Atom Section 1 Quantization of Energy Chapter 21 If light behaves like a particle, then photons should have momentum as well as energy; both quantities should be conserved in elastic collisions.
The American physicist Arthur Compton directed X rays toward a block of graphite to test this theory.
He found that the scattered waves had less energy and longer wavelengths than the incoming waves, just as he had predicted.
This change in wavelength, known as the Compton shift, supports Einstein’s photon theory of light. Compton Shift Section 1 Quantization of Energy Chapter 21 maximum kinetic energy of a photoelectron
KEmax = hf – hft
maximum kinetic energy = (Planck’s constant  frequency of incoming photon) – work function Because energy must be conserved, the maximum kinetic energy (of photoelectrons ejected from the surface) is the difference between the photon energy and the work function of the metal. The Photoelectric Effect, continued Chapter 21 De Broglie saw a connection between his theory of matter waves and the stable orbits in the Bohr model. Section 3 Quantum Mechanics He assumed that an electron orbit would be stable only if it contained an integral (whole) number of electron wavelengths. Matter Waves, continued Chapter 21 The dual nature of matter suggested by de Broglie is quite apparent in the wavelength and frequency equations, both of which contain particle concepts (E and mv) and wave concepts (l and f). Section 3 Quantum Mechanics In an analogy with photons, de Broglie postulated that the frequency of a matter wave can be found with Planck’s equation, as illustrated below: Matter Waves, continued Chapter 21 Examination of the diagram shows that the electron’s jump from energy level E4 to energy level E2 corresponds to Line 3 in the emission spectrum. Find the corresponding line in the emission spectrum. Section 2 Models of the Atom Sample Problem, continued Chapter 21 The emitted photons are responsible for the bright lines in the emission spectrum.
In both cases, there is a correlation between the “size” of an electron’s jump and the energy of the photon. Section 2 Models of the Atom Once an electron is in an excited state, there is a certain probability that it will jump back to a lower energy level by emitting a photon.
This process is called spontaneous emission. The Bohr Model, continued Chapter 21 Section 2 Models of the Atom An element can also absorb light at specific wavelengths.
The spectral lines corresponding to this process form what is known as an absorption spectrum.
An absorption spectrum can be seen by passing light containing all wavelengths through a vapor of the element being analyzed.
Each line in the absorption spectrum of a given element coincides with a line in the emission spectrum of that element. Atomic Spectra Chapter 21 A diagram or graph that indicates the wavelengths of radiant energy that a substance emits is called an emission spectrum.
Every element has a distinct emission spectrum. Section 2 Models of the Atom When the light given off by an atomic gas is passed through a prism, a series of distinct bright lines is seen. Each line corresponds to a different wavelength, or color. Atomic Spectra Chapter 21 Most of the alpha particles passed through the foil. Some were deflected through very large angles. Section 2 Models of the Atom Ernest Rutherford (1871–1937) later proved that Thomson’s model could not be correct.
In his experiment, a beam of positively charged alpha particles was projected against a thin metal foil. Early Models of the Atom Chapter 21 Section 2 Models of the Atom The model of the atom in the days of Newton was that of a tiny, hard, indestructible sphere.
The discovery of the electron in 1897 prompted J. J. Thomson (1856–1940) to suggest a new model of the atom.
In Thomson’s model, electrons are embedded in a spherical volume of positive charge like seeds in a watermelon. Early Models of the Atom Section 1 Quantization of Energy The energy of a light quantum, which corresponds to the energy difference between two adjacent levels, is given by the following equation: E = hf
energy of a quantum = Planck’s constant  frequency
Planck’s constant (h) ≈ 6.63  10–34 J•s Einstein later applied the concept of quantized energy to light. The units of light energy called quanta (now called photons) are absorbed or given off as a result of electrons “jumping” from one quantum state to another. Quantum Energy Chapter 21 Chapter 21 A blackbody is a perfect radiator and absorber and emits radiation based only on its temperature. Light enters this hollow object through the small opening and strikes the interior wall. Some of the energy is absorbed, but some is reflected at a random angle. After many reflections, essentially all of the incoming energy is absorbed by the cavity wall. Section 1 Quantization of Energy Physicists study blackbody radiation by observing a hollow object with a small opening, as shown in the diagram. Blackbody Radiation 8. What frequency of photon would be absorbed when an electron jumps from E2 to E3?
F. 1.89 eV
G. 4.56  1014 Hz
H. 6.89  1014 Hz
J. 2.85  1033 Hz Chapter 21 Standardized Test Prep Use the energy-level diagram for hydrogen to answer
questions 7–8. Multiple Choice, continued Atomic Physics The Dual Nature of Light http://prezi.com/user/sikaffy/
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