chapter two: the quantum mechanical model of the atom

What determines the overall size of an atom?

The electrons, which occupy most of the empty space that makes up the atom's volume.

Why must we understand electrons to understand the nature of matter?

An atom's electrons determine many of its chemical and physical properties.

What is the primary difference in behavior between the macroscopic (things you can see and touch every day) world and the quantum world (The extremely small world of atoms and subatomic particles)?

Unobserved quantum particles can exist in two different states at the same time.

How can unobserved quantum particles can exist in two different states at the same time?

Quantum superposition: a system behaves as a combination of all possible outcomes until an interaction forces it to choose a definite reality.

What forces a quantum particle out of its simultaneous dual-state and into one specific state?

The act of observation or measurement.

What was the original purpose of Erwin Schrödinger’s "Schrödinger’s cat" thought experiment?

To demonstrate that quantum strangeness does not transfer to the macroscopic world.

In Schrödinger's thought experiment, what state is the cat in while the chamber remains closed and unobserved?

The cat is both dead and alive (undead) at the same time.

What model explains the strange behavior of electrons within atoms?

The quantum-mechanical model of the atom.

What is light?

Electromagnetic radiation, a type of energy embodied in oscillating electric and magnetic fields

Simpler terms: a wave of moving energy made of invisible electric and magnetic forces that travel together through space

What is a magnetic field

A region of space where a magnetic particle experiences a force (think of the space around a magnet).

What is an electric field?

A region of space where an electrically charged particle experiences a force.

eg) a proton has an electric field around it. If you bring another charged particle into that field, that particle experiences a force.

What are the two fields that make up electromagnetic radiation?

An electric field and a magnetic field.

What is the main idea of wave–particle duality?

Light can behave like a wave in some experiments and like a particle in others.

What are the two ways light can be described?

As a wave and as a particle.

How are the electric and magnetic fields oriented in an electromagnetic wave?

They oscillate perpendicular to each other and propagate through space.

Simpler terms: In an electromagnetic wave, the electric and magnetic fields vibrate at right angles to each other (like a plus sign +) while the whole wave travels straight ahead.

If you imagine the wave moving forward like a car on a road, the electric field is constantly waving straight up and down, while the magnetic field is waving side to side. Because they vibrate sideways relative to the direction they are traveling, they form a perfect 90-degree angle with each other and with the path of the wave itself.

What is this image an example of? What do the different waves symbolize? What else is there to note?

What the Image Shows

• Electromagnetic radiation: Energy traveling through space as synchronized waves of electric and magnetic fields.

What the Components Symbolize

• Vertical wave: Represents the oscillating electric field.

• Horizontal wave: Represents the oscillating magnetic field.

• Straight center line: Represents the direction of propagation (the path the wave travels).

Key Technical Notes

• Perpendicular alignment: The electric field, magnetic field, and travel direction all sit at 90-degree angles to each other.

• Self-sustaining: A changing electric field creates a magnetic field, and vice versa, allowing the wave to travel through a vacuum without a physical medium.

• Constant speed: In a vacuum, all electromagnetic waves travel at the speed of light (\(3 \times 10^8\) meters per second).

What is the speed of light in a vacuum?

3.00 × 10⁸ m/s.

What is the approximate speed of sound in air?

340 m/s.

Why do you see lightning before hearing thunder?

Light travels much faster than sound.

What are three properties used to characterize a wave?

Amplitude, wavelength, and frequency

What is amplitude?

The vertical height of a wave's crest or the depth of its trough.

What does the amplitude of light determine?

Its intensity or brightness.

What happens to the brightness/intensity of light when amplitude increases?

The intensity increases.

What is wavelength?

The distance between adjacent crests, or between any two analogous points on a wave.

What symbol represents wavelength?

λ (lambda).

What units can wavelength be measured in?

Meters, micrometers, nanometers, etc.

What determines the color of visible light?

Its wavelength.

Identify the parts of a wavelength

Wavelength, amplitude, rest position, CREST, TROUGH

What is frequency?

The number of wave cycles or crests that pass a stationary point during a given amount of time.

What symbol represents frequency?

ν (nu).

What are the units of frequency?

Cycles per second (cycle/s), or s⁻¹.

What is another name for s⁻¹ as a unit of frequency?

Hertz (Hz).

What does 1 Hz mean?

1 cycle per second.

How are frequency and wavelength related?

They are inversely proportional.

If wavelength increases, what happens to frequency?

Frequency decreases.

If wavelength decreases, what happens to frequency?

Frequency increases.

If a wave has widely spaced crests, will its frequency be high or low?

Low.

If a wave has closely spaced crests, will its frequency be high or low?

High.

What equation relates frequency, speed, and wavelength for light?

ν = c/λ

What does c represent in ν = c/λ?

The speed of light.

What does λ represent in ν = c/λ?

Wavelength.

What does ν represent in ν = c/λ?

Frequency.

If you know the wavelength of light, what can you calculate?

Its frequency.

If you know the frequency of light, what can you calculate?

Its wavelength.

What happens to frequency when the wavelength of light gets shorter?

Frequency gets higher.

What happens to frequency when the wavelength of light gets longer?

Frequency gets lower.

What is visible light?

The portion of electromagnetic radiation that can be detected by the human eye.

What color of visible light has the longest wavelength?

Red.

What is the approximate wavelength of red light?

About 750 nm.

What color of visible light has the shortest wavelength?

Violet.

What is the approximate wavelength of violet light?

About 400 nm.

Put the visible colors in order from longest wavelength to shortest wavelength.

Red → orange → yellow → green → blue → indigo → violet.

Put the visible colors in order from shortest wavelength to longest wavelength.

Violet → indigo → blue → green → yellow → orange → red.

Which has the higher frequency: red or violet light?

Violet.

Which has the lower frequency: red or violet light?

Red.

Why does a red shirt appear red?

It predominantly reflects red light while absorbing most of the other colors.

Why does white light contain many colors?

White light contains a spectrum of different wavelengths.

What happens when white light passes through a prism?

It can be separated into its constituent colors.

What is the spectrum of visible light?

The array of colors produced when the different wavelengths of visible light are separated.

A bright green laser and a dim red laser differ in what two wave properties?

Their wavelength/frequency and their amplitude.

Which has the shorter wavelength: green light or red light?

Green light.

If the green laser is brighter, what does that tell you about its amplitude?

The green laser has greater amplitude.

Does greater amplitude necessarily mean greater frequency?

No. Amplitude and wavelength/frequency are independent properties.

What is the electromagnetic spectrum?

The complete range of wavelengths of electromagnetic radiation.

What portion of the electromagnetic spectrum can humans see

Visible light, which makes up only a tiny portion of the spectrum.

What is the general relationship between wavelength and frequency across the electromagnetic spectrum?

Shorter wavelength = higher frequency; longer wavelength = lower frequency.

What does the image present?

The electromagnetic spectrum.

What is the relationship between wavelength and energy?

Shorter wavelength = greater energy; longer wavelength = lower energy.

What is the relationship between frequency and energy?

Higher frequency = greater energy; lower frequency = lower energy.

What type of electromagnetic radiation has the shortest wavelength?

Gamma rays.

What type of electromagnetic radiation has the longest wavelength?

Radio waves.

Which side of the electromagnetic spectrum has short wavelengths and high frequencies?

The gamma-ray/X-ray side.

Which side has long wavelengths and low frequencies?

The radio-wave side.

Put these in increasing wavelength: X-rays, visible, infrared.

X-rays < visible < infrared.

Put these in decreasing wavelength: X-rays, visible, infrared.

Infrared > visible > X-rays.

Where is visible light located in the electromagnetic spectrum?

Between ultraviolet and infrared.

What type of electromagnetic radiation has the highest energy?

Gamma rays.

Why can excessive exposure to gamma rays be dangerous?

Their high energy can damage biological molecules.

eg) Gamma rays are produced by the sun, other stars, and certain unstable atomic nuclei on Earth.

Why can X-rays pass through the body to create images?

They pass through many substances that block visible light.

Can excessive X-ray exposure damage biological molecules?

Yes, while several annual exposures to X-rays are relatively harmless, too much exposure to X-rays increases cancer risk

What type of radiation is responsible for sunburn and suntan?

Ultraviolet (UV) radiation.

Too much exposure: Skin cancer, cataracts, and premature skin wrinkling.

Which has greater energy: violet visible light or red visible light?

Violet

Why does violet have greater energy than red?

Violet has a shorter wavelength and therefore a higher frequency.

What happens when visible light interacts with certain molecules in our eyes?

The molecules change shape, sending a signal to the brain that allows us to see.

Note: Visible light—at low to moderate intensity—does not carry enough energy to damage biological molecules.

What type of electromagnetic radiation is associated with heat from warm objects?

Infrared radiation.

Do warm objects emit infrared radiation?

Yes. All warm objects, including human bodies, emit infrared light.

Which has longer wavelengths: microwaves or visible light?

Microwaves.

Which has lower energy: microwaves or visible light?

Microwaves

What is interference?

The interaction of waves in which they can cancel each other or build each other up depending on their alignment.

What is constructive interference?

Interference in which waves build each other up.

What is destructive interference?

Interference in which waves cancel each other.

Know the differences between destructive and constructive interference.

Out of phase: Destructive (Bottom) Canceled Out

vs

In phase: Constructive (Top) Amplitude Doubles

What is diffraction?

The bending/spreading of a wave when it encounters an obstacle or slit comparable in size to its wavelength.

What happens when a wave passes through a small opening?

It spreads out.

What happens when light passes through two small slits?

The light diffracts through each slit and the resulting waves interfere with each other.

What does the two-slit experiment produce on a screen?

A pattern of bright and dark lines.

Why does each slit act as a new wave source?

The light waves emerging from each slit behave as waves that can interfere with one another.

What produces a bright line in the two-slit pattern?

Constructive interference.

What produces a dark line in the two-slit pattern?

Destructive interference.

At the center of the two-slit screen, why is there constructive interference?

The two waves travel equal distances and arrive in phase.