Chapter 30

The Nature of the Atom

AP Learning ObjectivesATOMIC AND NUCLEAR PHYSICS Atomic physics and quantum effects

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 ObjectivesATOMIC AND NUCLEAR PHYSICS Atomic physics and quantum effects

Atomic energy levelsStudents 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 ObjectivesATOMIC AND NUCLEAR PHYSICS Atomic physics and quantum effects

Wave-particle dualityStudents 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 Contents1. Rutherford Scattering and the Nuclear Atom2. Line Spectra3. The Bohr Model of the Hydrogen Atom4. De Broglie’s Expanation of Bohr’s Assumption about

Angular Momentum5. The Quantum Mechanical Picture of the Hydrogen

Atom6. The Pauli Exclusion Principle and the Periodic Table

of the Elements7. X-Rays8. The LASER9. Medical Applications of the LASER10. Holography

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 -

A Rutherford scattering experiment.

Rutherford 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

Quantum Model 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

xExxVdx

xd

m

2

22

2

ft

xAtx

sin,

Conceptual Example 1 Atoms are Mostly Empty Space

In the planetary (Bohr) model of the atom, the nucleus (radius = 10-15m) is analogous to the sun (radius = 7x108m). Electrons orbit (radius = 10-10m) the nucleus like the earth orbits(radius = 1.5x1011m) the sun. If the dimensions of the solar systemhad 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

The individual wavelengths emitted by two gases and thecontinuous spectrum of the sun.

Line Spectra

Lyman series

Balmer series

Paschen series

,4,3,2 1

1

1122

n

nR

,5,4,3 1

2

1122

n

nR

,6,5,4 1

3

1122

n

nR

The Line Spectrum of Hydrogen

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 0.02c at a distance of 5 1011 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 1016 Hz

c) 9.55 1015 Hz

d) 3.04 1015 Hz

e) 2.15 1015 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

In the Bohr model, a photon is emitted when the electron dropsfrom a larger, higher-energy orbit to a smaller, lower energyorbit.

hfEE fi

Bohr Model of H Atom

r

kZe

r

kZemv

E

2

EPEKE

2

22

21

The Energies and Radii of the Bohr Orbits

,3,2,1 2

nh

nrmvL nnn

,3,2,1 4

2

22

2

n

Z

n

mke

hrn

,3,2,1 m1029.52

11 nZ

nrn

Radii for Bohr orbits

Angular momentum is quantized.

Bohr Model of H Atom

,3,2,1 2

2

2

2

422

n

n

Z

h

emkEn

,3,2,1 J1018.22

218 n

n

ZEn

,3,2,1 eV 6.132

2

nn

ZEn

Bohr energy levels

Bohr Model of H Atom

Energy Level Diagrams

Example 3 The Ionization Energy of Li2+

Li2+ is a lithium atom (Z=3) with only one electron. Obtain the ionizationenergy of Li2+.

eV 1221

3eV 6.13eV 6.13

2

2

2

2

n

ZEn

eV 122energy Ionization

fifi

if

nnnn

nnch

emk

,3,2,1,

11

Z 21

222

3

422

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 3n 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 suggested standing particle waves as an explanationfor Bohr’s angular momentum assumption.

,3,2,1 2 nnr

De Broglie Explanation

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 Hydrogenatom.

1. The principal quantum number n. This number determines the total energy of the atom and can have only integer values.

,3,2,1 n

2. The orbital quantum number l. This number determines the orbital angular momentum of the electron integer values.

1,,3,2,1 n

2

1h

L angular momentum

Quantum Numbers

3. The magnetic quantum number ml. This number determines the effect of a magnetic field on the energy of the atom.

,,2,1,0,1,2,m

2

hmLz

z componentof the angularmomentum

4. The spin quantum number ms. This number is needed becausethe electron has an intrinsic property called spin.

21

21 or sm

Quantum Numbers

Quantum Numbers

Example 5 The Bohr Model Versus Quantum Mechanics

Determine the number of possible states for the hydrogen atomwhen the principal quantum number is (a) n=1 and (b) n=2.

Solution

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?

a) Bohr – noQuantum Mechanics - Yes

b) Bohr – No Quantum Mechanics - Possibly

1st Energy Level

2nd Energy Level

S Orbitals

2p orbitals

3p Orbitals

3d orbitals

4p Orbitals

4d orbitals

4f orbitals

5g orbitals

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 ml ms

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

4m

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

m

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 Aufbau

Electrons will usually fill the lowest energy level present

Hund’s Rule 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 bythe electrons in the ground state of hydrogen, helium, lithium,beryllium, and boron.

Sample Configurations

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: 1s22s22p63s23p5. 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: 1s22s22p5. 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 1s2 2s2 2p6. How many of these electrons have magnetic quantum number ml = 0?

a) 2

b) 4

c) 6

d) 8

e) 10

30.6.6. Consider the following list of electron configurations:(1) 1s2 2s2 3s2 (4) 1s2 2s2 2p6 3s2 3p6 4s2 (2) 1s2 2s2 2p6 (5) 1s2 2s2 2p6 3s2 3p6 4s2 3d6

(3) 1s2 2s2 2p6 3s1

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

Electrons are emitted from a heated filament and acceleratedthrough a large voltage.

When they strike the target, X-raysare emitted.

X-Rays

The sharp peaks are called characteristic X-rays because they arecharacteristic of the target material.

X-Rays

CT Scans

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

Spontaneous emission versus stimulated emission.

The LASER

LightAmplification by theStimulatedEmission of Radiation

An external energy sourcepopulates the higher levelwith electrons.

The LASER

The LASER

The LASER

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

Lasers being used to change the shape of the cornea.

Medical Uses of LASERs

LASIK Surgery

Chapter 30:The Nature of the Atom

Section 10:Holography

Holography

Holography

Holography