# Section 1: Light and Quantized Energy

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Section 1: Light and Quantized Energy
Light, a form of electromagnetic radiation, has characteristics of both a wave and a particle. K What I Know W What I Want to Find Out L What 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. Copyright © McGraw-Hill Education Light and Quantized Energy

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. Copyright © McGraw-Hill Education Light and Quantized Energy

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? Copyright © McGraw-Hill Education Light and Quantized Energy

frequency amplitude electromagnetic spectrum quantum Planck’s constant photoelectric effect photon atomic emission spectrum Light and Quantized Energy Copyright © McGraw-Hill Education

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. Copyright © McGraw-Hill Education Light and Quantized Energy

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. Copyright © McGraw-Hill Education Light and Quantized Energy

The Wave Nature of Light
The speed of light (3.00 × 108 m/s) is the product of it’s wavelength and frequency c = λν. Copyright © McGraw-Hill Education Light and Quantized Energy

The Wave Nature of Light
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. Copyright © McGraw-Hill Education Light and Quantized Energy

CALCULATING WAVELENGTH OF AN EM WAVE
KNOWN UNKNOWN ν = 3.44 × 109 Hz λ = ? m c = 3.00 × 108 m/s 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? SOLVE 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 = λν λ = 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. Response ANALYZE 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. Light and Quantized Energy Copyright © McGraw-Hill Education

CALCULATING WAVELENGTH OF AN EM WAVE
EVALUATE THE ANSWER The 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 Light and Quantized Energy Copyright © McGraw-Hill Education

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. Copyright © McGraw-Hill Education Light and Quantized Energy

The Quantum Concept In 1900, German physicist Max Planck ( ) 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 × 10–34 J ● s. Copyright © McGraw-Hill Education Light and Quantized Energy

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. Copyright © McGraw-Hill Education Light and Quantized Energy

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. Copyright © McGraw-Hill Education Light and Quantized Energy

Ephoton = (6.626 × 10-34 J•s)(7.230 × 1014 s-1)
CALCULATE THE ENERGY OF A PHOTON SOLVE FOR THE UNKNOWN State the equation for the energy of a photon. Ephoton = hν Substitute h = × J•s and ν = × 1014 s-1. Ephoton = (6.626 × J•s)(7.230 × 1014 s-1) Multiply and divide numbers and units. Ephoton = × J 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 × 1014 s-1? Response ANALYZE THE PROBLEM EVALUATE THE ANSWER As 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. KNOWN UNKNOWN ν = × 1014 s-1 Ephoton = ? J h = × J•s Copyright © McGraw-Hill Education Light and Quantized Energy

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. Copyright © McGraw-Hill Education Light and Quantized 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. Copyright © McGraw-Hill Education Light and Quantized Energy

Review Essential Questions Vocabulary
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 Copyright © McGraw-Hill Education Light and Quantized Energy