Physics Chapter 21 Atomic Physics
Everything emits electromagnetic radiation. Most objects absorb some incoming radiation and reflect the rest. An ideal system
that absorbs all incoming radiation is called a blackbody.
There was a disparity among scientists in the early 1900’s as to why short wavelengths of radiation do not have high energy.
Since the failed prediction occurred at the UV end of the visible light spectrum, it was called the ultraviolet catastrophe.
Max Plank developed a formula for blackbody radiation that agreed with experimental data on blackbody radiation at all
wavelengths. He proposed that energy is not released continuously but is released in packets, called quanta or photons.
E
=
hf
=J∙s
x
beats
=
Joules
s
Energy of a quantum (n=1) = Planck’s constant x frequency
The units of light energy called quanta or photons are absorbed or given off as a result of electrons “jumping” from one
quantum state to another. As seen in the equation above, if the quantum number (n) changes by one unit, the amount of
energy radiated changes by hf.
Resonators will only radiate or absorb energy when it changes quantum states. The idea that energy comes in discrete units or
quanta led to the theory called quantum mechanics.
Planck’s constant is h = 6.63 x 10-34 J ∙ s
When dealing with parts of atoms, energy is often expressed in electron volts, 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.
Since 1 V = 1J/C, the relation between the electron volt and the joule is as follows:
1 eV =
1.60 x 10-19 C ∙ V= 1.60 x 10-19 C ∙ J/C
=
1.60 x 10-19 J
There are 1.60 x 10-19 J in one electron volt. This is the charge of an electron.
The photo electric effect is the emission of electrons from a material surface that occurs when light of certain frequencies
shines on the surface of the material. For the photoelectric effect to be observed, the light frequency must exceed the
threshold frequency. This is like what turns the street lights on and off.
The number of photo electrons emitted is proportional to the light intensity but the max kinetic energy is independent of the
light intensity. The maximum kinetic energy increases with increasing frequency. Electrons are emitted almost
instantaneously, even at low intensities. These actual phenomena did not agree with Classical physics and it was Einstein that
proposed that all electromagnetic waves are quantized as photons. A photon is a unit or quantum of light; a particle of
electromagnetic radiation that has zero mass and carries a quantum of energy.
In order for an electron to be ejected from metal it must overcome the force that binds it to the metal. The work function is
the minimum energy needed to remove an electron from a metal atom.
Maximum kinetic energy = (Planck’s constant X frequency of incoming photon) - work function
KE max = h f-hf t
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In this equation, the work function is equal to hf t , where f t is the threshold frequency for the metal. Photons with energy
greater than hf t eject electrons from the surface of and from within the metal.
If the energy of an incoming photon is not equal to or greater than the work function, electrons will never be ejected from the
surface, regardless of how many photons are present. Above the threshold frequency, if the light intensity is doubled, the
number of photons is doubled, thus doubling the number of electrons ejected from the metal. The equation for the maximum
kinetic energy, however, shows that kinetic energy depends only on the light frequency and the work function, not on the light
intensity…..even though there are more electrons ejected, the maximum kinetic energy of individual electrons stays the same.
Arthur Compton helped out the particle theory of light when he showed that light particles behave like billiard balls. A collision
between an electron and a photon are similar between the collision between two pool balls.
Ernest Rutherford determined that the nucleus of an atom is positive. He called the mass at the center of the atom and the
positive charges collectively the nucleus.
Rutherford, however, basing his ideas on particle physics could not explain why atoms did not collapse; why didn’t the
electrons fall into the nucleus instead of remaining in discrete orbits?
Niels Bohr studied the emission and absorption spectra especially of hydrogen. Bohr decided that instead of radiating energy
continuously, electrons only give up energy or gain energy when they jump to a lower or higher energy orbit. An orbit farther
away from the nucleus was termed “excited”. Once an electron is excited, if it jumps to a lower energy level, it would most
likely release a photon of energy.
Planck’s equation deals with energy from one level to another, therefore, a move of more than a single level means that more
energy is emitted. It was determined by Bohr that these jumps between different levels correspond to the various spectral
lines that are observed for each element. This explanation also explains the “Northern Lights” or Aurora Borealis. As different
gases in the atmosphere are excited by charged particles from the sun, they release photons of energy as the electrons in the
gases fall back to lower energy levels. Oxygen excitation results in green colors and nitrogen gas excitation results in red lights.
The possible colors are thus dictated by the prevalent gases in our atmosphere.
Bohr’s theories could not always explain why electrons always have certain stable orbits.
It was Louis de Broglie that proposed that all forms of matter may have both wave and particle properties. De Broglie
developed the following two equations to support his idea that light can be described as wave and particle.
De Broglie wavelength
=
Planck’s constant
Momentum
λ
=
h
=
p
De Broglie frequency
h
mv
=
energy
Planck’s constant
f
=
E
h
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De Broglie showed how Bohr’s model provided stability for all levels by suggesting that as the electrons move in orbits, they
have wave-like characteristics and vibrate at frequencies similar to standing waves on a guitar string. The condition for an
electron orbit is that the circumference must contain an integral multiple of electron wavelengths.
Observation of particles that move as a wave have difficulties when it comes to trying to measure them or find out exactly
where they are. In 1927, Werner Heisenberg argued that it is fundamentally impossible to make simultaneous measurements
of a particle’s position and momentum with infinite accuracy. The very act of observing the particle could actually change the
particle.
In order for a person to see an electron and determine its location, at least one photon of light must bounce off the electron
and pass through the microscope into the observer’s eye. When the photon strikes the electron, it transfers some of its energy
and momentum to the electron.
The uncertainty principle states that it is impossible to simultaneously determine a particle’s position and momentum with
infinite accuracy.
In 1926, Erwin Schrodinger proposed a wave equation that described the manner in which de Broglie’s matter waves change in
space and time. Solving Schrödinger’s equation yields a quantity called the wave function, represented by the Greek letter psi,
ψ (looks like a triton).
Because an electron’s position cannot be precisely determined, it is important to describe the probability of finding the electron
at different locations. The absolute value squared of psi |ψ|2 is proportional to the probability of finding the electron at a given
position.
Schrodinger said that an electron is not confined to a particular orbital distance from the nucleus as assumed in the Bohr
model. The electron may be found at varying distances from the nucleus, but the probability of finding it at a distance
corresponding to a Bohr orbit is greater than that of finding it at any other distance.
Quantum mechanics says that an electron in the first orbit can be found in a spherical area somewhere around the nucleus,
kind of like somewhere within a spherical electron cloud.
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21A Quantum energy
At the peak of the sun’s radiation spectrum, each photon carries energy of about 2.7 eV. What is the frequency of this light?
E = hf
f
=
E
h
Ans. 6.5 EE 14 Hz
21B The photoelectric effect
Light of frequency of 1.00 x 1015 Hz illuminates a sodium surface. The ejected photoelectrons are found to have a maximum
kinetic energy of 1.78 eV. Find the threshold frequency for this metal.
First, convert 1.7 eV to Joules, this is the value for KE max.
There are 1.60 x 10-19 J in one electron volt.
h = 6.63 x 10-34 J ∙ s
Solve for f t in the KE max equation: KE max = h f-hf t
Ans: 5.70 x 1014 Hz
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21 C 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?
E6______________________________________E=-0.378 eV
E5______________________________________E=-.0544 eV
E4______________________________________E=-0.850 eV
E3______________________________________E=-1.51 eV
E2______________________________________E=-3.40eV
Find the energy of the photon: E = Einitial-Efinal
Use Planck’s equation to find the frequency:
E=hf
f=
E
h
There are 1.60 x 10-19 J in one electron volt.
h = 6.63 x 10-34 J ∙ s
Ans: 6.15 EE 14 Hz
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21D de Broglie Waves
With what speed would an electron with a mass of 9.109 EE-31 kg have to move if it had a de Broglie wavelength of 7.28 EE-11
m?
λ
=
h
mv
solving for v:
v
=
h
λm
h = 6.63 x 10-34 J ∙ s
Ans: 1.00 EE 7 m/s
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