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Unformatted text preview: Assignments 5/10/11 9:18 AM Student View Summary View Diagnostics View Print View withEdit Assignment
Answers Settings per Student MP_Assignment#10 [ Print ] Due: 9:35am on Monday, May 9, 2011
Note: You will receive no credit for late submissions. To learn more, read your instructor's Grading Policy Electron Transitions and Spectral Lines Conceptual Question
Description: Conceptual question on spectral lines corresponding to electron transitions.
The spectrum of a hypothetical atom is shown in the figure. Three distinct spectral series are shown, with the
center series corresponding to transitions to a final
state of
. The indicated spectral line
corresponds to the transition from an initial state of
to the final state
. Part A
Which of the lettered spectral lines corresponds to the transition from
Hint A.1 to ? Spectral series In many atoms, the spectral lines corresponding to transitions to the same final state are naturally
grouped together into spectral series. (In hydrogen, these series are given the names Lyman, Balmer,
Paschen, etc.) In the hypothetical atom under investigation, the same phenomenon occurs, where the
middle series corresponds to all of the transitions involving the final state
.
Hint A.2 Finding lines within a series Within any series, the lines furthest to the right correspond to the longest wavelength, and hence lowest
energy, transitions. As you move to the left within a series, the energy involved in the transition
increases.
ANSWER: D http://session.masteringphysics.com/myct/assignments Page 1 of 11 Assignments 5/10/11 9:18 AM Part B
Which of the lettered spectral lines corresponds to the transition from
Hint B.1 to ? Identifying different series Series are arranged such that transitions involving larger amounts of energy are to the left of series
involving smaller amounts of energy. Since the energy difference between successive energy levels gets
smaller as increases, this allows you to differentiate between different series.
Hint B.2 Identify the The series series involves transitions with a final energy state of between successive energy levels gets smaller as
the . Since the energy difference increases, is the series to the right or left of series? ANSWER: right
left ANSWER: H Part C
Which of the lettered spectral lines corresponds to the transition from
ANSWER: to ? A The Bohr Atom
Description: The problem applies quantization of angular momentum to the classical model of an electron
orbiting a nucleus.
Learning Goal: To understand the Bohr model of the hydrogen atom.
In 1913 Niels Bohr formulated a method of calculating the different energy levels of the hydrogen atom. He
did this by combining both classical and quantum ideas. In this problem, we go through the steps needed to
understand the Bohr model of the atom.
Part A
Consider an electron with charge
single proton) with charge and mass orbiting in a circle around a hydrogen nucleus (a . In the classical model, the electron orbits around the nucleus, being held http://session.masteringphysics.com/myct/assignments Page 2 of 11 Assignments 5/10/11 9:18 AM in orbit by the electromagnetic interaction between itself and the protons in the nucleus, much like planets
orbit around the sun, being held in orbit by their gravitational interaction. When the electron is in a circular
orbit, it must meet the condition for circular motion: The magnitude of the net force toward the center,
,
is equal to . Given these two pieces of information, deduce the velocity of the electron as it orbits around the nucleus.
Hint A.1 Electrostatic force Recall that the force between two charged particles is
, where and are the charges on the particles, is the separation of the particles, and is the permittivity of free space. This is the force that keeps the electron in a circular orbit, so
Express your answer in terms of , , , and . , the permittivity of free space. ANSWER:
= Part B
The key insight that Bohr introduced to his model of the atom was that the angular momentum of the
electron orbiting the nucleus was quantized. He introduced the postulate that the angular momentum could
only come in quantities of
, where is Planck's constant and is a nonnegative integer (
). Given this postulate, what are the allowable values for the velocity of the electron in the Bohr atom? Recall that, in circular motion, angular momentum is given by the formula
Express your answer in terms of , Planck's constant , , and . . ANSWER:
= Part C
In Parts A and B you found two different expressions to describe the allowed electron velocities
these two values (eliminating
Express in terms of , , ) and solve for the allowable radii
, , and . Equate in the Bohr model. . ANSWER:
= http://session.masteringphysics.com/myct/assignments Page 3 of 11 Assignments 5/10/11 9:18 AM As the electron orbits the nucleus with a speed
potential energy. The total energy at a radius , it has both kinetic energy and electric of the electron can be expressed as
. Part D
In Parts B and C you saw that, according to Bohr's postulate, the electron radius
velocity and the electron only have certain allowable values. Plug the values obtained for these two quantities into the energy statement given above to arrive at a new statement for the allowed energy levels in the Bohr atom.
Express your answer in terms of , , , , and . ANSWER:
= The standard formula for energy in the Bohr model is
.
Despite the serious flaws of the Bohr model, such as casually mixing quantum and classical ideas
with little if any justification, this formula turns out to be equivalent to the energy formula for hydrogen
obtained from quantum mechanics. To adequately deal with atoms other than hydrogen, however,
requires the full quantum theory. The Photoelectric Effect Experiment
Description: Three part problem to understand the photoelectric effect experiment.
Learning Goal: To understand the experiment that led to the discovery of the photoelectric effect.
In 1887, Heinrich Hertz investigated the phenomenon of light striking a metal surface, causing the ejection of
electrons from the metal. The classical theory of electromagnetism predicted that the energy of the electrons
ejected should have been proportional to the intensity of the light. However, Hertz observed that the energy
of the electrons was independent of the intensity of the light. Furthermore, for low enough frequencies, no
electrons were ejected, no matter how great the intensity of the light became. The following problem outlines
the methods used to investigate this new finding in physics: the photoelectric effect.
Suppose there is a potential difference between the metal that ejects the electrons and the detection
device, such that the detector is at a lower potential than the metal. The electrons slow down as they go
from higher to lower electric potential; since they must overcome this potential difference to reach the
detector, this potential is known as the stopping potential . To reach the detector, the initial kinetic energy of
an ejected electron must be greater than or equal to the amount of energy it will lose by moving through
the potential difference.
http://session.masteringphysics.com/myct/assignments Page 4 of 11 Assignments 5/10/11 9:18 AM Part A
If there is a potential difference between the metal and the detector, what is the minimum energy that an electron must have so that it will reach the detector?
Hint A.1 Relating potential difference to energy Recall that potential difference is defined as the difference in energy for a particle that is moved
between two points, divided by the charge of the particle:
, where
is the potential
difference, is the energy difference, and Express your answer in terms of
ANSWER: is the charge of the particle. and the magnitude of the charge on the electron, . = For the incident light to cause the ejection of an electron, the light must impart a certain amount of
energy to the electron to overcome the forces that constrain it within the metal. The minimum amount of
energy required to overcome these forces is called the work function . Different metals will have different
values for . For an electron to reach the detector, the light must impart enough energy for the electron to overcome both the work function and the stopping potential.
Part B
Suppose that the light carries energy . What is the maximum stopping potential that can be applied while still allowing electrons to reach the detector?
Hint B.1 Find the energy of the ejected electron What will be the energy of the electron immediately after it leaves the metal? Express your answer in terms of
ANSWER: and . = Now, think about how this answer relates to what you found in Part A.
Express your answer in terms , , and . ANSWER:
= http://session.masteringphysics.com/myct/assignments Page 5 of 11 Assignments 5/10/11 9:18 AM Part C
Classical electromagnetism predicted that should have increased as the intensity of the incident light increased. On the contrary, it was found that
voltage increased as the frequency of the light increased. The was found to obey the following linear relationship:
, where and are numerical constants (representing the slope and the intercept, respectively). By comparing this equation to your answer from Part B, find an expression for the intercept . (Notice that
in this equation changes with different light but
Express your answer in terms of is a constant of the metal.) and . ANSWER:
= Part D
In a 1905 paper that later won him a Nobel Prize, Albert Einstein postulated that the energy of light was
proportional to its frequency. The constant of proportionality turned out to be Planck's constant :
. Using your previous results, and the equation given in Part C, find an expression for in terms of experimentally determinable quantities.
Express your answer in terms of the slope
ANSWER: and . = Part E
Suppose that two sets of values were recorded in this experiment:
Stopping potential Frequency ( ( ) ) Using these data, extrapolate a numerical value for Planck's constant
Hint E.1 Finding the value of http://session.masteringphysics.com/myct/assignments . from the data Page 6 of 11 Assignments 5/10/11 9:18 AM In Part C, you were told that the voltage is proportional to the frequency of the light that strikes the metal:
.
A numerical value for the slope can be found from the two data points, using the fact that
. By entering this value for into the relationship you obtained in Part D, you can obtain a numerical value for Planck's constant . Express your answer in joule  seconds to three significant figures.
ANSWER:
= Part F
Using the data given, find a numerical value for the work function
Hint F.1 of the metal. How to determine the constant in a linear equation In Part C, you were told that the voltage is proportional to the frequency of the light that strikes the metal:
.
In Part E, you should have determined the numerical value of the slope
into the equation here, along with one of the sets of the data points (for . By substituting this value of
and you can determine the numerical value of . Finally, using the relationship between ) given in Part E,
and determined in Part C, you can obtain the numerical value of the work function.
Express your answer in joules to two significant figures.
ANSWER:
= Photon Density Ranking Task
Description: Ranking task on the number of photons in beams of different frequency EM radiation with the
same energy. (ranking task)
Part A
Beams of different frequency electromagnetic radiation are listed below. Each beam has the same total
energy. Rank these beams on the number of photons in each beam.
http://session.masteringphysics.com/myct/assignments Page 7 of 11 Assignments Hint A.1 5/10/11 9:18 AM Photon energy The energy of a single photon is proportional to its frequency.
Hint A.2 Radio waves By examining a radio dial, you will discover that FM radio stations broadcast with frequencies between
88 and 108
(megahertz, or millions of cycles per second) and AM radio stations broadcast
between 520 and 1720
Hint A.3 (kilohertz, or thousands of cycles per second). Frequency spectrum of electromagnetic waves Different frequency electromagnetic waves have historically been given different names. The traditional
names for the various frequencies are listed below. Hint A.4 Number of photons in the beam The number of photons in a beam of electromagnetic energy is inversely proportional to the energy of
each individual photon. This means that more low  energy photons are needed than high  energy
photons to achieve the same beam energy.
Rank from largest to smallest. To rank items as equivalent, overlap them.
ANSWER: View http://session.masteringphysics.com/myct/assignments Page 8 of 11 Assignments 5/10/11 9:18 AM Conceptual Question 39.11
Description: The figure shows the energy level diagram of Element X. (a) What is the ionization energy of
Element X? (b) An atom in the ground state absorbs a photon, then emits a photon with a wavelength of
1240 nm. What conclusion can you draw about the...
The figure shows the energy level diagram of Element
X. Part A
What is the ionization energy of Element X?
Express your answer using two significant figures.
ANSWER: = Part B
An atom in the ground state absorbs a photon, then emits a photon with a wavelength of 1240 . What conclusion can you draw about the energy of the photon that was absorbed ?
Express your answer using two significant figures.
ANSWER: = Part C
An atom in the ground state has a collision with an electron, then emits a photon with a wavelength of
1240
. What conclusion can you draw about the initial kinetic energy of the electron ?
Express your answer using two significant figures.
ANSWER:
http://session.masteringphysics.com/myct/assignments Page 9 of 11 Assignments 5/10/11 9:18 AM ANSWER: = Problem 39.6
Description: (a) Use Millikan's photoelectric effect data in Figure 39.10 in the textbook to determine the
work function, in eV, of cesium. (b) Use Millikan's photoelectric effect data in Figure 39.10 in the textbook
to determine an experimental value of...
Part A
Use Millikan's photoelectric effect data in Figure 39.10 in the textbook to determine the work function, in
, of cesium.
Express your answer using three significant figures.
ANSWER: = Part B
Use Millikan's photoelectric effect data in Figure 39.10 in the textbook to determine an experimental value
of Planck's constant.
Express your answer using three significant figures.
ANSWER:
= Problem 39.16
Description: The diameter of the nucleus is about 10 fm. (a) What is the kinetic energy, in MeV, of a
proton with a de Broglie wavelength of 10 fm ?
The diameter of the nucleus is about 10 fm.
Part A
What is the kinetic energy, in MeV, of a proton with a de Broglie wavelength of 10 fm ?
ANSWER:
MeV http://session.masteringphysics.com/myct/assignments Page 10 of 11 Assignments 5/10/11 9:18 AM Score Summary:
Your score on this assignment is 0%.
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This note was uploaded on 12/28/2011 for the course PHYSICS 270 taught by Professor Drake during the Fall '08 term at Maryland.
 Fall '08
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