Light, a form of electromagnetic radiation, has characteristics of both a wave and a particle. Section 1: Light and Quantized Energy K What I Know W What

Light, a form of electromagnetic radiation, has characteristics of both a wave and a particle.

Section 1: Light and Quantized Energy

KWhat I Know

WWhat I Want to Find Out

LWhat I Learned

• 6(B) Understand the electromagnetic spectrum and the mathematical relationships between energy, frequency, and wavelength of light.

• 6(C) Calculate the wavelength, frequency, and energy of light using Planck's constant and the speed of light.

• 2(G) Express and manipulate chemical quantities using scientific conventions and mathematical procedures, including dimensional analysis, scientific notation, and significant figures.

• 2(I) Communicate valid conclusions supported by the data through methods such as lab reports, labeled drawings, graphs, journals, summaries, oral reports, and technology–based reports.

Light and Quantized EnergyCopyright © McGraw-Hill Education

• 3(A) In all fields of science, analyze, evaluate, and critique scientific explanations by using empirical evidence, logical reasoning, and experimental and observational testing, including examining all sides of scientific evidence of those scientific explanations, so as to encourage critical thinking by the student.


Essential Questions

• How do the wave and particle natures of light compare?• How is a quantum of energy related to an energy

change of matter?• How do continuous electromagnetic spectra and atomic

emission spectra compare and contrast?


Review• radiation

New• electromagnetic radiation• wavelength• frequency• amplitude• electromagnetic spectrum• quantum• Planck’s constant• photoelectric effect• photon• atomic emission spectrum


Vocabulary

The Atom and Unanswered Questions

Recall that in Rutherford's model, the atom’s mass is concentrated in the nucleus and electrons move around it. • The model doesn’t explain how the electrons were arranged around

the nucleus.• The model doesn’t explain why negatively charged electrons aren’t

pulled into the positively charged nucleus.

In the early 1900s, scientists observed certain elements emitted visible light when heated in a flame. Analysis of the emitted light revealed that an element’s chemical behavior is related to the arrangement of the electrons in its atoms.


The Wave Nature of Light

Visible light is a type of electromagnetic radiation, a form of energy that exhibits wave-like behavior as it travels through space. All waves can be described by several characteristics.• The wavelength (λ) is the shortest distance between equivalent

points on a continuous wave.• The frequency (ν) is the number of waves that pass a given point

per second.• The amplitude is the wave’s height from the origin to a crest.



The speed of light (3.00 × 108 m/s) is the product of it’s wavelength and frequency c = λν.



Sunlight contains a continuous range of wavelengths and frequencies. A prism separates sunlight into a continuous spectrum of colors. The electromagnetic spectrum includes all forms of electromagnetic radiation.



CALCULATING WAVELENGTH OF AN EM WAVE

Use with Example Problem 1.

Problem Microwaves are used to cook food and transmit information. What is the wavelength of a microwave that has a frequency of 3.44 × 109 Hz?

ResponseANALYZE THE PROBLEM

You are given the frequency of a microwave. You also know that because microwaves are part of the electromagnetic spectrum, their speeds, frequencies, and wavelengths are related by the formula c = λν. The value of c is a known constant. First, solve the equation for wavelength, then substitute the known values and solve.

KNOWN UNKNOWN

ν = 3.44 × 109 Hz

λ = ? m

c = 3.00 × 108 m/sSOLVE FOR THE UNKNOWN

Solve the equation relating the speed, frequency, and wavelength of an electromagnetic wave for wavelength (λ).

• State the electromagnetic wave relationship. Solve for λ.

c = λνλ = c/ν

• Substitute c = 3.00 × 108 m/s and ν = 3.44 × 109 Hz.

Note that hertz is equivalent to 1/s or s-1.

Hz 10 44.3m/s 10 3.00 λ 9

8


CALCULATING WAVELENGTH OF AN EM WAVE

EVALUATE THE ANSWERThe answer is correctly expressed in a unit of wavelength (m). Both of the known values in the problem are expressed with three significant figures, so the answer should have three significant figures, which it does. The value for the wavelength is within the wavelength range for microwaves.

SOLVE FOR THE UNKNOWN

• Divide numbers and units.

λ = 8.72 × 10-2 m

1-

8

s 910 44.3

m/s 10 3.00 λ

The Particle Nature of Light

The wave model of light cannot explain all of light’s characteristics. Some examples include:• Why heated objects emit only certain frequencies of light at a given

temperature. • Why some metals emit electrons when light of a specific frequency

shines on them.


The Quantum Concept

In 1900, German physicist Max Planck (1858-1947) began searching for an explanation of this phenomenon as he studied the light emitted by heated objects. Planck’s study led him to a startling conclusion: • Matter can gain or lose energy only in small, specific amounts called

quanta.• A quantum is the minimum amount of energy that can be gained or

lost by an atom.

• Planck’s constant has a value of 6.626 × 10–34 J ● s.


The Photoelectric Effect

The photoelectric effect is when electrons are emitted from a metal’s surface when light of a certain frequency shines on it.


Light’s Dual Nature

Albert Einstein proposed in 1905 that light has a dual nature. • A beam of light has wavelike and particle-like properties.• A photon is a particle of electromagnetic radiation with no mass

that carries a quantum of energy.



CALCULATE THE ENERGY OF A PHOTON

EVALUATE THE ANSWERAs expected, the energy of a single photon of light is extremely small. The unit is joules, an energy unit, and there are four significant figures.

Use with Example Problem 2.

Problem Every object gets its color by reflecting a certain portion of incident light. The color is determined by the wavelength of the reflected photons, thus by their energy. What is the energy of a photon from the violet portion of the Sun’s light if it has a frequency of 7.230 × 1014 s-1?ResponseANALYZE THE PROBLEM

KNOWN UNKNOWN

ν = 7.230 × 1014 s-1 Ephoton = ? J

h = 6.626 × 10-34 J•s

SOLVE FOR THE UNKNOWN

• State the equation for the energy of a photon.

Ephoton = hν

• Substitute h = 6.626 × 10-34 J•s and ν = 7.230 × 1014 s-1.

Ephoton = (6.626 × 10-34 J•s)(7.230 × 1014 s-1)

• Multiply and divide numbers and units.

Ephoton = 4.791 × 10-19 J

Atomic Emission Spectra

Light in a neon sign is produced when electricity is passed through a tube filled with neon gas and excites the neon atoms. The excited atoms return to their stable state by emitting light to release energy.


Atomic Emission Spectra

The atomic emission spectrum of an element is the set of frequencies of the electromagnetic waves emitted by the atoms of the element. Each element’s atomic emission spectrum is unique.



Review

Essential Questions

• How do the wave and particle natures of light compare?• How is a quantum of energy related to an energy change of

matter?• How do continuous electromagnetic spectra and atomic

emission spectra compare and contrast?

Vocabulary• electromagnetic radiation

• wavelength• frequency• amplitude

• electromagnetic spectrum

• quantum• Planck’s constant

• photoelectric effect

• photon• atomic emission

spectrum

Documents

Light, a form of electromagnetic radiation, has characteristics of both a wave and a particle. Section 1: Light and Quantized Energy K What I Know W What