c What would be the increase in temperature of the water if all the kinetic energy were converted to heat?. The wavelength of visible light, for instance, is on the order of nano- meter
Trang 1A 44.0-g sample of an unknown metal at 99.0°C was placed in
a constant-pressure calorimeter containing 80.0 g of water at 24.0°e The final temperature of the system was found to be 28.4 °C Calculate the specific heat of the metal (The heat capacity of the calorimeter is 12.4 We.)
A student mixes 88.6 g of water at 74.3°C with 57.9 g of water at
24.8°C in an insulated flask What is the final temperature of the combined water?
Producer gas (carbon monoxide) is prepared by passing air over
red-hot coke:
C(s) + W z(g) - CO(g) Water gas (a mixture of carbon monoxide and hydrogen) is
prepared by passing steam over red-hot coke:
C(s) + H z O (g) • CO (g) + H z(g)
For many years, both producer gas and water gas were used
as fuels in industry and for domestic cooking The large-scale
preparation of these gases was calTied out alternately, that is, first
producer gas, then water gas, and so on Using thermochemical reasoning, explain why this procedure was chosen
Compare the heat produced by the complete combustion of
I mole of methane (C~) with a mole of water gas (0.50 mole Hz
and 0.50 mole CO) under the same conditions On the basis of
your answer, would you prefer methane over water gas as a fuel?
Can you suggest two other reasons why methane is preferable to water gas as a fuel?
The so-called hydrogen economy is based on hydrogen produced from water using solar energy The gas is then burned as a fuel:
A primary advantage of hydrogen as a fuel is that it is
nonpolluting A major disadvantage is that it is a gas and therefore is harder to store than liquids or solids Calculate the
number of moles of Hz required to produce an amount of energy equivalent to that produced by the combustion of a gallon of
octane (CsH Is) The density of octane is 2.66 kg lga l , and its
standard enthalpy of formation is -249.9 kJ/mo!
Ethanol (CzHsOH) and gasoline (assumed to be all octane,
CsHIs) are both used as automobile fue! If gasoline is selling for
$2.20/ga l , what would the price of ethanol have to be in order
to provide the same amount of heat per dollar? The density and
t::.H 'f of octane are 0.7025 g/mL and - 249.9 kJ/mol, respectively, and of ethanol are 0.7894 g/ mL and - 277.0 kJ/mol, respectively (1 gal = 3.785 L)
The combustion of how many moles of ethane (CZH6) would be
required to heat 855 g of water from 25.0°C to 98.0°C?
If energy is conserved, how can there be an energy crisis?
The heat of vaporization of a liquid (t:: H vap ) is the energy required
to vaporize 1.00 g of the liquid at its boiling point In one experiment, 60.0 g of liquid nitrogen (boiling point = - 196°C)
is poured into a Styrofoam cup containing 2.00 X 102 g of water
at 55.3°e Calculate the molar heat of vaporization of liquid nitrogen if the final temperature of the water is 41.0°e
Explain the cooling effect experienced when ethanol is rubbed on
your skin, given that
A certain gas i.nitially at 0.050 L undergoes expansion until its
volume is 0.50 L Calculate the work done (in joules) by the gas if
it expands (a) against a vacuum and (b) against a constant pressure
of 0.20 atm (The conversion factor is I L atm = 101.3 J.)
Calculate the standard enthalpy of formation for diamond, given that
C(graphite) + 0 2 (g) - _ CO 2( g)
C(diamond) + O z(g) • COzCg)
t::.W = -393.5 kJ/mol t::.H o = - 395.4 kJ/mol
(a) For most efficient use, refrigerator freezer compartments
should be full y packed with food What is the thermochemical basis for this recommendation? (b) Starting at the same
temperature, tea and coffee remain hot longer in a thermal flask than chicken noodle soup Explain
Calculate the standard enthalpy change for the fermentation process, in which glucose (C6H 12 06) is converted to ethanol (CzHsOH) and carbon dioxide
Portable hot packs are available for skiers and people engaged
in other outdoor activities in a cold climate The air-permeable paper packet contains a mixture of powdered iron, sodium
chloride, and other components, all moistened by a little water
The exothermic reaction that produces the heat is a very common
one- the rusting of iron:
When the outside plastic envelope is removed, O2 molecules penetrate the paper, causing the reaction to begin A typical packet contains 250 g of iron to warm your hands or feet for up
to 4 hours How much heat (in kJ) is produced by this reaction?
(Hi nt: See Appendix 2 for t::.H 'f values.)
A man ate 0.50 pound of cheese (an energy intake of 4 X 103 kJ) Suppose that none of the energy was stored in his body What
mass (in grams) of water would he need to perspire in order to maintain his original temperature? (It takes 44.0 kJ to vaporize
I mole of water.)
The total volume of the Pacific Ocean is estimated to be 7.2 X
lOs km3 A medium-sized atomic bomb produces 1.0 X 1015 J of energy upon explosion Calculate the number of atomic bombs needed to release enough energy to raise the temperature of the water in the Pacific Ocean by 1°e
A woman expends 95 kJ of energy in walking a kilometer The energy is supplied by the metabolic breakdown of food intake and has a 35 percent efficiency How much energy can she save
by driving a car over the same distance if the car gets 8.2 km per liter of gasoline (approximately 20 mi/gal)? Compare the efficiencies of the two processes The density of gasoline is
0.71 g/mL , and its enthalpy of combustion is - 49 kJ /g
Trang 25.99 The carbon dioxide exhaled by sailors in a submarine is often
removed by reaction with an aqueous lithium hydroxide
solution (a) Write a balanced equation for this process ( Hint:
The products are water and a soluble salt.) (b) If every sailor
consumes 1.2 X 104 kJ of energy every day and assuming that
this energy is totally supplied by the metabolism of glucose (C6H1Z0 6), calculate the amounts of COz produced and LiOH
required to purify the air
5.100 The enthalpy of combustion of benzoic acid (C6HsCOOH) is
commonly used as the standard for calibrating constant-volume
bomb calorimeters; its value has been accurately determined to
be - 3226.7 kJ / mol When l.9862 g of benzoic acid are burned
in a calorimeter, the temperature rises from 2l.84°C to 25.67°C
What is the heat capacity of the bomb? (Assume that the quantity
of water surrounding the bomb is exactly 2000 g.)
5.101 Calcium oxide (CaO) is used to remove sulfur dioxide generated
by coal-burning power stations:
NaZS04 + lOHzO(s) - _ NaZS04 + 10Hz O(I)
!1H o = 74.4 kJ / mol
As a result, this compound is used to regulate the temperature
in homes It is placed in plastic bags in the ceiling of a room
During the day, the endothermic melting process absorbs heat from the surroundings, cooling the room At night, it gives
off heat as it freezes Calculate the mass of Glauber's salt in
kilograms needed to lower the temperature of air in a room by 8.2°C The mass of air in the room is 605.4 kg; the specific heat
of air is 1.2 Jig' DC
An excess of zinc metal is added to 50.0 mL of a 0.100 M
AgN03 solution in a constant-pressure calorimeter like the one
pictured in Figure 5.8 As a result of the reaction
Zn(s) + 2Ag + (aq) • Znz+(aq) + 2Ag(s) the temperature rises from 19.25°C to 22 17°C If the heat
capacity of the calorimeter is 98.6 WC, calculate the enthalpy change for the given reaction on a molar basis Assume that the density and specific heat of the solution are the same as those for water, and ignore the specific heats of the metals
(a) A person drinks four glasses of cold water (3.0°C) every day
The volume of each glass is 2.5 X lOz mL How much heat (in
kJ) does the body have to supply to raise the temperature of the water to 37°C, the body temperature? (b) How much heat would your body lose if you were to ingest 8.0 X 10z g of snow at O°C
to quench your thirst? (The amount of heat necessary to melt
snow is 6.01 kJ / mo! )
A driver's manual states that the stopping distance quadruples as
the speed doubles; that is, if it takes 30 ft to stop a car moving at
25 mph then it would take 120 ft to stop a car moving at 50 mph
Justify this statement by using mechanics and the first law of
thermodynamics [Assume that when a car is stopped, its kinetic energy Gmu z ) is totally converted to heat.]
-.106 At 25°C the standard enthalpy of formation of HF (a q) is
-320.1 kJ/mol; of OH - (aq), it is -229.6 kJ / mol; of F - (a q), it
is - 329.1 kJ/mol; and of HzO(l), it is -285.8 kJ/mo!
(a) Calculate the standard enthalpy of neutralization of HF (aq) :
Why can't we obtain the standard enthalpy of formation directly
by measuring the enthalpy of the following reaction?
A 46-kg person drinks 500 g of milk, which has a "caloric" value
of approximately 3.0 kJ/g If only 17 percent of the energy in
milk is converted to mechanical work, how high (in meters) can the person climb based on this energy intake? [Hint: The work done in ascending is given by mgh, where m is the mass (in kg),
g is the gravitational acceleration (9.8 rnJs\ and h is theheight
(in meters).]
The height of Niagara Falls on the American side is 51 m
(a) Calculate the potential energy of 1.0 g of water at the top of the falls relative to the ground level (b) What is the speed of the
falling water if all the potential energy is converted to kinetic
energy? (c) What would be the increase in temperature of the
water if all the kinetic energy were converted to heat? (See
Problem 5.109 for information.)
In the nineteenth century two scientists named Dulong and Petit
noticed that for a solid element, the product of its molar mass and
its specific heat is approximately 25 J / ° C This observation, now
called Dulong and Petit's law, was used to estimate the specific
heat of metals Verify the law for the metals listed in Table 5.2
The law does not apply to one of the metals Which one is it?
Why?
Determine the standard enthalpy of formation of ethanol
(CzHsOH) from its standard enthalpy of combustion
(-1367.4 kJ/mol)
Acetylene (CzHz) and benzene (C6H6) have the same empirical formula In fact, benzene can be made from acetylene as follows:
The enthalpies of combustion for CzHz and C6H6 are - 1299.4
and -3267.4 kJ / mol, respectively Calculate the standard
enthalpies of formation of CzHz and C6H6 and hence the enthalpy change for the formation of C6H6 from CzHz
Ice at O°C is placed in a Styrofoam cup containing 361 g of a soft drink at 23°C The specific heat of the drink is about the same
as that of water Some ice remains after the ice and soft drink
reach an equilibrium temperature of O°C Determine the mass of ice that has melted Ignore the heat capacity of the cup (Hint: It
takes 334 J to melt I g of ice at O°C.)
Trang 3A gas company in Massachusetts charges 27 cents for a mole
of natural gas (CH4) Calculate the cost of heating 200 mLof
water (enough to make a cup of coffee or tea) from 20°C to
100°C Assume that only 50 percent of the heat generated by the
combustion is used to heat the water; the rest of the heat is lost to the surroundings
How much metabolic energy must a 5.2-g hummingbird expend
to fly to a height of 12 m? (See the hint in Problem 5.109.)
Acetylene (C2H2) can be made by reacting calcium carbide
(CaC2) with water (a) Write an equation for the reaction (b) What is the maximum amount of heat (in joules) that can be
obtained from the combustion of acetylene, starting with 74.6 g ofCaC2?
The average temperature in deserts is high during the day but quite cool at night, whereas that in regions along the coastline is
more moderate Explain
Both glucose and fructose are simple sugars with the same
molecular formula of C6H 120 6 Sucrose (C12H220 Il ), or table
sugar, consists of a glucose molecule bonded to a fructose molecule (a water molecule is eliminated in the formation of
sucrose) (a) Calculate the energy released when a 2.0-g glucose
tablet is burned in air (b) To what height can a 65-kg person
climb after ingesting such a tablet, assuming only 30 percent
of the energy released is available for work (See the hint for
Problem 5.109.) Repeat the calculations for a 2.0-g sucrose
tablet
About 6.0 X 1013 kg of CO2 is fixed (converted to more complex
organic molecules) by photosynthesis every year (a) Assuming
all the CO2 ends up as glucose (C6H 120 6), calculate the energy
(in kJ) stored by photosynthesis per year (b) A typical coal
-burning electric power station generates about 2.0 X 106 W per
year How many such stations are needed to generate the same amount of energy as that captured by photosynthesis
(1 W = 1 J /s)?
When 1.034 g of naphthalene (CIOHS) is burned in a volume bomb calorimeter at 298 K, 41.56 kJ of heat is evolved
constant-Calculate t.U and w for the reaction on a molar basis
From a thermochemical point of view, explain why a carbon dioxide fire extinguisher or water should not be used on a magnesium fire
5.123
5.124
5.125
5.126
Consider the reaction
Under atmospheric conditions (1.00 atm) it was found that the
formation of water resulted in a decrease in volume equal to
73.4 L Calculate D.U for the process DJ[ = - 571.6 kJ/moJ (The
conversion factor is 1 L· atm = 1Ol.3 J.)
Lime is a term that includes calcium oxide (CaO, also called quicklime) and calcium hydroxide [Ca(OH)z, also called slaked
lime] It is used in the steel industry to remove acidic impurities,
in air-pollution control to remove acidic oxides such as S02' and
in water treatment Quicklime is made industrially by heating limestone (CaC03) above 2000°C:
CaC03(s) - _ CaO(s) + Cozeg) t.w = 177.8 kJ / mol
Slaked lime is produced by treating quicklime with water:
CaO(s) + H 2 0(I) - _ Ca(OHMs) DJ[ 0 = -65.2 kJ/mol
The exothermic reaction of quicklime with water and the rather
small specific heats of both quicklime [0.946 J/(g • 0C)] and
slaked lime [l.20 J /(g 0C)] make it hazardous to store and transport lime in vessels made of wood Wooden sailing ships carrying lime would occasionally catch fire when water leaked into the hold (a) If a 500.0-g sample of water reacts with an
equimolar amount of CaO (both at an initial temperature of
25°C), what is the final temperature of the product, Ca(OHh?
Assume that the product absorbs all the heat released in the reaction (b) Given that the standard enthalpies of formation
of CaO and H20 are -635.6 and -285.8 kJ/mol, respectively,
calculate the standard enthalpy of formation of Ca(OH)2
A 4.117-g impure sample of glucose (C6H I20 6) was burned in
a constant-volume calorimeter having a heat capacity of 19.65
kJfOC If the rise in temperature is 3 134°C, calculate the percent
by mass of the glucose in the sample Assume that the impurities
are unaffected by the combustion process and that t.U = t.H See Appendix 2 for thermodynamic data
The combustion of 0.4196 g of a hydrocarbon releases 17.55 kJ
of heat The masses of the products are CO2 = 1.419 g and H20 = 0.290 g (a) What is the empirical formula of the compound? (b) If the approximate molar mass of the compound
is 76 g/mo!, calculate its standard enthalpy of formation
PRE-PROFESSIONAL PRACTICE EXAM PROBLEMS:
PHYSICAL AND BIOLOGICAL SCIENCES
A bomb calorimeter was calibrated by burning 1.013 g of benzoic acid
(C7H60 2) (D.U comb = 3.221 X 103 kJ / mol) The temperature change in the
calorimeter during the calibration combustion was 5.19°C A nutritional
chemist then used the calibrated calorimeter to determine the energy
con-tent of food The chemist carefully dried a sample of food and placed
0.8996 g of the sample in the calorimeter with sufficient oxygen for the
combustion to go to completion Combustion of the food sample caused
the temperature of the calorimeter to increase by 4.42°C
1 Approximately how many moles of O2 gas were consumed in the
calibration combustion?
a) 0.008
b) 0.1
c) 0.2 d) 0.06
2 What is the heat capacity (C v) of the calorimeter?
a) 5.15 kJJOC b) 5.08 kJJOC
c) 5.12 kJ/oC
d) 4.97 kJJOC
Trang 43 What is the energy content of the food?
a) 22.8 kJ/g
b) 4.97 kJ /g
c) 25.3 kJ/g
d) 0.201 kJ /g
4 What would be the effect on the result if the food sample were not
completely dried prior to being placed in the calorimeter?
a) The combustion of the sample would be incomplete
b) The calculated energy content per gram would be too low
c) The calculated energy content per gram would be too high
d) There would be no effect on the result
ANSWERS TO IN-CHAPTER MATERIALS
Answers to Practice Problems
5.1A (a) 1.13 X 103 J, (b) 4 5.1B (a) 370 mis, (b) neither 5.2A - 4.32 X
104 kJ 5.2B 6.95 X 105 kJ, lieat is absorbed 5.3A 8.174 X 104 kJ
5.3B 1.60 X 103 g 5.4A 151 kJ 5.4B 52 2°C 5.5A 28°e 5.5B 42 g
Answers to Applying What You've Learned
a) 1.2 X 102 Cal b) 92°e c) 380 Cal d) - 35,340 kJ/ mol (using !::.H r
values from Appendix 2, H 2 0(I) • H20(g), !::.W = + 44.0 kJ / mol)
Trang 5• The Electromagnetic Spectrum
• The Double-Slit Experiment
• Atomic Line Spectra
• The Line Spectrum of Hydrogen
• The de Broglie Hypothesis
• Diffraction of E lectrons
• The Uncertainty Principle
• The Schrodinger Equation
• The Quantum Mechanical
Description of the Hydrogen Atom
• Principal Quantum Number (n )
• Angular Momentum
Quantum Number (C)
• Magnetic Quantum Number (m e )
• Electron Spin Quantum
• The Pauli Exclusion Principle
• The Aufbau Principle
Trang 6Lasers in Medicine
Over the past two decades, the use of lasers has revolutionized many medical
proce-dures, including the excision of malignant tumors, the treatment of the symptoms
associ-ated with an enlarged prostate, and a wide variety of cosmetic procedures The benefits
of laser surgery typically include smaller incisions, les s bleeding, less pain, and shorter
recovery times than with traditional surgical methods Among the most popular laser
procedures is LASIK surgery to improve eyesight In LASIK, it neariy · clrcillar"lncislon
is made in the cornea, creating a hinged flap on the surface of the eyeball The flap is
then lifted, and a laser is used to reshape the cornea by selective ablation or vaporization
of the underlying corneal tissue The flap is then replaced, conforming to the reshaped
cornea Many patients report an immediate improvement in vision, and typical recovery
times are very short
The light emitted by a laser is the result of electronic transitions and is powerful enough
to vaporize biological tissue Although the nuclear model that Rutherford proposed based
on his gold-foil experiment specified the location of the protons and the neutrons in an
atom, it failed to describe the location or behavior of the electrons Early in the twentieth
century, the application of a radical new theory in physics called quantum theory, and the
ingenious interpretation of experimental evidence by Max Planck, Albert Einstein, and
others, led to our current understanding of the electronic structure of atoms This
under-standing of electronic structure is what makes such things as lasers possible
• • •
LAS I K is an a cro n y m f or lAs e r-a ss i s ted in Situ
Ke rato m ileus is
Central cornea flattened
In This Chapter, You Will Learn about some of the properties of electromagnetic radiation or light and how these properties have been used to study and elucidate the electronic structure of atoms You will also learn how to determine the
arrangement of electrons in a particular atom
•
Before you begin, you should review
• Tracking units [ ~~ Section 1.6]
• The nuclear model of the atom [ ~~ Section 2.2]
Lasers are used in a variety of surgical procedures, including
cosmetic procedures Laser resurfacing, shown here, is done to
rejuvenate the appearance of the face
Trang 7194 CHAPTER 6 Quantum Theory and the Electronic Structure of Atoms
The s peed of l ight is an exact number and
usually does not l imit the number of significant
figures in a calcu l ated result In most calculations,
however, the speed of light is rounded to three
sign ifi cant figures: c = 3.00 X 108 mls
Frequency is expres se d as cycles per second,
or simp l y reciprocal seconds (s -1), which is a l so
known as hertz ( Hz )
The Nature of Light
the electromagnetic spectrum In addition to visible light, the electromagnetic spectrum includes
radio waves, microwave radiation , infrared and ultraviolet radiation, X rays, and gamma rays,
as s hown in Figure 6.1 Some of these terms may be familiar to you For instance , the danger of
during a routine dent a l checkup or after breaking a bone; and you may recall from Chapter 2 that
Properties of Waves
point s on s uccessi ve waves (e.g., s ucces s ive peak s or s uccessive troughs) The frequency JJ (nu)
i s the number of waves that pas s through a particular point in 1 seco nd Amplitude is the vertical
distance from the midline of a wave to the top of the peak or the bottom of the trough
c,- l ii 2.99792458 X 108 mls The speed, wavelength, and frequency of a wave are related by the
equation
•
~h~r~ ' ~ ' ~~i ~ ~~ ~x ' p~~s~~d i~ ' ~~t~rs ' (~) a~d ' ~eciprocal seconds (S - I) , respectively While
wave-length in meters is convenient for this eq uation, the unit s customarily used to express the
wave-length of electromagnetic radiation depend on the type of radiation and the magnitude of the corre spo nding wavelength The wavelength of visible light, for instance, is on the order of nano- meter s (nm, or 10 - 9 m), and that of microwave radiation is on the order of centimeters (cm, or
Xray Sun lamp s Heat lamps Microwave ovens, UHF TV, FM radio, VHF TV AM radio
police radar, ce llular
sa tellit e stat ions telephones
Figure 6.1 Electromagnetic spectrum Each type of radiation is spread over a specific range of wavelengths (and frequencies) Visible light ranges
from 400 run (violet) to 700 run (red)
Trang 8SECTION 6.1 The Nature of Light 195
Wavelength = distance between peaks
AA= 2AB = 4Ac
The Electromagnetic Spectrum
In 1873 James Clerk Maxwell proposed that visible light consisted of electromagnetic waves
According to Maxwell's theory, an electromagnetic wave has an electric field component and a
magnetic field component These two components have the same wavelength and frequency, and
of light In particular, his model accurately describes how energy in the form of radiation can be
The Double-Slit Experiment
inteifer-e nce When a light source passes through a narrow opening, called a slit, a bright line is generated
in the path of the light through the slit When the same light source passes through two closely
each slit, but rather a series of light and dark lines known as an inteiference pattern When the
light sources recombine after passing through the slits, they do so constructively where the two
w aves are in phase (giving rise to the light lines) and destructively where the waves are out of
p hase (giving rise to the dark lines) Constructive interference and destructive interference are
p roperties of waves
The various types of electromagnetic radiation in Figure 6.1 differ from one another in
w avelength and frequency Radio waves, which have long wavelengths and low frequencies, are
Figure 6.3 Electric field and magnetic field components of an electromagnetic wave These two components have the same wavelength, frequency, and amplitude, but they
vibrate in two mutually perpendicular planes
Trang 9196 CHAPTER 6 Quantum Theory and the Electronic Structure of Atoms
Think About It Make sure your
units cancel properly A common
error in this type of problem is
neglecting to convert wavelength
emitted by large antennas, such as those used by broadcasting stations The shorter, visible light
waves are produced by the motions of electrons within atoms and molecules The shortest waves, which also have the highest frequency, are 'Y (gamma) rays, which result from nuclear processes [ ~~ Section 2.2] A s we will see shortly, the higher the frequency, the more energetic the radia-tion Thus, ultraviolet radiation, X rays, and 'Y rays are high-energy radiation, whereas infrared radiation, microwave radiation, and radio waves are low-energy radiation
Sample Problem 6.1 illustrates the conversion between wavelength and frequency
~
' Samp ' ~ l~ :P;oblein6:' r ' ' ; " , _:~ ~ _ _ _ _ ~ "~ <, , n·7~-o-.;,~:< -::i;c~
The wavelength of a laser used in the treatment of vascular skin lesions has a wavelength of 532 nm
What is the frequency of this radiation?
Strategy Wavelength and frequency are related by Equation 6.1 (c = A.v) : so we must reanange Equation 6.1 to solve for frequency Because we are given the wavelength of the electromagnetic radiation in nanometers, we must convert this wavelength to meters and use c = 3.00 X 108 m/s
Setup Solving for frequency gives v = ci A Next we convert the wavelength to meters:
Trang 10SECTION 6.2 Quantum Theory 197
Checkpoint 6.1 The Nature of Light
6 1 1 Calculate the wavelength of light with 6 1 2 Calculate the frequency of light with
frequency 3.45 X 1014 S-I wavelength 126 nm a) 1.15 X 10- 6 nm a) 2.38 X 1015 S- I
b) 1.04 X 1023 nm b) 4.20 X 10- 16 S-I c) 8.70 X 102 nm c) 37.8 S-I
e) 9.66 X 10- 24 nm e) 3.51 X 1019 S-I
Quantum Theory
of subatomic particle s usin g the law s o f cla ss ical ph ys ics that govern the b e h av ior of macr oscop ic
object s It took a lon g time to reali ze and a n even longer time to accept t hat the prop erties of
Quantization of Energy
When a s olid i s heated , it emits electromagnetic radi a tion , known as blackbody radiation, over a
wide range of wavelengths The red glow of the element of an electric stove and the bri ght w hit e
light of a tung s ten lightbulb are examples of blackb ody radi a tion Meas ur e m en t s taken in the
lat-ter part of the ninete e nth century s h owe d th at the a m o un t of energy g i ven off by an object at a
this dependence in t e rm s of es tabli s hed wave theory an d th ermo d ynamic law s were only partially
the longer wavelength s Another theory acc o unted for the l onger wave len gt h s bu t failed for s hort
wavelength s With no o ne theor y that could ex plain both observations, it see med that so mething
In 1900 , Max Planckl provid e d the so luti o n and l aunc h e d a n ew era in physic s wit h an
idea that departed dra s tically from accepted concepts Class ic a l physics assumed that radiant
energy was continuou s; that i s, it could be emitted or absorbed in any amount Ba se d on d a ta f rom
blackbody radiation experiments , Pl a nck proposed t ha t radi a n t energy co uld on l y be emitte d or
absorbed in di sc rete quantitie s, like s mall pa ckages o r bundl es Plan ck gave the name quantum t o
radiation The energy E of a s in g le qu a ntum of energy is given b y
where h is called Plan ck' s con~tq!1:f a.n~ Y ~~ th<:-.fr:e.qu~nc:t of t~.~ ~~di~t.i.C?~ T.h~ va l u e: of 'pl~p~~.'.s
constant is 6.63 X 10 - 34 J s
At the time Planck pre s ented hi s th eo r y, h e co uld not explain w h y energies shou ld be fixed or
quantized in this manner Starting with this h ypot h es i s, howe ve r , he had no difficulty correlating
-mental data s upport e d his n ew quantum theOl Y
The idea that energy i s quanti zed rather than cont inu ous ma y seem s trange , but t h e co ncep t
of quantization ha s many eve ryda y analogie s For exa mpl e, ve ndin g machines di s pen se cans or
bottle s of soft drink s only in whole number s (yo u can ' t bu y part of a can or bottle from a machine )
Each can or bottle i s a quantum of it s so ft drink Even proce sses in li v in g sys tem s in vo l ve
quan-tized phenomena The eggs laid by hens ar e quan ta ( hens l ay only who le eggs) Similarly , when a
I Ma x K ar l Ern s t Ludwig Planck ( 1 858-1947) Gennan ph ysic i st Plan ck r eceived t h e Nobel Prize in Ph ys ic s in 1918 for
hi s quantum the o r y H e al so mad e s i g nifi ca n t co n tri buti o n s in th ennody n amics and ot h e r ar eas of p h ys ic s
The National Institute of Standards and
significant figures are sufficient for solving
,
Trang 11198 CHAPTER 6 Quantum Theory and the Electronic Structure of Atoms
Figure 6.5 Apparatus for studying
the photoelectric effect Light of a
certain frequency falls on a clean metal
surface Ejected electrons are attracted
toward the positive electrode The flow
of electrons is registered by a detecting
meter
dog or cat gives birth to a litter, the number of offspring is always an integer Each puppy or kitten
is a quantum of that animal Planck's quantum theory revolutionized physics Indeed, the flurry of research that ensued altered our concept of nature forever
Photons and the Photoelectric Effect
In 1905 , only 5 years after Planck presented his quantum theory, Albert Einstein2 used the theory to
explain another mysterious physical phenomenon, the photoelectric effect, a phenomenon in which
electrons are ejected from the surface of a metal exposed to light of at least a certain minimum
frequency, called the thresholdfr e quency (Figure 6.5) The number of electrons ejected was tional to the intensity (or brightness) of the light, but the energies of the ejected electrons were not Below the threshold frequency no electrons were ejected no matter how intense the light
propor-The photoelectric effect could not be explained by the wave theory of light, which ated the energy of light with its intensity Einstein, however, made an extraordinary assumption
associ-He suggested that a beam of light is really a stream of particles These particles of light are now called photons Using Planck's quantum theory of radiation as a starting point, Einstein deduced that each photon must possess energy E given by the equation
Ephot o n = hv
where h is Planck's constant and v is the frequency of the light Electrons are held in a metal
by attractive forces, and so removing them from the metal requires light of a sufficiently high frequency (which corresponds to a sufficiently high energy) to break them free Shining a beam
of light onto a metal surface can be thought of as shooting a beam of particles photons at the
metal atoms If the frequency of the photons is such that hv exactly equals the energy that binds the electrons in the metal, then the light will have just enough energy to knock the electrons loose
If we use light of a higher frequency, then not only will the electrons be knocked loose, but they will also acquire some kinetic energy This situation is summarized by the equation
where KE is the kinetic energy of the ejected electron and W is the binding energy of the electron
in the metal Rewriting Equation 6.3 as
KE = hv - W
shows that the more energetic the photon (i.e., the higher its frequency), the greater the kinetic energy of the ejected electron If the frequency of light is below the threshold frequency, the photon will simply bounce off the surface and no electrons will be ejected If the frequency is equal to the threshold frequency, it will dislodge the most loosely held electron Above the threshold frequency,
it will not only dislodge the electron, but also impart certain kinetic energy to the ejected electron
Now consider two beams of light having the same frequency (greater than the threshold frequency) but different intensities The more intense beam of light consists of a larger number of photons, so it ejects more electrons from the metal's surface than the weaker beam of light Thus, the more intense the light, the greater the number of electrons emitted by the target metal; the higher the frequency of the light, the greater the kinetic energy of the ejected electrons
Sample Problem 6.2 shows how to deteunine the energy of a single photon of light of a given wavelength
Sample Problem 6.2
Calculate the energy (in joules) of (a) a photon with a wavelength of 5.00 X 104 nm (infrared region) and (b) a photon with a wavelength of 5.00 X 10 - 2 nm (X-ray region)
Strategy In each case we are given the wavelength of light Use Equation 6.1 to convert wavelength
to frequency, and then use Equation 6.2 to determine the energy of the photon for each wavelength
2 Albert Ein s tein (1879-1955) German-born American physicist Regarded by many as one of the two greate s t physicists the world ha s known ( the other is I s aac Newton) The three papers (on special relativity, Brownian motion, and the photo- electric effect ) that he published in 1905 while employed a s a technical assistant in the Swiss patent office in Berne have profoundly influenced the development of physics He received the Nobel Prize in Physics in 1921 for his explanation of the photoelectric effect
Trang 12SECTION 6.2 Quantum Theory 199
This is the energy of a single photon with wavelength 5.00 X 104 run
(b) Following the same procedure as in part (a), the energy of a photon of wavelength
Practice Problem A Calculate the energy (in joule s) of ( a ) a photon with wavelength 2.11 X 102 cm
and (b) a photon with wavelength 1.69 X 103 mm
Practice Problem B Calculate the wavelength ( in run ) of (a ) light with energy 1.89 X 10- 20 J per
Einstein's theory of light posed a dilemma for scientists On the one hand, it explains the
photoelectric effect On the other hand , the particle theory of light i s inconsistent with the known
wavelike properties of light The only way to resolve the dilemma i s to accept the idea that light
possesses properties characteristic of both particles and waves Depending on the experiment ,
physicists had thought about matter and radiation, and it took a long time for them to accept it We
will see in Section 6.4 that possessing properties of both particles and wave s is not unique to light
Bringing Chemistry to life
Laser Pointers
e ven children raising some significant safety concerns Although the human blink reflex
intentional prolonged exposure of the eye to the beam from a laser pointer can be dangerous Of
particular concern are the new green laser pointers that emit a wavelength of 532 nm The laser s
How-e ver, some of the inexpensive imported lasers do not bear adequate safety labeling and the filter s
Think About It Remember that
frequency and wavelength are
inv e rs e ly proportional (Equation 6.1) Thus , as wavelength
ar e easily removed potentially resulting in the emi ss ion of dangerous radiation
Strategy Use the s ame approach as in Sample Problem 6.2 That is, con v ert each wa ve length to
( C o ntinued )
Altho u g h t h e 1 06 4- n m lase r beam is l es s
e n erg e tic t h an the 53 2 - nm beam , it poses a
gr e at er dang er to the e y e b e cause i t i s not v i s ibl e and doe s not evok e the b l ink re s p onse that
v i sible w a vel e ngt h s d o Des p i te no t b ei ng v i si ble,
a 1 0 64- n m b e am pa s se s through the anterior
st r uct ures of th e ey e a n d d a mage s t he retin a
B e cause t he bea m is not v i s ib l e, t he d a mage i s
no t im med ia t e l y appare n t, but i t is per m anent
Trang 13200 CHAPTER 6 Quantum Theory and the Electronic Structure of Atoms
Think About It A s wavelen g th
decreases, frequency increa s e s
to frequency , also in c rease s
If y ou h a ve e v er seen a r a i nbow, yo u a r e
fa mil i a r w i t h t his p h e n ome n on The ra in b ow
is t h e visi b le portion of t h e su n 's emission
The differ e nce between them i s ( 3 7 4 X 10 - 19 J ) - ( 3.13 X 10 - 19 J ) = 6.1 X 10-20 J Therefore ,
a photon of green light ( "A = 532 nm) has 6 1 X 10 - 20 J mor e energy than a photon of red light
( "A = 6 3 5 nm )
Practice Problem A Ca l culate th e differ e nce in ener g y ( in joule s ) between a photon with
"A = 680 nm (red ) and a photon with "A = 442 nm ( blue)
Practice Problem B In what re g i o n of th e e l e ctromagnetic s pectrum i s a photon found that pos s esse s
twice a s much energy a s o ne in th e blue r eg ion ("A = 442 nm ) of the visib l e s pectrum?
Bohr's Theory of the Hydrogen Atom
In addition to explaining the photoelectric effect , Planck 's quantum theory and Einstein ' s idea s made it po ss ible for scientists to unravel another nineteenth-century my stery in physics: atomic line s pectra
In the s eventeenth century , Newton had shown that s unlight is composed of various color
' co ' mpo ' n e nt s ' th a t ' c a n ' ht :< re co mbln e cl ' to ' p ro Ciiic e ' white light Since that time, chemists and physi
-ci s t s have s tudied the characteri s tics of such emission spectra The emis sion spectrum of a stance can be seen by energizing a s ample of material with either thermal energy or some other
sub-form of energy (such as a high-voltage electr i cal disc h arge if the s ubstance is a gas) A "red-hot"
or " white-hot" iron bar fre s hly removed from a fire produces a characteristic glow The glow is the
vi s ible portion of its emis sion spectrum The heat given off by the s ame iron bar is another portion
of its emis s ion spectrum the infrared region A feature common to the emission spectrum of the
sun and that of a heated solid is that both are continuous; that is, all wave l engths of visible light are
pre s ent in e ach spectrum (Figure 6.6)