Kelter P., Mosher M., Scott A. Chemistry. The Practical Science

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a. If the value of H for the reaction is −453 kJ, what is the

value of H for the reverse of the reaction?

b. What is the value of H for this reaction if 10.0 g of

phosphoric acid is produced?

c. Is this reaction endothermic or exothermic?

d. If 1.50 g of P

(s) and 2.50 mL of water were mixed,

how many grams of phosphoric acid would result?

e. What is the enthalpy change for the process outlined in

part d?

f. If 10.0 g of P

were mixed with 1.00 kg of water at

25.0°C, what would be the ﬁnal temperature of the water?

101. Sodium hydroxide pellets can be used to unclog a drain.

a. What is the enthalpy change when 15.0 g sodium

hydroxide is added to 1.00 L water?

b. What is the molarity of this solution? (Assume that the

volume change is negligible.)

102. A student wishes to prove the existence of silver ions in a

particular solution that was supposedly made by dissolving

silver nitrate in water.

a. Explain how this could be determined using a solution of

sodium sulﬁde, and write a reaction that illustrate this

method.

b. What is the molar enthalpy change for the reaction of a

solution of silver nitrate and sodium sulﬁde?

103. A 0.10 lb sample of sodium metal is added to 1.00 gallon

water.

a. Assuming no change occurs in the volume of the sample,

what would be the concentration of the resulting solution

of sodium hydroxide?

b. What is the enthalpy change for this process?

Thinking Beyond the Calculation

104. Phosphoric acid is used in many soft drinks to add tartness.

This acid can be prepared through the following reaction:

(s) + 6H

O(l) → 4H

(aq)

208 Chapter 5 Energy

22.7°C

152.06 g =

Mass of

calorimeter

Water

added

Metal block

at 96.3°C

234.95 g =

Mass of

calorimeter

and water

257.88 g =

Mass of

calorimeter,

water, and

metal block

24.1°C

Phosphoric acid

96. A student’s coffee cup calorimeter, including the water it

contains, has been calibrated in a manner similar to that de-

scribed in Problem 46. The heat capacity was found to be

55.5

◦

. If a 65.8-g sample of an unknown metal, at 100.0°C,

was placed in the calorimeter initially at 25°C, and an equi-

librium temperature of 29.1°C was reached, what is the

speciﬁc heat of the metal?

97. The foods we eat provide fuel to keep us alive. Burning a

0.500-g sample of vegetable oil provides enough heat to

raise the temperature of a calorimeter by 2.5 K. Assuming

the heat capacity of the calorimeter to be 7.5

, determine

the heat of combustion for 1 g of the oil.

98. A student performs the experiment shown graphically here.

What is the speciﬁc heat of the block of metal used in the ex-

periment? (Assume that the heat capacity of the empty

calorimeter is 7.5

◦

99. The reaction of the gases ethane (C

) and oxygen gives

gaseous carbon dioxide and water vapor.

a. Write the balanced chemical reaction for this combustion.

b. What is the enthalpy change for this process?

c. If 250.0 grams of ethane is consumed in the reaction, how

many grams of carbon dioxide would be produced?

d. Why should precautions be taken to avoid performing

the reaction outlined in part c in an enclosed space?

100. Under certain conditions, the reaction of chlorine gas with

metallic iron can produce iron(III) chloride.

a. Write the balanced chemical reaction for this reaction.

b. If 8.44 grams of iron(III) chloride are produced, how

many grams of iron were required?

c. What is the enthalpy change required to produce 8.44

grams of iron(III) chloride? (

H(FeCl

) =−399 kJ/mol;

S(FeCl

) = 142 J/kmol; 

G =−344 kJ/mol.)

209

Scanning tunneling microscope (STM)

image showing iron atoms adsorbed on

a copper surface forming a “quantum

corral” at a very low temperature (4 K).

The image shows the contour of elec-

tron density. The corral is about 14.3 nm

in diameter.

209

Contents and Selected Applications

6.1 Introducing Quantum Chemistry

6.2 Electromagnetic Radiation

6.3 Atomic Emission and Absorption Spectroscopy, Chemical

Analysis and the Quantum Number

Chemical Encounters: Simultaneous Determination of Elements in Water

6.4 The Bohr Model of Atomic Structure

Chemical Encounters: The Nature and Applications of Lasers

6.5 Wave–Particle Duality

6.6 Why Treating Things as “Waves” Allows Us to Quantize Their

Behavior

6.7 The Heisenberg Uncertainty Principle

6.8 More About the Photon—the de Broglie and Heisenberg

Discussions

6.9 The Mathematical Language of Quantum Chemistry

6.10 Atomic Orbitals

Chemical Encounters: The Scanning Tunneling Microscope

6.11 Electron Spin and the Pauli Exclusion Principle

Chemical Encounters: Nuclear Spin and Magnetic Resonance Imaging

6.12 Orbitals and Energy Levels in Multielectron Atoms

6.13 Electron Conﬁgurations and the Aufbau Principle

Quantum

Chemistry:

The Strange

World

of Atoms

Go to college.hmco.com/pic/kelterMEE for online learning resources.

210

Funny things happen when you shrink the

scale of observation down below that which you

can see with your eye, even when it is aided by the

most powerful optical microscope. Things that once ap-

peared to have a single value, a single space on the lab bench,

or a single speed at which they move through space now get

smeared out over time and space so that you can discuss only the prob-

ability of where they might be at a given time or how fast they might be trav-

eling when you ﬁnally catch up with them. Nothing at this level seems absolute

anymore.

The ﬁeld of chemistry that models the behavior of atoms and molecules at the

atomic level is called

quantum chemistry, and the physical description of this model is

called

quantum mechanics. Because our everyday

experiences do not easily prepare us for what

we observe in experiments done on the

atomic level, the whole idea of quantum me-

chanics might at ﬁrst appear strange or even

incomprehensible. However, the rules, or pos-

tulates, of quantum theory are elegant and

precise, of great utility, and readily under-

standable if we put aside our “macroscopic”

expectations.

Why is it useful for us to know about

quantum chemistry?

Quantum chemistry is important because

we use it to predict chemical reactivity and

other kinds of chemical properties. For exam-

ple, we need quantum chemistry to answer

questions such as, How is the energy of sun-

light captured by plants? and Why do leaves and ﬂowers have distinctive colors?

There is so much richness in our macroworld that is truly revealed only by looking

deep within, at the nanoworld that underlies it.

The colors of these ﬂowers, and the fact that sunlight helps them grow, can

be explained in terms of the basic interactions of light with matter. These

interactions are governed by quantum chemistry.

The smallest unit of

water is H

6.1 Introducing Quantum Chemistry

A liter of water can be divided in half to give two half-liters of water. Each of those

half-liters can itself be divided into halves (two quarter-liters), and so on. But

the process cannot go on indeﬁnitely because we will eventually be left with a

single water molecule. We could break this molecule down into two hydrogen

atoms and an oxygen atom, but the pieces would no longer be water. The H

molecule is the smallest unit, or quantum, of water. Energy can be quantized, too.

The quantum of light is called a

photon, the smallest possible amount of light

energy there can be. In general, a

quantum (plural quanta) is a single indivisible

unit of something. Many familiar things also come in quanta, including eggs,

cats, and chemistry books. Yet it is the quantization of light energy into photons

that will play a key part in our understanding of atomic and molecular

structure—and in all the chemistry we can explain and predict as a result. Light

energy is a type of electromagnetic radiation, so let us begin by looking at it from

that point of view.

6.2 Electromagnetic Radiation 211

6.2 Electromagnetic Radiation

When you open your eyes in the morning, information carried by light, a type of

electromagnetic radiation, ﬂoods into your brain. Light lets you see where you

are, notice what sort of day it is, and perhaps locate the button to turn on the tele-

vision news. The television signal arrives from the television station—or, in more

recent times, from a communication satellite—in the form of electromagnetic ra-

diation, as does most of the other information we need to live our lives. Studying

electromagnetic radiation from stars enables scientists to ﬁgure out the structure

of the universe. Studying the interaction of atoms with electromagnetic radiation

led to the modern view of atomic structure, the subject of this chapter.

Electromagnetic radiation, such as visible light, can be described as electro-

magnetic waves that transmit energy through space. Each wave is just a part of

the

electromagnetic spectrum, the entire range of electromagnetic radiation that is

possible. These waves have a wavelength, λ (the Greek letter lambda), frequency,

ν (the Greek letter nu), and speed (see Figure 6.1). The

wavelength is deﬁned

as the distance from the top of one crest of the wave to the top of the next crest. In the

past, wavelengths were measured using a unit known as the

angstrom (Å),where

1Å = 10

−10

m. The use of this unit of length has been supplanted by units in the

SI system, such as nanometers. The

frequency of electromagnetic radiation is

deﬁned as the number of waves that pass a given point per second. So, the frequency

is reported in units of 1/s (s

−1

), known as a hertz (Hz).

The speed of light in a vacuum is given the symbol c and is a fundamental

physical constant equal to 299,792,458 meters per second (this is usually rounded

to 3.00 × 10

−1

). How fast is the speed of light? We can get a handle on this

by considering that the Sun is, on average, 93 million miles, or 1.5 ×10

m, from

the Earth. Sunlight takes a little more than 8 minutes to reach our planet.

1.5 ×10

m ×

3.00 ×10

= 500 s (= 8.3 min)

We can also use the speed of electromagnetic radiation to tell us about dis-

tances on smaller scales. New global positioning system (GPS) devices receive

signals from at least three of the more than two-dozen GPS satellites in orbit

20,200 km (12,500 mi) above the Earth’s surface. At that distance, it takes about

Long wave

(low frequency) Wavelength

Wavelen

th Wavelen

Short wave

(high frequency)

FIGURE 6.1

Sine waves of similar amplitude, with

wavelength and frequency illustrated.

Application

Video Lesson: The Wave Nature

of Light

0.07 s for signals from each satellite to reach the receiver. Each satellite’s signal will

take a slightly different amount of time than the others to reach the running

watch or car receiver, because each is a little farther from or closer to you, de-

pending on your location. The differences in time of receipt of the signal—on the

order of milliseconds—from just three of these satellites can be used to locate

your position within a meter or two in three dimensions (Figure 6.2).

Wavelength, frequency, and speed are interrelated by the equation

ν =

Note the inverse relationship between frequency, ν, and wavelength, λ. As one in-

creases,the other decreases.The illustrationof thewavesin Figure6.1also indicates

the

amplitude of a wave, which is the distance between its highest point and zero.

EXERCISE 6.1 Conversion Between Frequency and Wavelength

What frequency of light has a wavelength of 585 nm, which appears orange to

human eyes?

Solution

Because the speed of light is expressed in meters per second, it is useful to convert

the wavelength, 585 nm, to meters:

585 nm ×

1 ×10

−9

1nm

= 5.85 × 10

−7

We can use the relationship among the speed of light, wavelength, and frequency to

solve for frequency:

ν =

3.00 ×10

m·s

−1

5.85 ×10

−7

= 5.13 ×10

−1

We can also do the equivalent calculation by dimensional analysis:

3.00 ×10

5.85 ×10

−7

= 5.13 × 10

−1

PRACTICE 6.1

What is the wavelength of light that has a frequency of 7.45 × 10

Hz? Should the

wavelength be shorter or longer than that in the exercise?

See Problems 5a, 6a, and 11–14.

212 Chapter 6 Quantum Chemistry: The Strange World of Atoms

(latitude, longitude)

FIGURE 6.2

A GPS watch and how it works. The watch

receives signals from at least three satellites.

On the basis of the time it takes each signal

to reach the watch, the distance from each

satellite is calculated. The exact position of

the watch is then triangulated from the three

distances.

Even though we mention that light is a wave, no matter is actually “waving” as the

light travels through space. When electromagnetic radiation travels through

matter, such as water, air, or a pane of glass, the electrons and nuclei of the matter

tend to follow the oscillatory motion of the electromagnetic radiation, slowing

the wave a little. The end result is that electromagnetic radiation travels a bit

more slowly through matter than in a vacuum.

If we allow an electromagnetic wave to strike a more dense transparent mate-

rial at an angle, the radiation will change direction as it enters. We use this effect

in lenses made for eyeglasses, cameras, or telescopes. The angle through which a

ray of light or other electromagnetic ray bends depends on its frequency; higher-

frequency (shorter-wavelength) rays are bent more than lower-frequency ones.

This is why a glass prism, shown in Figure 6.3, is used to separate the frequencies

of light to generate a spectrum, familiar to us as the colors of a rainbow.

The visible light spectrum of Figure 6.3 represents only a small fraction of the

entire electromagnetic spectral range, shown in Figure 6.4. Our eyes do not re-

spond to anything outside the visible range, but our technology can detect and

use the invisible frequencies. For example, very long wavelengths are used for

radio transmission and are called radio waves. The shortest radio waves, at tenths

of meters, are called microwaves and are used in cellular phone communications,

radar systems, and microwave ovens.

6.2 Electromagnetic Radiation 213

Less dense

More dense

The direction in which light travels is

bent as the electromagnetic radiation

moves from a substance of given density

to another.

Orange

Red

Yellow

Green

Blue

Indigo

Violet

Spectrum

Sunlight

Prism

FIGURE 6.3

The glass prism separates out the frequencies of light from

the electromagnetic spectrum by wavelength.

Visible spectrum

400450500550600650750 700

Frequency (s

–1

)

Wavelength (nm)

Gamma

rays

Near

infrared

Far

infrared

TV FM AM

Radio waves

X-raysMicrowaves

Visible

Radar

Far

ultra-

violet

Near

ultra-

violet

FIGURE 6.4

Electromagnetic spectrum as a function of energy.

Visualization: Refraction of

White Light

214 Chapter 6 Quantum Chemistry: The Strange World of Atoms

33.0

33.4

36.0

37.0

37.6

38.0

38.6

39.5

40.0

40.5

41.0

42.5

43.5

45.5

46.9

47.0

47.2

48.2

50.2

50.4

51.4

52.6

54.25

Gigahertz

FIGURE 6.5

The radiofrequency band is packed with assigned frequencies. How will we add more as new technologies become available?

1. McClain, Dylan Loeb, “Directing Trafﬁc in the Radio Spectrum’s

Crowded Neighborhood,” New York Times, February 24, 2000 p. D7.

2. International Telecommunications Union, http://www.itu.int/

(accessed October 2005).

When we think of trafﬁc jams, images of

cars stuck in a sea of smog and blaring

horns come to mind. Yet with the furious surge of tech-

nological innovation in consumer products such as cel-

lular phones and other two-way mobile communications

devices, a new electromagnetic trafﬁc jam has been pro-

duced. The frequencies of the radio wave part of the

electromagnetic spectrum are becoming uncomfortably

cluttered, and the assignment of the frequencies in this

range of about 3 kilohertz (3000 s

−1

) to 300 gigahertz

(3.00 × 10

−1

) is becoming what one newspaper re-

porter called “a high-wire act achieved through techno-

logical advances and the careful management of the

radio spectrum.”

The International Telecommunications Union

(ITU), headquartered in Geneva, Switzerland, is respon-

sible for developing standards and procedures related to

the assignment of radio frequencies “based on the prin-

ciple of equal rights of all countries, large or small, to

equitable access to these bands.”

In the United States, there is a dual system of admin-

istration. Federal use is administered by the National

Telecommunications and Information Administration

(NTIA). All other uses are managed by the Federal Com-

munications Commission (FCC). About 93.1% of the

total spectrum has shared use; only 5.5% is exclusively

allocated for private use and 1.4% for government use.

Figure 6.5 shows the division of the radio spectrum

into 450 bands, many of which have speciﬁc allocations.

To keep up with the extraordinary demand for new radio

frequency assignments, and to resolve the occasionally

complex issues that accompany these assignments, the

ITU began to meet every

2 years starting in 1993

instead of the prior

meeting schedule

of every 20 years. In the

United States, one of the

most complex issues is

the allocation of frequen-

cies in response to ever

more requests. How can

we make it technologi-

cally possible to stuff

more users into a ﬁnite

wavelength region by

reducing the necessary

“bandwidth” (how wide

the frequency band needs

to be for the transmis-

sion) for each user? Is it

possible to create com-

munications devices that

use alternative frequencies? The personal cellular phone

was just a dream 30 years ago. Digital audio was not even

on the horizon. What advances might we anticipate in

the next 20 years that will squeeze the frequency range

even more?

Issues and Controversies

Putting the Squeeze on Radio Frequencies

Cell phones, video phones, and

text messaging are just some of

the modern conveniences that

are squeezing the available

bandwidth.

6.2 Electromagnetic Radiation 215

How do we use the different regions of the electromag-

netic spectrum? Infrared radiation (IR), spans about 10

−6

−3

m in wavelength and can be detected with special

“heat-sensing” scopes. IR rays are associated with the vibra-

tions of molecules, so you can feel the warmth they generate

in your skin.

The Sun’s ultraviolet radiation (UV) at approximately

−7

m can give you a tan, or a burn, depending on the wave-

length and how long you sit in the sun or under a UV lamp.

The short wavelength of X-ray radiation, at about 10

−10

m, is approximately the

same size as atomic distances. This allows X-rays to be used to detect the spatial

arrangements of atoms. Gamma rays have the shortest waves in the electromag-

netic spectrum and are also the most energetic. They are a by-product of many

nuclear reactions and are very damaging to most materials, including those that

make up living things. Table 6.1 gives selected commercial (that is, related to

commerce) uses for radiation from various regions of the electromagnetic

spectrum.

The shorter the wavelength, or the higher the frequency, of the electromag-

netic radiation, the greater the energy associated with it. This relationship

between wavelength, or frequency, and the energy of a single photon was deter-

mined in 1900 by Albert Einstein (1879−1955) by extending the work of Max

Planck (1858−1947).

E = hν =

In this equation, E is the energy carried by each photon of the electromagnetic ray,

and h is

Planck’s constant, equal to 6.6260693 × 10

−34

s. This equation enables

us to calculate the energy of a single quantum of electromagnetic energy. As we’d

predict, the energy each photon carries is very small.

EXERCISE 6.2 The Energy of Electromagnetic Radiation

Compare the energy of a photon of visible radiation at 605 nm, the red light that we

detect with our eyes, and that of the X-ray radiation at 2.00 × 10

−10

m that we use

in medical diagnosis.

First Thoughts

Which has greater energy, a photon of red light or an X-ray? Our own experience

tells us that the calculation should result in a higher energy value for the X-ray.

Some Commercial Uses of Electromagnetic Radiation

Region Example of Use

Radio wave Communication

Microwave Cooking and reheating foods

Infrared Heating, drying, and cameras for ﬁnding thermal “hot spots” in products

Visible Detection of low concentrations of elements in steel, milk, water, etc.

Ultraviolet Germicide for killing bacteria in foods, in water, and on surfaces

X-ray Skeletal imaging, inspecting luggage at airports

Gamma ray Finding defects in pipe welds and castings,

inspecting containers

TABLE 6.1

An infrared picture of a home can show where most of the heat

is lost. Note that most of the heat loss in this home, shown as

bright yellow colors, occurs through its windows.

Solution

We use Planck’s constant and the speed of light to obtain the energies of each

wavelength:

E =

(6.626 ×10

−34

J·s) ×(3.00 ×10

m·s

−1

)

6.05 ×10

−7

= 3.29 ×10

−19

J for visible light

E =

(6.626 × 10

−34

J·s) × (3.00 × 10

m·s

−1

)

2.00 ×10

−10

= 9.94 × 10

−16

J for X-rays

Further Insights

The energy of the X-ray is 3000 times greater than that of the visible light. Does our

answer make sense?

Yes, it does, because our experience and our discussion up to

this point agree that X-rays are much more powerful than visible radiation. This

also explains why X-rays can do a lot more damage to living tissue than visible light.

Used with caution, however, they can penetrate the body and help physicians diag-

nose broken bones and tumors. Their damaging powers can also be used to destroy

cancerous tissue.

PRACTICE 6.2

What is the energy associated with microwaves of wavelength 8.00 mm?

See Problems 5b, 5c, 6b, 6c, and 15–24.

6.3 Atomic Emission and Absorption

Spectroscopy, Chemical Analysis

and the Quantum Number

Electromagnetic radiation can be used to transfer energy to and from atoms and

molecules. Energy emitted from or absorbed by an atom or molecule is often

found as a collection of discrete wavelengths that depend on the structure of the

atom or molecule. Using the technique known as

spectroscopy, chemists can

identify and quantify elements in all types of samples—from food and water to

brass and stainless steel. Spectroscopy, the study of how substances interact with

electromagnetic radiation as a function of wavelength or frequency, helps us deter-

mine the molecular composition of both synthetic and natural drugs, as well as

the kinds of organic molecules present in interstellar space or a sample of blood.

Figure 6.6 shows the solar spectrum, the range of visible light that is emitted

from the Sun. Note in the ﬁgure the discrete dark lines. These are an all-

important feature in atomic spectroscopy because, much like each person’s

unique ﬁngerprint in a crime scene analysis, each element leaves its unique ﬁn-

gerprint that we can use to identify it unequivocally via

emission spectroscopy

(studying radiation emitted vs. wavelength) or absorption spectroscopy (studying

radiation absorbed vs. wavelength).

Spectra have been obtained from the Sun since the beginning of the nine-

teenth century, and elemental analysis via emission spectroscopy has been done

since the late 1850s. For example, Kirchhoff and Bunsen, who published their

discovery of the elements cesium (in 1860) and rubidium (in 1861), did so by

looking at the emission spectra of these elements in a ﬂame. However, they did

not understand the relationship of the wavelengths of light that they observed to

the atomic structure of the elements. Unraveling this connection was left to

216 Chapter 6 Quantum Chemistry: The Strange World of Atoms

Video Lesson: Absorption and

Emission

Johann J. Balmer, a mathematician who numerically analyzed in detail

the hydrogen spectrum obtained by the physicist Anders Ångstrom

and others, and who published his results in 1885. The next part of our

discussion shows how we can get a hydrogen spectrum and how

Balmer’s conclusions advanced the understanding of atomic structure.

Obtaining the Hydrogen Spectrum

The hydrogen emission spectrum can be obtained using a quartz tube

with a metal electrode at each end. If the tube is then ﬁlled with hydro-

gen gas (H

) and a very high voltage is applied across the electrodes, the

tube glows as shown in Figure 6.7. In this apparatus, electrons jump

from the negative electrode to the positive electrode, transferring

energy to the hydrogen molecules in the tube. Enough energy is trans-

ferred to make some of the molecules dissociate into energetically ex-

cited hydrogen atoms (

∗

). The extra energy can be released if the

atoms emit light, represented by the expression

∗

→ H + hν

where

is the frequency of the light emitted by the excited hydrogen

(

∗

) and h is Planck’s constant. If you wished, you could write the

energy term as hc/λ:

∗

→ H +

In this case, you would talk instead about the wavelength of light

emitted.

After they lose energy by emitting radiation, the hydrogen atoms

(H) eventually recombine to form H

, the stable form of hydrogen

under normal conditions.

H + H

→

Each of the recombined molecules is then able to absorb more energy

from the electrical discharge to dissociate into two more excited atoms,

and the cycle begins again. This makes the tube glow continuously as

electrical energy is converted into electromagnetic energy.

If we pass the light emitted by the excited hydrogen atoms through a

prism, we can separate the light into individual wavelengths to get the

hydrogen

emission spectrum, as shown in Figure 6.7. Note that unlike the

Sun’s emission, only speciﬁc, discrete wavelengths of light are emitted in

the hydrogen emission spectrum.

6.3 Atomic Emission and Absorption Spectroscopy, Chemical Analysis and the Quantum Number 217

750

700

650

600

550

500

450

400

Wavelengths

(nm)

Absorption

lines

393 nm Calcium

397 nm Calcium

410 nm Hydrogen

423 nm Calcium

431 nm Iron, Calcium

434 nm Hydrogen

438 nm Iron

447 nm Helium

471 nm Helium

492 nm Helium

587 nm Helium

667 nm Helium

501 nm Helium

467 nm Iron

486 nm Hydrogen

496 nm Iron

517 nm

518 nm

527 nm Iron

656 nm Hydrogen

687–688 nm Oxygen (O

)

759–762 nm Oxygen (O

)

628– 629 nm Oxygen (O

)

Magnesium

Sodium

589 nm

590 nm

FIGURE 6.6

The spectrum of light from the Sun

includes dark bands at certain frequen-

cies, caused by particular elements in

the Sun absorbing light at these fre-

quencies. This phenomenon can be used

to identify which elements are present

in the sun. The existence of helium was

postulated by this method.

FIGURE 6.7

The hydrogen emission spectrum. An electric current is passed

through a tube of hydrogen gas, which causes some of the mole-

cules to dissociate to form excited hydrogen atoms (H*). The H*

atoms lose the energy by emitting radiation, which is separated

by wavelength with a glass prism. The intensity of the emitted

radiation can then be observed directly with your eye or can

be captured on ﬁlm with electronic detectors such as a photo-

multiplier tube, or a change-coupled device.