Quantum Mechanics and Electromagnetic Spectrum

Unit 4 Lesson 1: Quantum Mechanics

Quantum Mechanics

Have you ever seen the night sky light up with green, red, orange, blue, or pink lights? If you live in Alaska, chances are good that you have seen the Northern Lights, an amazing display of colorful lights.

In this lesson, you'll learn about how something called quantum mechanics determines how light and electrons interact to cause the Northern Lights — and to cause more ordinary things you see, like light coming out of a lightbulb.

The aurora borealis, known as the northern lights, is caused by changes in electrons in the atmosphere.

Objectives

• Calculate wave speed, frequency, and wavelength.

• Compare the energy of different wavelengths of light.

• Explain the concept of electron transitions.

• Assign quantum numbers to electrons.

• Describe how light and electron transitions are connected.

Part 1: Waves

Waves

People use tanning beds to get a tan without having to be outside in the sun. Tanning beds work by producing ultraviolet (UV) radiation, which is the same type of radiation that comes into the atmosphere from the sun. UV radiation is often also called UV light or UV rays.

Scientists have shown that exposure to UV radiation is a cause of skin cancer and other skin problems. As a result, some countries have considered prohibiting businesses from making tanning beds available to the public. Many U.S. agencies, such as the U.S. Public Health Service, have recommended that people avoid them

Energy in Waves

Waves carry energy.

UV light is energy in the form of a wave.

A wave is something that carries energy through space, whether it is a light wave, a sound wave, or a wave in the ocean.

In fact, the energy released from an underwater earthquake can travel through the ocean, causing a series of huge waves called a tsunami.

Frequency

Frequency is a measure of how many waves pass a point in 1 second.

One way to determine a wave's energy level is to measure its frequency. Frequency is how many waves pass a point in 1 second.

The unit for frequency is waves per second, which is called a hertz (Hz). You might be familiar with hertz because radio station frequencies are reported in kilohertz (kHz) and megahertz (MHz). FM station numbers are actually frequencies in MHz, and AM station numbers are frequencies in kHz.

Measure frequency in the exercise below by counting the number of waves that pass by a point in 1 second. 

Wavelength

Wavelength is the distance between wave peaks.

Another way to measure the energy of a wave is by using wavelength. A wavelength is the distance between the highest points, or peaks, of two waves.

If two waves of the same type have the same frequency but different wavelengths, the wave with the shorter wavelength has more energy. 

Multiple Choice

What is the wavelength of the wave shown above?

• 1 cm

• 1.5 cm

• 2 cm

• 3 cm

Wave Velocity

• Different types of waves move at different velocities. Some waves move very quickly, or have a high velocity, whereas others move slowly, with a low velocity.

• Velocity is just speed, but with direction taken into account.

• Wave velocity is measured in meters per second (m/s) and has the symbol v.

• A light wave has a much higher velocity, or is much faster, than a sound wave. That's why you see lightning before you hear thunder (which is the sound of lightning).

• In fact, you can figure out your distance from a lightning storm by counting the number of seconds between the time you see the lightning and the time you hear thunder. To determine how many miles away the storm is, divide the number of seconds by 5.

Velocity, Frequency, and Wavelength

Velocity equals frequency times wavelength; wavelength equals velocity divided by frequency.

There is a relationship between wave velocity (symbolized as v ),

 frequency (symbolized as f ),

and wavelength (symbolized as λ ).

This equation is true for all types of waves:

Practice Finding Wavelength

To solve for the wavelength, substitute known values of velocity and frequency.

Imagine that a wave has a velocity of 10 m/s and a frequency of 2 hertz (Hz).

A hertz is a cycle per second, which can be written in units of 1 divided by time in seconds (s), which is symbolized as simply 1/s.

What is the wavelength of this wave?

To solve this problem, use the equation for wavelength.

Substitute the known values for v and f: 

Multiple Choice

Sound travels through air at about 340 m/s. If a sound wave has a frequency of 260 Hz, what is its wavelength?

• 80 m

• 1.3 m

• 0.76 m

• 600 m

Multiple Choice

What is the velocity of a sound wave in helium with a frequency of 240 Hz and a wavelength of 4.0 m?

• 60 m/s

• 480 m/s

• 960 m/s

• 3940 m/s

Multiple Choice

Sound travels through air at about 340 m/s. If a sound wave has a wavelength of 5 cm (0.05 m), what is its frequency?

• 17 Hz

• 68 Hz

• 1700 Hz

• 6800 Hz

Multiple Choice

A wave on a stretched rope travels with a speed of 100 m/s. What is the frequency of a wave that has a wavelength of 20 cm (0.20 m)?

• 5.0 Hz

• 20 Hz

• 500 Hz

• 2000 Hz

Multiple Choice

Sound travels through air at a constant rate. As the wavelength of a sound wave increases, the frequency decreases.

• True

• False

Electromagnetic Waves

There are many types of electromagnetic waves.

In chemistry, the most important kind of wave to know about is a light wave. Light is also called an electromagnetic wave, or EM wave. There are many types of electromagnetic waves, covering a range that is called the electromagnetic spectrum.

Visible Light

Visible light changes from red to blue as wavelength decreases.

The section of the electromagnetic spectrum that humans can see is called visible light. The images below show how the wavelengths of red, green, and blue light compare.

Multiple Choice

What color is light of wavelength 500 nm?

• Red

• Green

• Blue

• Purple

Mixing Colors

Light at 750 nm looks red to us.

Other colors all have shorter wavelengths: Violet is the shortest, then indigo, blue, green, yellow, orange, and finally red.

What color do you think light is when all the colors of light are mixed together?

Hint: Light from the sun is all the colors of light mixed together.

Multiple Choice

When red, orange, yellow, green, blue, and violet light are mixed together, what color do you think the resulting light is?

• White

• Gray

• Brown

• Black

White Light

Light that is a mixture of all colors looks white.

The image to the left shows you a test of an engine on a space shuttle. The engine is burning hydrogen, and the flame looks almost colorless.

Visible light waves from the sun, "full spectrum" lightbulbs, and fluorescent lights contain all the colors of light — and yet look colorless.

This is because when waves of all the colors of light in the electromagnetic spectrum are added together, they cancel each other out, resulting in light that looks white.

The variety of colors in the hydrogen emission spectrum is why light from burning hydrogen gas looks colorless.

Infrared Light

Infrared waves have a lower frequency than do those of visible light.

Waves that have a frequency lower than those of visible light include infrared light, microwaves, and radio waves.

Infrared light is the type of light used in laser tag and laser pointers, and it also carries signals from your remote control to your TV.

Infrared light is also the kind of radiation that allows night-vision goggles to work.

Night-vision goggles work in one of two ways:

1. They sense the small amount of infrared light present in the atmosphere; they then amplify this light so people can see objects at night.

2. They sense infrared light given off by warm objects, such as animals or people.

Microwave and Radio Waves

Microwave and radio waves are long-wavelength waves in the EM spectrum.

The waves responsible for wireless Internet signals and the energy in microwave ovens both fall within the microwave region of the electromagnetic spectrum. Microwaves have a wavelength of around 1 cm, which is just the right wavelength to heat the water, fat, and sugar molecules in food.

Waves responsible for the signals from radio stations fall within the radio/TV region of the electromagnetic spectrum. Radio waves are among the longest EM waves: A single radio wave can measure hundreds of meters long.

High-Frequency EM Waves

Both UV rays and X-rays have a high frequency.

UV rays have a higher frequency than does visible light. UV rays are a source of energy for plants and are necessary for human life. However, if humans are exposed to too many UV rays, the rays can interact with DNA molecules and cause dangerous changes within cells.

X-rays have a higher frequency than do UV rays, which means they have a shorter wavelength. They can pass through a human body but not through bone. This fact makes them very useful to doctors treating people with suspected broken bones. In an X-ray image, bones appear white, whereas breaks and other problems appear darker.

The Speed of Light

Light is the fastest thing in the universe.

In 1 second, light could travel around the Earth 7.5 times. In fact, the speed of light (c) — 3.0  10⁸ m/s — is faster than anything else in the universe. Light travels at about 186,000 miles per second!

The relationship between wave velocity (v), frequency (f), and wavelength () applies to all types of waves, including light.

v = f

When the wave is a light wave, then the wave velocity is the speed of light, c.

So this is the relationship between the speed, frequency, and wavelength of light:

c = f

Energy in EM Waves

The energy of an EM wave depends on its frequency.

An EM wave can be useful. For example, visible light allows you to see, and microwaves allow you to cook dinners quickly. High-frequency EM waves — such as those used in medical tests or treatments — can also be useful, but X-rays or gamma rays can be very dangerous if not used in very small and controlled amounts. That's why you wear a lead apron when you get an X-ray at the dentist's office.

The higher the frequency of an EM wave, the more energy it has. Here is the equation for calculating the energy of any EM wave:

E = hf

The letter h represents a constant called Planck's constant. It always has the value 6.626 × 10^–34 J·s. 

Multiple Choice

What is the energy of a radio wave with a wavelength of 1000 m?

• 0.02 J

• 2 x 10^–28 J

• 2 x 10⁴⁰ J

Multiple Choice

Why is UV light more dangerous than visible light or radio waves?

• UV light has a higher energy than does visible light or radio waves.

• UV light has a lower frequency than does visible light or radio waves.

• UV light has a longer wavelength than does visible light or radio waves.

Turn in your paper to the bin and work on something quietly.