Science of Technology Genius by Design The Battery Exam Practice

Science of TechnologyDr. Jones
Exam #3
This entire exam is due between 12:00 – 1:50 p.m. on 5/11, no later or points will be
deducted.
Exam 3, Part 1
1. Write an essay 1 full page double-spaced include references if needed. Do not plagiarize.
If you wish to quote or paraphrase a source, be sure to indicate that you are quoting or
paraphrasing and reference the source. (20 points)
As technology evolves midcentury (2030-2070), what jobs do you think will flourish? How
will the evolution of technology change the way we work? Think about the PowerPoint
presentations of your classmates. Be specific in your answer and example(s).
2. Chapter 9; Genius by Design – The “Battery” (20 points)
a)
b)
c)
d)
e)
What was Edison’s nickname?
What improvements did Edison make to his Electric pen?
Why was his invention not successful?
How did it evolve over time?
What other products did Edison come up with in this chapter?
3. Who sold the patent for the “Incandescent Electric Light Bulb with a carbon filament” to
the United States Electric Company in 1881? Why do you think this inventor was not
mentioned along with the other inventors in this chapter? (10 points)
Exam 3, Part II
All of these answers should be understandable to someone not familiar with science and
should be based on lab/activity observations or assigned reading.
A.
For each of the following indicate if the statement is true or false. Explain the reason
for your choice. You get no credit if there is no explanation. Reference to a particular
observation made in a class activity is an acceptable explanation. (3 points each)
1. In 1905 Einstein published three papers that solved three of the greatest mysteries in
physics one of which was the photoelectric effect.
2. An incident photon transfers all of its energy to an atomic electron in the reflecting
material.
3. The principal quantum number n governs the total energy of the electron, and
corresponds to the quantum number n of the Bohr Theory.
4. The amount of energy required to move an electron up and the energy separating the
various levels gets larger at higher levels.
B. Short Answers – Explain the reason for your choice.
You get no credit if there is
no explanation. Reference to a particular observation made in a class activity is an
acceptable explanation. (4 points each)
1. It turns out that people refer to allowed electron states in solids as bands in distinction
to levels in atoms. Why do you think that may make sense?
2. Based on your observations, what is the effect of increasing the: a) width of the well? B)
height of the wells? And c) separation between the wells?
3. In what way are the locations of energy levels for 1023 atoms similar to that of one atom?
4. Which metal surface would make possible (work best) the operation of such devices as
television picture tubes, in which metal filaments or specifically coated cathodes at a high
temperature supply a dense stream of electrons.
5. Why did the maximum wavelength (minimum frequency) change when you changed the
target material?
6. What is the maximum number of paths for de-excitation available to a hydrogen atom
excited to the n=3 level in changing to the ground state?
7. The photographic representation of the electron probability-density distribution for
several energy states below bears a remarkable resemblance to those of the Bohr model,
why?
Exam 3, Part III (20 points)
Quantum Theory of Light
The electromagnetic theory of light accounts so well for such a variety of phenomena that it
must contain some measure of truth to it, yet this well founded theory if completely at odds
with the photoelectric effect. In 1905 Albert Einstein found that the paradox presented by
the photoelectric effect could be understood only by carrying further a radical notion
proposed five years earlier by the German theoretical physicist Max Planck. Planck was
seeking to explain the characteristics of the radiation emitted by bodies of condensed
matter. We are all familiar with the glow of a hot piece of metal, which gives off visible
light, but other wavelengths to which our eyes do not respond to are present as well. He
was able to derive a formula for the spectrum of this radiation (the relative brightness of
the various wavelengths present) as a function of the temperature of the radiating body
provided; Planck assumed that the radiation is emitted discontinuously in little bursts, an
assumption completely at odds with electromagnetic theory. These bursts are called
quanta. Planck found that the quanta associated with a particular frequency v of light must
all have the same energy and that this energy E is directly proportional to v. Therefore,
quantum energy is represented by the formula:
E = hv
where h, today is known as Planck’s constant and has a value of 6.626 x 10-34 J-s. While he had to
assume that the electromagnetic energy radiated by an object emerges intermittently, Planck did
not doubt that it propagates through space as continuous electromagnetic waves. Einstein
proposed that light not only is emitted a quantum at a time, but it also propagates as individual
quanta, a more drastic break with classical physics. In terms of this hypothesis the photoelectric
effect can be readily explained. The empirical formula is:
hv = Kmax + hvo
Einstein’s proposal defined the three terms above in his equation as: 1) hv = energy content of
each quantum of the incident light, 2) Kmax = maximum photoelectron energy and 3) hvo =
minimum energy needed to dislodge an electron from the metal surface being illuminated.
There must be a minimum energy required by an electron in order to escape from a metal
surface, or else electrons would pour out even in the absence of light. The energy hvo
characteristic of a particular surface is called its work function. It states that:
Quantum energy = maximum electron energy + work function of the surface
Some examples of the photoelectric work function are provided in the table below. To
detach an electron from a metal surface generally takes about half as much energy as that
needed to detach an electron from a free atom of that metal. For instance, the ionization
energy of cesium is 3.9 eV compared with its work function of 1.9 eV. Since the visible
spectrum extends from about 4.2 to about 7.9 x 1014 Hz, which corresponds to quantum
energies of 1.7 to 3.3 eV, it is clear from the table below, that the photoelectric effect is a
phenomenon of the visible and ultraviolet regions.
As shown in the equation above, photons of light whose frequency is v, have the energy hv.
To express hv in electronvolts (eV), recall that 1eV = 1.60 x 10-19 J
YOU MUST SHOW ALL WORK OR NO CREDIT WILL BE GIVEN. YOU DO NOT HAVE TO
TYPE THE MATH.
Photoelectric Work Functions
Metal
Symbol
Work Function, eV
Cesium
Potassium
Sodium
Lithium
Calcium
Copper
Silver
Platinum
Cs
K
Na
Li
Ca
Cu
Ag
Pt
1.9
2.2
2.3
2.5
3.2
4.5
4.7
5.6
Hence the formula E = hv now becomes for a single photon energy:
E = 6.626 x 10-34 J-s X v = 4.14 x 10-15 v eV-s
1.60 x 10-19 J/eV
This equation allows us to find immediately the energy in electronvolts of a photon of
frequency v. If we are given the wavelength λ of the light instead, then since v = c/λ we
have
E = (4.14 x 10-15 v eV-s) X 3.0 X 108 m/s) = 1.24 x 10-6 eV-m
λ
λ
when λ is expressed in meters. When λ is expressed in angstrom units (Å), where 1nm = 10-10m,
then
E = 1.24 x 104 eV-Å
λ
This is the photon energy. Now that you have enough information, please solve the
problem below.
PROBLEM: Find the maximum kinetic energy of the photoelectrons emitted when
ultraviolet light of wavelength 3,500 Å falls on the eight surfaces in the above table. Which
metal surface would make possible (work best) the operation of such devices as television
picture tubes, in which metal filaments or specifically coated cathodes at high temperature
supply a dense streams of electrons. The emitted electrons evidently obtain their energy
from the thermal agitation of the particles constituting the metal, and we should expect
that the electrons must acquire a certain minimum energy in order to escape. This
minimum energy is always close to the photoelectric work function for the surface.