Photons, the photoelectric effect, Compton scattering, x-rays
Students should understand the nature and production of x-rays, so they can calculate the shortest wavelength of x-rays that may be produced by electrons accelerated through a specified voltage
AP Learning Objectives
ATOMIC AND NUCLEAR PHYSICS
Atomic physics and quantum effects
Atomic energy levels
Students should understand the concept of energy levels for atoms, so they can:
Calculate the energy or wavelength of the photon emitted or absorbed in a transition between specified levels, or the energy or wavelength required to ionize an atom.
Explain qualitatively the origin of emission or absorption spectra of gases.
Calculate the wavelength or energy for a single-step transition between levels, given the wavelengths or energies of photons emitted or absorbed in a two-step transition between the same levels.
Draw a diagram to depict the energy levels of an atom when given an expression for these levels, and explain how this diagram accounts for the various lines in the atomic spectrum.
AP Learning Objectives
ATOMIC AND NUCLEAR PHYSICS
Atomic physics and quantum effects
Students should understand the concept of de Broglie wavelength, so they can:
Calculate the wavelength of a particle as a function of its momentum.
Describe the Davisson-Germer experiment, and explain how it provides evidence for the wave nature of electrons
Table Of Contents
Rutherford Scattering and the Nuclear Atom
The Bohr Model of the Hydrogen Atom
De Broglie’s Expanation of Bohr’s Assumption about Angular Momentum
The Quantum Mechanical Picture of the Hydrogen Atom
The Pauli Exclusion Principle and the Periodic Table of the Elements
Medical Applications of the LASER
Chapter 30: The Nature of the Atom Section 1: Rutherford Scattering and the Nuclear Atom
Thompson Plum Pudding Model
Cathode Ray Tube
Negatively charged particles
Since the atom is neutral
Positive charges must also be present
Simplest distribution is random + and -
Rutherford Experiment A Rutherford scattering experiment.
Rutherford Nuclear Atom
Rutherford wanted to test if the atom was completely random or if it has some structure
Only way to explain results was very small collection of positive charges
Electrons still randomly around the nucleus.
If nucleus is the size of a nickel
Atomic radius of ~ 5 km
Bohr Model of the Atom
To explain discrete line spectra
Bohr said their must be fixed energy level in the atom
Those correspond to fixed radii of orbit for the electrons
Model works perfectly for Hydrogen
Fails to predict any other element
After input from several scientist
Schrodinger created a model based on standing waves
Mathematically it works, but tough to understand what the math means
Time Independent Eqn:
( x ) is wavefunction
V ( x ) potential energy function
E total energy of particle
Conceptual Example 1 Atoms are Mostly Empty Space In the planetary (Bohr) model of the atom, the nucleus (radius = 10 -15 m) is analogous to the sun (radius = 7x10 8 m). Electrons orbit (radius = 10 -10 m) the nucleus like the earth orbits (radius = 1.5x10 11 m) the sun. If the dimensions of the solar system had the same proportions as those of the atom, would the earth be closer to or farther away from the sun than it actually is? The Earth would need to be 10x farther from the sun than Pluto
30.1.1. Which one of the following statements concerning the plum-pudding model of the atom is false? a) Positive charge is spread uniformly throughout the plum-pudding model atom. b) Negative electrons are dispersed uniformly within the positively charged “pudding” within the plum-pudding model atom. c) There is no nucleus at the center of the plum-pudding model atom. d) The plum-pudding model was proven correct in experiments by Ernest Rutherford. e) The plum-pudding model was proposed by Joseph J. Thomson.
30.1.2. Which of the following atomic models is most representative of the current model of the atom? a) Wave model b) Thomson model c) Rutherford model d) Bohr model e) Witten model
30.1.3. Why was the observation of backscattered alpha particles so surprising to Rutherford in his experiment? a) He thought atoms were mostly empty space, which couldn’t scatter material particles. b) He realized that the positive charge must be concentrated in a very small region within the atom. c) He was trying to produce flashes of light on a zinc sulfide screen; and there were none. d) He thought alpha particles were waves that would simply be diffracted by the gold atoms. e) He was trying to produce lead from gold by using the alpha particles; and they weren’t absorbed by the gold.
Chapter 30: The Nature of the Atom Section 2: Line Spectra
Line Spectra The individual wavelengths emitted by two gases and the continuous spectrum of the sun.
The Line Spectrum of Hydrogen Lyman series Balmer series Paschen series
30.2.1. Experiments show that each element in the periodic table has a unique set of spectral lines. What is the best explanation for this observation? a) Each element has a unique nucleus. b) The number of electrons within each atom is unique. c) Each element has a unique set of interactions between its electrons and its protons. d) The motion of the electrons within each atom is unique. e) Each atom has a unique set of energy levels.
30.2.2. Using the planetary model of the atom, an electron is orbiting a nucleus with a speed of 0.02 c at a distance of 5 10 11 m. Since the electron is orbiting, it is also accelerating. What is the frequency of light emitted as the electron orbits? a) No light is emitted from the atom in this case. b) 1.91 10 16 Hz c) 9.55 10 15 Hz d) 3.04 10 15 Hz e) 2.15 10 15 Hz
30.2.3. What happens to an atom when it emits a photon? a) The mass of the atom increases. b) The mass of the atom remains the same. c) The mass of the atom decreases. d) The mass of the atom temporarily becomes negative.
Chapter 30: The Nature of the Atom Section 3: The Bohr Model of the Hydrogen Atom
Bohr Model of H Atom In the Bohr model, a photon is emitted when the electron drops from a larger, higher-energy orbit to a smaller, lower energy orbit.
The Energies and Radii of the Bohr Orbits
Bohr Model of H Atom Radii for Bohr orbits Angular momentum is quantized.
Bohr Model of H Atom Bohr energy levels
Energy Level Diagrams
Example 3 The Ionization Energy of Li 2+ Li 2+ is a lithium atom ( Z=3 ) with only one electron. Obtain the ionization energy of Li 2+ .
The Line Spectra of the H Atom
30.3.1. Which one of the following statements concerning the Bohr model is false? a) The Bohr model could accurately calculate the wavelengths of the spectral lines of hydrogen. b) The Bohr model explained why accelerating electrons did not radiate. c) The Bohr model accounted for the stability of the hydrogen atom. d) The Bohr model explained the relative intensities of various hydrogen spectral lines. e) The Bohr model could not accurately calculate the spectral lines of non-hydrogen atoms.
30.3.2. In the Bohr model, what is the angular momentum of the electron in the ground state of the hydrogen atom? a) zero b) h c) h / d) h /(2 ) e) any of the above values
30.3.3. Which of the following most closely resembles the Bohr model of the hydrogen atom? a) A solid metal sphere with a net positive charge. b) A hollow metal sphere with a net negative charge. c) A tray full of mud with pebbles uniformly distributed throughout. d) The Moon orbits the Earth. e) Two balls, one large and one small, connected by a spring.
30.3.4. Imagine an atom that has only four possible, discrete energy levels. Assuming that all transitions between these levels are allowed, how many spectral lines can this imaginary atom produce? a) 8 b) 7 c) 6 d) 5 e) more than 8
30.3.5. The figure shows an energy level diagram for the hydrogen atom. Several transitions are shown and are labeled by letters. Note : The diagram is not drawn to scale. Which transition corresponds to the absorption of the photon with the longest wavelength? a) A b) B c) C d) D e) E
30.3.6. The figure shows an energy level diagram for the hydrogen atom. Several transitions are shown and are labeled by letters. Note : The diagram is not drawn to scale. Which transition involves the longest wavelength line in the visible portion of the hydrogen spectrum? a) A b) B c) C d) D e) E
30.3.7. Which of the following statements concerning electromagnetic waves emitted from atoms is true? a) A collection of atoms emits electromagnetic radiation only at specific wavelengths. b) Atoms only emit radiation in the visible part of the electromagnetic spectrum. c) Free atoms have 3 n unique lines in their atomic spectra, where n is the number of electrons. d) The wavelengths of electromagnetic radiation emitted by free atoms is specifically characteristic of the particular element.
Chapter 30: The Nature of the Atom Section 4: De Broglie’s Expanation of Bohr’s Assumption about Angular Momentum
De Broglie Explanation De Broglie suggested standing particle waves as an explanation for Bohr’s angular momentum assumption.
30.4.1. What is the primary reason electrons occupy orbits with particular energies in atoms? a) The electric force acts only at particular distances. b) Electrons are particles that come in particular sizes. c) Electrons are limited by Heisenberg’s Uncertainty Principle to occupy only certain positions. d) The strong nuclear force determines the particular electron orbits. e) The particular orbit has a circumference that is an integer number of electron wavelengths.
30.4.2. Which one of the following assumptions did Bohr make in his model of the atom that was later confirmed by de Broglie? a) The electron orbital momentum is quantized. b) The charge of an electron is quantized. c) The wavelength of an electron is quantized. d) The electron orbit would be stable only if the circumference contained an integral number of electron wavelengths. e) The nucleus of the atom contains an integer number of protons and neutrons.
30.4.3. How did de Broglie interpret the nature of the electron in the Bohr model? a) The electron is a particle that orbits the nucleus much like a planet orbits the Sun. b) The electron is a particle wave and an integer number of its wavelength fit into the circumference of a given orbit. c) The electron helps to hold the nucleus together via the Coulomb force. d) All of the electrons within atoms occupy a single orbit. e) The electron in the hydrogen atom is always found in the ground state.
30.4.4. Why didn’t Bohr’s model of the atom yield completely accurate results? a) Bohr failed to treat the electron as a confined matter wave. b) The potential well is infinite only for the hydrogen atom. c) All atoms larger than hydrogen have neutrons. d) Bohr did not believe in quantum mechanics and didn’t include quantization in his model.
Chapter 30: The Nature of the Atom Section 5: The Quantum Mechanical Picture of the Hydrogen Atom
Quantum mechanics reveals that four different quantum
numbers are required to describe each state of the Hydrogen
The principal quantum number n. This number determines the
total energy of the atom and can have only integer values.
2. The orbital quantum number l. This number determines the orbital angular momentum of the electron integer values. angular momentum
Quantum Numbers 3. The magnetic quantum number m l . This number determines the effect of a magnetic field on the energy of the atom. z component of the angular momentum
The spin quantum number m s . This number is needed because
the electron has an intrinsic property called spin.
Example 5 The Bohr Model Versus Quantum Mechanics Determine the number of possible states for the hydrogen atom when the principal quantum number is (a) n=1 and (b) n=2.
Conceptual Example 6 The Bohr Model Versus Quantum Mechanics Consider two hydrogen atoms. There are no external magnetic fields present, and the electron in each atom has the same energy. According to the Bohr model and to quantum mechanics, is it possible for the electrons in these atoms (a) to have zero orbital angular momentum and (b) to have different angular momenta?
Bohr – no
Quantum Mechanics - Yes
b) Bohr – No Quantum Mechanics - Possibly
1 st Energy Level
2 nd Energy Level
30.5.1. Which one of the following statements concerning the electron in the ground state in a hydrogen atom is true within the quantum mechanical model of the atom? a) The ground state electron has zero ionization energy. b) The ground state electron has zero orbital angular momentum. c) The ground state electron has zero binding energy. d) The ground state electron has zero spin angular momentum. e) The ground state electron has zero kinetic energy.
30.5.2. A hydrogen atom is in a state for which the principle quantum number is n = 2. How many possible states are there for which the magnetic quantum number is equal to one? a) zero b) one c) two d) four e) six
30.5.3. A hydrogen atom is in a state for which the principle quantum number is six and the magnetic quantum number is three. What are the possible values for the orbital quantum number? a) 0 or 3 only b) 3 or 5 only c) 4 or 6 only d) 3, 4, or 5 only e) 4, 5, or 6 only
30.5.4. Which one of the following sets of quantum numbers is not possible? n l m l m s a) 2 3 2 +1/2 b) 4 3 +2 +1/2 c) 3 1 0 1/2 d) 6 2 1 +1/2 e) 5 4 4 1/2
30.5.5. An electron in a hydrogen atom is described by the quantum numbers: n = 8 and . What are the possible values for the orbital quantum number ? a) only 0 or 4 b) only 4 or 7 c) only 5 or 8 d) only 5, 6, 7, or 8 e) only 4, 5, 6, or 7
30.5.6. Which one of the following values of is not possible for = 2? a) zero b) 1 c) +1 d) +2 e) +3
30.5.7. For a given principal quantum number, can the angular momentum ever have a value of zero? a) While the Bohr model indicates the answer is “no,” quantum mechanics allows a value of zero. b) Both the Bohr model and quantum mechanics indicate the answer is “yes.” c) While quantum mechanics indicates the answer is “yes,” the Bohr model allows a value of zero. d) Both the Bohr model and quantum mechanics indicate the answer is “no.”
Chapter 30: The Nature of the Atom Section 6: The Pauli Exclusion Principle and the Periodic Table of the Elements
Electron Configuration Rules
Electrons will usually fill the lowest energy level present
Electrons will try to maximize the number of half-filled equal energy orbitals
NYC Subway rule
If the seats are equal
Sit by yourself before you sit with strangers
Pauli Exclusion Principle
No two electrons in an atom can have the same set of values for the four quantum numbers.
Maximum of 2 electrons in any given orbital
Example 8 Ground States of Atoms Determine which of the energy levels in the figure are occupied by the electrons in the ground state of hydrogen, helium, lithium, beryllium, and boron.
30.6.1. Which one of the following subshells is not compatible with a principle quantum number of n = 4? a) d b) f c) g d) p e) s
30.6.2. A neutral atom has the following electronic configuration: 1s 2 2s 2 2p 6 3s 2 3p 5 . How many electrons are in the L shell of this atom? a) 2 b) 4 c) 6 d) 7 e) 8
30.6.3. A neutral atom has the following electronic configuration: 1s 2 2s 2 2p 5 . How many protons are in the nucleus of this atom? a) 3 b) 5 c) 9 d) 16 e) There is no way to tell from an electron configuration.
30.6.4. Determine the maximum number of electron states with principal quantum number n = 3? a) 2 b) 3 c) 6 d) 9 e) 18
30.6.5. The ground state electronic configuration of a neon atom is 1s 2 2s 2 2p 6 . How many of these electrons have magnetic quantum number m l = 0? a) 2 b) 4 c) 6 d) 8 e) 10
30.6.6. Consider the following list of electron configurations: (1) 1s 2 2s 2 3s 2 (4) 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 (2) 1s 2 2s 2 2p 6 (5) 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 6 (3) 1s 2 2s 2 2p 6 3s 1 Which electronic configuration is characteristic of noble gases? a) 1 b) 2 c) 3 d) 4 e) 5
Chapter 30: The Nature of the Atom Section 7: X-Rays
X-Rays Electrons are emitted from a heated filament and accelerated through a large voltage. When they strike the target, X-rays are emitted.
X-Rays The sharp peaks are called characteristic X-rays because they are characteristic of the target material.
30.7.1. Which one of the following statements concerning the cutoff wavelength typically exhibited in X-ray spectra is true? a) The cutoff wavelength depends on the instrument used to detect the X-rays. b) The cutoff wavelength depends on the target material. c) The cutoff wavelength occurs because an incident electron cannot give up all of its energy. d) The cutoff wavelength occurs because of the mutual shielding effects of K-shell electrons. e) The cutoff wavelength depends on the potential difference across the X-ray tube.
30.7.2. Consider the two graphs shown that are labeled A and B for X-ray intensity per unit wavelength versus wavelength. Which of the following statements is true? a) The X-ray tubes are operating at different potential differences. b) The X-ray tubes contain different elements. c) The X-ray tubes are identical. d) The tube represented by graph B is operating at a higher potential difference than the tube represented by graph A. e) All of the above statements are true.
Chapter 30: The Nature of the Atom Section 8: The LASER
The LASER Spontaneous emission versus stimulated emission. L ight A mplification by the S timulated E mission of R adiation
The LASER An external energy source populates the higher level with electrons.
30.8.1. Which one of the following statements best explains why a neon sign does not emit visible light after it is turned off? a) All of the neon atoms have principle quantum number n = 0. b) All of the neon atoms are ionized. c) None of the neon atoms are in the n = 2 state. d) Most of the neon atoms are in the ground state. e) Only some of the neon atoms have returned to the n = 1 state.
30.8.2. An electron makes a transition from a higher energy state to a lower one without any external provocation. As a result of the transition, a photon is emitted and moves in a random direction. What is the name of this emission process? a) stationary emission b) spontaneous emission c) spectral emission d) stimulated emission e) specular emission
Chapter 30: The Nature of the Atom Section 9: Medical Applications of the LASER
Medical Uses of LASERs Lasers being used to change the shape of the cornea.
Chapter 30: The Nature of the Atom Section 10: Holography