AP Exam Review
Modern Physics
Name:
Modern Physics
Important Experiments in Understanding the Atom
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Rutherford’s Gold Foil Experiment (1911): Rutherford projected alpha particles (nuclei of helium
atoms) at a thin metal foil. He found that
a. most of the alpha particles went straight through the foil
b. some of the alpha particles were scattered off to the side
c. a few of the alpha particles came straight back.
This led to the conclusion that the atom has a very small positively charged nucleus, and that
the electrons are moving in orbits around the nucleus.
Millikan’s Oil Drop Experiment (1909): Millikan suspended charged oil drops in a known electric
field. From this he was able to determine the charge on each oil drop. He concluded that the
smallest charge is 1.6 x 10-19 C (the charge of one electron) and that charge is quantized (comes in
multiples of 1.6 x 10-19 C).
J.J. Thompson (1897) – by projecting electrons in cathode rays into a magnetic field, Thompson
discovered the charge to mass ratio of the electron. Once Millikan found the charge of one
electron, the mass of an electron became known.
Chadwick (1932) – using conservation of momentum and energy in the elastic collisions between
subatomic particles, Chadwick determined the mass of a neutron and found that it carried no net
charge.
Important Characteristics of an Atom
1.
Atoms contain a nucleus with protons and neutrons. Isotopes of the same element contain the
same number of protons but different number of neutrons. Each proton has a charge of 1.6 x 10-19
C and a mass of one amu (atomic mass unit = 1.67 x 10 -27 kg). Each neutron has a mass of one
amu, but no net charge. Atoms such as hydrogen have a radius of about 1 Angstrom (10 -10 m or
10 nanometers). The radius of the nucleus is about 10 -5 Angstrom.
2.
The strong nuclear force (stronger than the weak nuclear force, the electrostatic force or the
gravitational force) is the strongest force yet identified. Another way to think about what holds the
nucleus together is to realize that when combined in the nucleus, the particles lose some mass.
Since
E  mc 2
where c is the speed of light, the lost mass appears as binding energy holding the nucleus
together.
3.
The electrons (mass of 0 amu – or 9.11 x 10-31 kg and charge of -1.6 x 10-19 C) orbit in shells
around the nucleus. Each atom has electrons in specific orbits (designated by energy levels). The
electrons can NOT be anywhere (unlike satellites orbiting the earth which can have any altitude or
radius. This realization established quantum theory at the atomic level.
The Bohr Model of the Atom – Energy Levels for Electrons in Atoms
If zero represents the lowest energy level for an electron in a specific atom, higher levels would
have to have positive energy. Such energy is often expressed in electron volts (1 ev = 1.6 x 10-19 J of
energy). The energy required to ionize an atom (i.e. remove an electron) represents the energy needed to
take an electron from its lowest energy level up to where it escapes from the pull of the positively charged
nucleus. For hydrogen, the amount of energy required is 13.6 ev.
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Once energy levels are determined, when an electron moves down toward the nucleus, it emits a
photon (a particle) of light (i.e. it emits the extra energy no longer needed as light energy). All the possible
electron level jumps downward determine the line emission spectrum for that atom. The equation:
E  hf
predicts what frequency (and therefore wavelength from c = λf) is associated with the energy level jump.
The electron energy levels for a particular atom also determine the specific frequency of photons
that will be absorbed if polychromatic light is allowed to go through the substance. This results in the
absorption spectrum – the dark lines missing form the continuous spectrum representing absorbed photons
of a specific frequency, wavelength and energy. Dark lines in the spectrum from the sun have enabled us
to discover which elements are present in the sun!
If zero represents the energy as an electron reaches the highest energy level – it is just free of the
atom – then lower energy levels would have a negative value. In the case of hydrogen, the lowest energy
level would be –13.6 ev.
The Photoelectric Effect and the Particle Characteristics of Light
In Einstein’s Nobel Prize winning experiment, he determined that incident light shone on some
metals could produce ejected electrons. This is the principle used in a photoelectric cell – light results in a
current, the flow of the ejected electrons. When the intensity is increased (i.e. more photons strike the
surface of the metal), the number of electrons emitted increases in direct proportion – but the kinetic energy
of each emitted electron (measured by retarding voltage – the voltage required to stop the electron/current)
remains the same. When the frequency of light was increased (i.e. same number of photons but each has
more energy), the kinetic energy of each electron increased. When the frequency of light was decreased
(i.e. the energy of the photons decreased), the kinetic energy of each electron decreased until, below a
certain threshold frequency, no electrons were emitted.
Plotting Kinetic Energy of the emitted electrons as a function of the frequency of light shone on the
metal results in a straight-line graph. The slope of this graph represents Planck’s Constant (h = 6.63 x 10 -34
Js). This slope is the SAME for all metals that exhibit the photoelectric effect. The x-intercept represents
the threshold frequency (the minimum frequency of light needed to eject electrons) and the y-intercept
represents the work function (minimum energy needed to overcome the attractive forces within the atom).
Remember, the work function describes the minimum work that must be done on the electron before it can
escape from the metal (i.e. the energy needed to raise it to its highest energy level). These results lead to
the equation:
K max  hf  
where Kmax is the kinetic energy of the ejected photon, hf is the energy of the photon, and Φ is the work
function.
The photoelectric effect provides conclusive evidence that light has particle characteristics. A
photon is a particle of light. If light were a wave, increasing the intensity should increase the energy of the
wave and should result in the ejection of electrons. Since increasing the intensity does NOT cause
electrons to be ejected, this was conclusive proof that light acts as a particle. The energy of a photon is
given by:
E  hf
Visible light is just a small part of the electromagnetic spectrum. As you go from radio waves (long
wavelength, low frequency, low energy photons) to microwave (AM, TV, FM, cell phones) to infrared to
visible to ultraviolet to x-rays to gamma rays, you increase the energy of each photon, increase the
frequency and decrease the wavelength.
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For a given frequency, each photon has the same energy. To increase the intensity (brightness) of
the light emitted, you would increase the number of photons per second. Remember, power x time =
energy. This would equal the energy of each photon times the number of photons.
Photons, as particles, also have momentum. As a photon is massless, we cannot determine the
momentum by using p = mv. To determine the momentum of a photon:
p
h

As in any collision, when a photon collides with other photons or other particles, in the absence of outside
forces, momentum will be CONSERVED.
The Wave Properties of Particles
Just as light has some particle characteristics, the smallest particles we know (electrons and
protons) exhibit wave characteristics. Davisson-Germer (1927) sent electrons one by one through two
narrow slits and observed an interference pattern as the electrons went through the two narrow slits,
analogous to Young’s double slit experiment with light. Hence all matter has some wave-like characteristics
that become more pronounced as the mass approaches zero. From this DeBroglie found every particle has
a wavelength (and frequency) that is a function of its momentum. This is called the DeBroglie Wavelength:
B 
h
p
Compton Scattering
Additional support for light acting as a particle comes from x-rays being diverted by atoms in a
metal. The scattered light has a longer wavelength (less frequency, thus less energy) since some of the
incident photon energy was converted to kinetic energy in the metal during the collision between the photon
and the metal. Such interactions could be explained using the conservation of momentum, meaning light
acts like a particle. The momentum of a photon can be found using:
p
h

Nuclear Reactions
Recall: for any atom shown on the periodic table, the top number is known as the atomic mass (the
number of protons and neutrons OR nucleons). The bottom number is known as the atomic number (the
number of protons).
Some nuclei are unstable and emit radioactivity to become more stable. Radioactivity is hard to
detect – photographic film or a Geiger counter are used. There are three types of radioactivity:
1.
Gamma Radiation – photons of high frequency and high energy, no mass. As these photons have
such high energy, they can penetrate through hundreds of feet of most materials. Gamma rays are
often emitted when an excited nucleus moves to a lower energy level. A nucleus may be excited
as a result of a collision with another particle or from energy associated with previous radioactive
decay.
2.
Beta Particles – same mass and charge as an electron EXCEPT beta particles come from the
nucleus. When a beta particle is emitted, a neutron breaks down into a proton and the beta
particle. The beta particle escapes and now acts just like an electron. The new nucleus has one
more proton so it has moved over one place to the right on the periodic table. A beta particle has
an atomic number of –1. Beta Decay occurs when there is an unstable isotope (i.e. too many
neutrons) of an atom. On the flip side, there is also Positive Beta Decay. This would occur if an
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isotope had too few neutrons. In this case, a proton would break down and become a neutron and
a positron (a positively charged electron)!
The existence of the neutrino (very small amu, no charge) had to be postulated in order to reconcile
experimental data from Beta Decay with fundamental conservation laws. Physicists found that
during Beta Decay, the emitted beta particle did not always take all the energy from the destruction
of mass. They concluded another particle, the neutrino (little neutral one) had to be involved in the
process and receive the extra energy.
3.
Alpha Particles – equivalent to two protons and two neutrons (the nucleus of a helium atom). By
far the heaviest (4 amu) and when emitted (known as Alpha Decay), the atom moves to the left two
places on the periodic table as it has lost two protons. Alpha decay occurs because the strong
nuclear force of attraction can’t overcome the electrostatic force of repulsion. Since the alpha
particle is heavier, it tends to move more slowly than beta particles. Typically, but not always, it
has less kinetic energy than an emitted beta particle and is therefore easier to stop.
Radioactivity was once called the strange suicide of atoms since the atom, upon radioactive decay, changes
to a new element. In all three types of radioactive decay, classic conservation laws apply (i.e. conservation
of energy, momentum and charge). All also have a conservation in the total number of nucleons before and
after the decay.
Fusion: When light nuclei come together to form heavy nuclei. For example:
2
1
H  12 H  24 He energy
This happens to be one of the more frequent fusion reactions taking place on our sun, and is the
source of all our warmth and sunshine! The energy comes from the lost mass being converted to energy
(E=mc2). The total mass of the unstable atoms is greater than the mass of the stable combined atom.
Fission: The splitting of a heavy nucleus into two or more fragments. For example:
1
0
141
921
1
n  235
92 U  56 Ba  36 Kr  3 0 n  energy
Again, the energy comes from the lost mass. What is special about the above reaction is the
neutron needed for the fission to occur. The reaction produces 3 neutrons. These go on to fission more
atoms and produce and uncontrolled chain reaction. In a very brief time, an incredible amount of energy is
created – the basic principal behind the uranium atomic bomb. The energy from this bomb often starts the
fusion process in a hydrogen bomb, releasing even larger quantities of energy.
In all the nuclear reactions, MASS NUMBER (as in total amu on both sides of the equation) and
CHARGE are conserved. Hence, adding both the atomic numbers and the atomic weight of all nuclei on
both sides of the nuclear equations will give equal results.
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Practice Problems
2011b
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2011
6
2010b
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2010
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2008b
9
2008
10
2007
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2006b
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