ap-physics-b-review-modern-physics modern physicis review

1. AP Phys B
Test Review
Modern Physics
5/9/2008

2. Overview
 Basics
 Photoelectric Effect
 Bohr Model of the atom
• Energy Transitions
 Nuclear Physics

3. Basics
 Quantization: the idea that light and
matter come in discreet, indivisible
packets
• Wave-particle duality in light and matter
• Matter behaves both as a wave and as a
particle.

4. Energy of a photon
 Blackbody radiation
• Ultraviolet catastrophe
• Planck came up with the idea that light is emitted by
certain discreet resonators that emit energy packets
called photons
• This energy is given by:
E h= ν

5. Photoelectric Effect Schematic
 When light strikes E,
photoelectrons are emitted
 Electrons collected at C and
passing through the ammeter
are a current in the circuit
 C is maintained at a positive
potential by the power supply

6. Photoelectric Current/Voltage
Graph
 The current increases with
intensity, but reaches a
saturation level for large ΔV’s
 No current flows for voltages
less than or equal to –ΔVs, the
stopping potential
• The stopping potential is
independent of the radiation
intensity

7. Features Not Explained by
Classical Physics/Wave Theory
 No electrons are emitted if the incident light
frequency is below some cutoff frequency that is
characteristic of the material being illuminated
 The maximum kinetic energy of the photoelectrons is
independent of the light intensity
 The maximum kinetic energy of the photoelectrons
increases with increasing light frequency
 Electrons are emitted from the surface almost
instantaneously, even at low intensities

8. Einstein’s Explanation
 A tiny packet of light energy, called a photon, would
be emitted when a quantized oscillator jumped from
one energy level to the next lower one
• Extended Planck’s idea of quantization to
electromagnetic radiation
 The photon’s energy would be E = hƒ
 Each photon can give all its energy to an electron in
the metal
 The maximum kinetic energy of the liberated
photoelectron is
KE = hƒ – Φ

9. Explanation of Classical
“Problems”
 The effect is not observed below a certain cutoff
frequency since the photon energy must be greater
than or equal to the work function
• Without this, electrons are not emitted, regardless
of the intensity of the light
 The maximum KE depends only on the frequency
and the work function, not on the intensity
 The maximum KE increases with increasing
frequency
 The effect is instantaneous since there is a one-to-
one interaction between the photon and the electron

10. Verification of Einstein’s Theory
 Experimental
observations of a
linear relationship
between KE and
frequency confirm
Einstein’s theory
 The x-intercept is the
cutoff frequency
cf
h
Φ
=

11. 27.4 X-Rays
 Electromagnetic radiation with short
wavelengths
• Wavelengths less than for ultraviolet
• Wavelengths are typically about 0.1 nm
• X-rays have the ability to penetrate most
materials with relative ease
 Discovered and named by Roentgen in
1895

12. Production of X-rays
 X-rays are produced
when high-speed
electrons are suddenly
slowed down
• Can be caused by the
electron striking a metal
target
 A current in the
filament causes
electrons to be emitted

13. Production of X-rays
 An electron passes
near a target nucleus
 The electron is
deflected from its
path by its attraction
to the nucleus
 It will emit
electromagnetic
radiation when it is
accelerated

14. 27.8 Photons and
Electromagnetic Waves
 Light has a dual nature. It exhibits both wave
and particle characteristics
• Applies to all electromagnetic radiation
 The photoelectric effect and Compton
scattering offer evidence for the particle nature
of light
• When light and matter interact, light behaves as if it
were composed of particles
 Interference and diffraction offer evidence of
the wave nature of light

15. 28.9 Wave Properties of
Particles
 In 1924, Louis de Broglie postulated that because
photons have wave and particle characteristics,
perhaps all forms of matter have both properties
 The de Broglie wavelength of a particle is
 The frequency of matter waves is
mv
h
=λ
h
E
=ƒ

16. The Davisson-Germer
Experiment
 They scattered low-energy electrons from a
nickel target
 The wavelength of the electrons calculated
from the diffraction data agreed with the
expected de Broglie wavelength
 This confirmed the wave nature of electrons
 Other experimenters have confirmed the wave
nature of other particles

17. 27.10 The Wave Function
 In 1926 Schrödinger proposed a wave equation that
describes the manner in which matter waves change
in space and time
 Schrödinger’s wave equation is a key element in
quantum mechanics
 Schrödinger’s wave equation is generally solved for
the wave function, Ψ
i H
t
∆Ψ
= Ψ
∆

18. The Wave Function
 The wave function depends on the
particle’s position and the time
 The value of |Ψ|2
at some location at a
given time is proportional to the
probability of finding the particle at that
location at that time

19. 27.11 The Uncertainty Principle
 When measurements are made, the
experimenter is always faced with
experimental uncertainties in the
measurements
• Classical mechanics offers no fundamental
barrier to ultimate refinements in
measurements
• Classical mechanics would allow for
measurements with arbitrarily small
uncertainties

20. The Uncertainty Principle
 Quantum mechanics predicts that a barrier to
measurements with ultimately small
uncertainties does exist
 In 1927 Heisenberg introduced the uncertainty
principle
• If a measurement of position of a particle is made
with precision Δx and a simultaneous measurement
of linear momentum is made with precision Δp, then
the product of the two uncertainties can never be
smaller than h/4π

21. The Uncertainty Principle
 Mathematically,
 It is physically impossible to measure
simultaneously the exact position and the
exact linear momentum of a particle
 Another form of the principle deals with
energy and time:
π
≥∆∆
4
h
px x
π
≥∆∆
4
h
tE

22. Early Models of the Atom
 Rutherford’s model
• Planetary model
• Based on results of
thin foil experiments
• Positive charge is
concentrated in the
center of the atom,
called the nucleus
• Electrons orbit the
nucleus like planets
orbit the sun

23. Experimental tests
Expect:
1. Mostly small
angle scattering
2. No backward
scattering events
Results:
1. Mostly small
scattering events
2. Several
backward
scatterings!!!

24. Difficulties with the Rutherford
Model
 Atoms emit certain discrete characteristic
frequencies of electromagnetic radiation
• The Rutherford model is unable to explain this
phenomena
 Rutherford’s electrons are undergoing a centripetal
acceleration and so should radiate electromagnetic
waves of the same frequency
• The radius should steadily decrease as this
radiation is given off
• The electron should eventually spiral into the
nucleus

25. 28.2 Emission Spectra
 A gas at low pressure
has a voltage applied to it
 When the emitted light is
analyzed with a
spectrometer, a series of
discrete bright lines is
observed
• Each line has a different
wavelength and color

26. Emission Spectrum of Hydrogen
 The wavelengths of hydrogen’s spectral lines can
be found from
• RH is the Rydberg constant
• RH = 1.0973732 x 107
m-1
• n is an integer, n = 1, 2, 3, …
• The spectral lines correspond to
different values of n
 A.k.a. Balmer series






−=
λ 22H
n
1
2
1
R
1

27. Absorption Spectra
 An element can also absorb light at specific
wavelengths
 An absorption spectrum can be obtained by
passing a continuous radiation spectrum through a
vapor of the gas
 The absorption spectrum consists of a series of
dark lines superimposed on the otherwise
continuous spectrum
• The dark lines of the absorption spectrum coincide with the
bright lines of the emission spectrum

28. 28.3 The Bohr Theory of
Hydrogen
 In 1913 Bohr provided an explanation of
atomic spectra that includes some features of
the currently accepted theory
 His model includes both classical and non-
classical ideas
 His model included an attempt to explain why
the atom was stable

29. Bohr’s Assumptions for
Hydrogen
 The electron moves in circular orbits
around the proton under the influence of
the Coulomb force of attraction
 Only certain electron orbits are stable
• These are the orbits in which the atom
does not emit energy in the form of
electromagnetic radiation
• Therefore, the energy of the atom
remains constant and classical
mechanics can be used to describe the
electron’s motion
 Radiation is emitted by the atom when the
electron “jumps” from a more energetic
initial state to a lower state
• The “jump” cannot be treated
classically
i fE E hf− =

30. Bohr’s Assumptions
 More on the electron’s “jump”:
• The frequency emitted in the “jump” is related
to the change in the atom’s energy
• It is generally not the same as the frequency
of the electron’s orbital motion
 The size of the allowed electron orbits is determined
by a condition imposed on the electron’s orbital
i fE E hf− = , 1,2,3,...
2
e
h
m vr n n
π
 
= = ÷
 

31. Results
 The total energy of the atom
•
 Newton’s law
 This can be used to rewrite kinetic energy as
2
21
2
e e
e
E KE PE m v k
r
= + = −
r2
ek
E
2
e
−=
2 2
2e e e
e v
F m a or k m
r r
= =
2 2
2 2
e
mv e
KE k
r
≡ =

32. Bohr Radius
 The radii of the Bohr orbits are quantized
• This shows that the electron can only exist in
certain allowed orbits determined by the integer n
•When n = 1, the orbit has the smallest radius,
called the Bohr radius, ao
•ao = 0.0529 nm


,3,2,1n
ekm
n
r 2
ee
22
n ==
2
h
π=

33. Radii and Energy of Orbits
 A general expression for the radius of
any orbit in a hydrogen atom is
• rn = n2
ao
 The energy of any orbit is
• En = - 13.6 eV/ n2
 The lowest energy state is called the
ground state
• This corresponds to n = 1
• Energy is –13.6 eV
 The next energy level has an energy of –
3.40 eV
 The ionization energy is the energy
needed to completely remove the
electron from the atom

34. Energy Level Diagram
 The value of RH from Bohr’s analysis is in
excellent agreement with the experimental
value
 A more generalized equation can be used to
find the wavelengths of any spectral lines
• For the Balmer series, nf = 2
• For the Lyman series, nf = 1
 Whenever a transition occurs between a
state, ni and another state, nf (where ni > nf),
a photon is emitted






−=
λ 2
i
2
f
H
n
1
n
1
R
1

35. Quantum Number Summary
 The values of n can increase from 1 in integer steps
 The values of ℓ can range from 0 to n-1 in integer steps
 The values of mℓ can range from -ℓ to ℓ in integer steps

36. Atomic Transitions – Energy
Levels
 An atom may have
many possible energy
levels
 At ordinary
temperatures, most of
the atoms in a sample
are in the ground state
 Only photons with
energies corresponding
to differences between
energy levels can be
absorbed

37. Atomic Transitions – Stimulated
Absorption
 The blue dots represent
electrons
 When a photon with
energy ΔE is absorbed,
one electron jumps to a
higher energy level
• These higher levels
are called excited
states
• ΔE = hƒ = E2 – E1

38. Atomic Transitions –
Spontaneous Emission
 Once an atom is in
an excited state,
there is a constant
probability that it will
jump back to a lower
state by emitting a
photon
 This process is
called spontaneous
emission

39. Atomic Transitions – Stimulated
Emission
 An atom is in an excited
stated and a photon is
incident on it
 The incoming photon
increases the
probability that the
excited atom will return
to the ground state
 There are two emitted
photons, the incident
one and the emitted
one

40. 29.1 Some Properties of Nuclei
 All nuclei are composed of protons and neutrons
• Exception is ordinary hydrogen with just a proton
 The atomic number, Z, equals the number of
protons in the nucleus
 The neutron number, N, is the number of neutrons
in the nucleus
 The mass number, A, is the number of nucleons in
the nucleus
• A = Z + N
• Nucleon is a generic term used to refer to either a proton or
a neutron
• The mass number is not the same as the mass

41. Charge and mass
Charge:
 The electron has a single negative charge, -e (e = 1.60217733 x 10-19
C)
 The proton has a single positive charge, +e
• Thus, charge of a nucleus is equal to Ze
 The neutron has no charge
• Makes it difficult to detect
Mass:
 It is convenient to use atomic mass units, u, to express masses
• 1 u = 1.660559 x 10-27
kg
 Mass can also be expressed in MeV/c2
• 1 u = 931.494 MeV/c2

42. The Size of the Nucleus
 First investigated by
Rutherford in scattering
experiments
 The KE of the particle
must be completely
converted to PE
2
2
4 ek Ze
d
mv
=
( ) ( )2 1 2
21
2
e e
e Zeq q
mv k k
r d
= = or

43. Size of Nucleus
 Since the time of
Rutherford, many
other experiments
have concluded the
following
• Most nuclei are
approximately
spherical
3
1
oArr =

44. Density of Nuclei
 The volume of the nucleus (assumed to be
spherical) is directly proportional to the total
number of nucleons
 This suggests that all nuclei have nearly the
same density
 Nucleons combine to form a nucleus as
though they were tightly packed spheres

45. Nuclear Stability
 There are very large repulsive electrostatic forces
between protons
• These forces should cause the nucleus to fly apart
 The nuclei are stable because of the presence of
another, short-range force, called the nuclear (or
strong) force
• This is an attractive force that acts between all nuclear
particles
• The nuclear attractive force is stronger than the Coulomb
repulsive force at the short ranges within the nucleus

46. Nuclear Stability chart
 Light nuclei are most
stable if N = Z
 Heavy nuclei are most
stable when N > Z
• As the number of protons
increase, the Coulomb force
increases and so more
nucleons are needed to keep
the nucleus stable
 No nuclei are stable when
Z > 83

47. Isotopes
 The nuclei of all atoms of a particular element must contain
the same number of protons
 They may contain varying numbers of neutrons
• Isotopes of an element have the same Z but differing N
and A values
C11
6
C14
6C13
6C12
6

48. 29.2 Binding Energy
 The total energy of
the bound system
(the nucleus) is less
than the combined
energy of the
separated nucleons
• This difference in
energy is called the
binding energy of the
nucleus
• It can be thought of as
the amount of energy
Binding Energy per NucleonBinding Energy per Nucleon

49. Binding Energy Notes
 Except for light nuclei, the binding energy is
about 8 MeV per nucleon
 The curve peaks in the vicinity of A = 60
• Nuclei with mass numbers greater than or less than 60
are not as strongly bound as those near the middle of
the periodic table
 The curve is slowly varying at A > 40
• This suggests that the nuclear force saturates
• A particular nucleon can interact with only a limited
number of other nucleons

50. 29.3 Radioactivity
 Radioactivity is the spontaneous
emission of radiation
 Experiments suggested that radioactivity
was the result of the decay, or
disintegration, of unstable nuclei
 Three types of radiation can be emitted
• Alpha particles
• The particles are 4
He nuclei
• Beta particles
• The particles are either electrons or positrons

51. Distinguishing Types of
Radiation
 The gamma particles
carry no charge
 The alpha particles are
deflected upward
 The beta particles are
deflected downward
• A positron would be
deflected upward

52. Penetrating Ability of Particles
 Alpha particles
• Barely penetrate a piece of paper
 Beta particles
• Can penetrate a few mm of aluminum
 Gamma rays
• Can penetrate several cm of lead

53. The Decay Constant
 The number of particles that decay in a given
time is proportional to the total number of
particles in a radioactive sample
• λ is called the decay constant and determines the rate
at which the material will decay
 The decay rate or activity, R, of a sample is
defined as the number of decays per second
N
R N
t
λ
∆
= =
∆ ( )N N tλ∆ = − ∆

54. Decay Curve
 The decay curve
follows the equation
 The half-life is also a
useful parameter
λ
=
λ
=
693.02ln
T 21
0
t
N N e λ−
=

55. Units
 The unit of activity, R, is the Curie, Ci
• 1 Ci = 3.7 x 1010
decays/second
 The SI unit of activity is the Becquerel,
Bq
• 1 Bq = 1 decay / second
• Therefore, 1 Ci = 3.7 x 1010
Bq
 The most commonly used units of
activity are the mCi and the µCi

56. Alpha Decay
 When a nucleus emits an alpha particle it
loses two protons and two neutrons
• N decreases by 2
• Z decreases by 2
• A decreases by 4
HeYX 4
2
4A
2Z
A
Z +→ −
−

57. Beta Decay
 During beta decay, the daughter nucleus has the
same number of nucleons as the parent, but the
atomic number is one less
 In addition, an electron (positron) was observed
 The emission of the electron is from the nucleus
• The nucleus contains protons and neutrons
• The process occurs when a neutron is
transformed into a proton and an electron
• Energy must be conserved

58. Beta Decay – Electron Energy
 The energy released in the decay process
should almost all go to kinetic energy of the
electron
 Experiments showed that few electrons had
this amount of kinetic energy
 To account for this “missing” energy, in
1930 Pauli proposed the existence of
another particle
 Enrico Fermi later named this particle the
neutrino
 Properties of the neutrino
• Zero electrical charge
• Mass much smaller than the electron,
probably not zero
• Spin of ½
• Very weak interaction with matter

59. Gamma Decay
 Gamma rays are given off when an excited nucleus “falls” to a lower
energy state
• Similar to the process of electron “jumps” to lower energy states and
giving off photons
 The excited nuclear states result from “jumps” made by a proton or neutron
 The excited nuclear states may be the result of violent collision or more
likely of an alpha or beta emission
 Example of a decay sequence
• The first decay is a beta emission
• The second step is a gamma emission
γ+→
ν++→ −
C*C
e*CB
12
6
12
6
12
6
12
5