# Wavelengths and energy relationship to power

### Wavelength, Wavelength Formula, Wavelength to Frequency | [email protected]

ENERGY UNITS AND RELATED QUANTITIES. Power. Intensity. THE QUANTUM NATURE OF RADIATION. Photon Energy. Frequency. Wavelength. An inverse relationship exists; electromagnetic radiation with shorter wavelengths is more energetic. The relation- ship between energy and frequency is given. From the basic wave relationship, the distance traveled in one period is vT = λ, so the energy is transported one wavelength per period of the oscillation.

In general, only relational values will be needed no exact values calculated. The result is how the energy depends upon the wavelength of light.

• Energy Transport and the Amplitude of a Wave
• 6.3 How is energy related to the wavelength of radiation?
• Frequency, Wavelength and Energy

If you increase the frequency of a light source by a factor of 30, how much does the energy of the photons change? If a light sources wavelength is 25 times smaller than before how does that change the energy of the photons?

You could also figure this out by looking at how the frequency changes when you change the wavelength. If the wavelength is 25 times smaller than the frequency is 25 times larger. Wien's Law - This law is used for black bodies, perfect radiation light emitters and absorbers and indicates at which wavelength they tend to give off most of their light.

This law is used to explain why the colors of objects change as you change their temperatures. Basically as the temperature goes up, max goes up and vice versa. If you increase the temperature of a black body by a factor of 5, how does its value of max change? The value of max is 5 times smaller than what it was before. An object has a temperature of 10, K. What is its value of max?

How To: Find Wavelength / Frequency (EASY EQUATION w/ problems)

Stefan-Boltzmann Law - This law is used for black bodies, perfect radiation light emitters and absorbers and indicates how much total energy they give off. Interesting thing to note - the energy they give off depends only on their temperatures, nothing else about the object matters like what it is made of.

Also this measure the total energy given off, so all energy at all wavelengths is what this indicates. But you have to be careful, T is taken to the fourth power, so a small change in it results in a very large change in the total amount of energy given off.

More massive slinkies have a greater inertia and thus tend to resist the force; this increased resistance by the greater mass tends to cause a reduction in the amplitude of the pulse. Different materials also have differing degrees of springiness or elasticity.

A more elastic medium will tend to offer less resistance to the force and allow a greater amplitude pulse to travel through it; being less rigid and therefore more elasticthe same force causes a greater amplitude. Energy-Amplitude Mathematical Relationship The energy transported by a wave is directly proportional to the square of the amplitude of the wave.

## Photon energy

This energy-amplitude relationship is sometimes expressed in the following manner. This means that a doubling of the amplitude of a wave is indicative of a quadrupling of the energy transported by the wave.

A tripling of the amplitude of a wave is indicative of a nine-fold increase in the amount of energy transported by the wave. And a quadrupling of the amplitude of a wave is indicative of a fold increase in the amount of energy transported by the wave. The table at the right further expresses this energy-amplitude relationship. Observe that whenever the amplitude increased by a given factor, the energy value is increased by the same factor squared.

For example, changing the amplitude from 1 unit to 2 units represents a 2-fold increase in the amplitude and is accompanied by a 4-fold 22 increase in the energy; thus 2 units of energy becomes 4 times bigger - 8 units. As another example, changing the amplitude from 1 unit to 4 units represents a 4-fold increase in the amplitude and is accompanied by a fold 42 increase in the energy; thus 2 units of energy becomes 16 times bigger - 32 units.

Earthquakes and other geologic disturbances sometimes result in the formation of seismic waves. Seismic waves are waves of energy that are transported through the earth and over its surface.

Earthquakes are given a Richter scale rating that indicates how intense the earthquake is. Use the Earthquake Energy widget below to explore the relationship between the Richter scale magnitude and the amount of energy transmitted by seismic waves. It is typically expressed in watts per square meter or watts per square centimeter. Intensity is also used to express relative values of x-ray exposure rate, light brightness, radio frequency RF signal strength in MRI, etc.

We have seen that electromagnetic radiation is packaged as individual photons or quanta. This is sometimes referred to as the quantum nature of radiation and becomes an important concept in understanding how radiation is created and absorbed. The Quantum Nature of Radiation and Matter Here we see an illustration of the basic quantum characteristics of both radiation and matter.

When we consider the structure of matter in another chapter we will find that electrons within atoms generally reside at specific energy levels rather than at arbitrary energy levels. Electrons can move from one energy level to another, but they must go all the way or not at all. These discrete electron energy levels give matter certain quantum characteristics.

In simple terms, matter prefers to exchange energy in predefined quantities rather than in arbitrary amounts. Radiation travels through space as a shower of individual photons. Eventually the photon is absorbed by transferring its energy back to an electron. The chance of its absorption is greatly enhanced if it encounters a material with electron energy levels close to its energy content.

The important point here is that radiation photons are created and absorbed individually through energy exchanges within certain materials. Although radiation photons are differentiated by several physical quantities, as shown here, all electromagnetic radiation travels with the same velocity through space.

Because light is one of the most common forms of electromagnetic radiation and its velocity is known, it is often said that electromagnetic radiations travel with the speed of light. If we assume that the average x-ray photon travels 1 m between the time it is created and the time it is absorbed, the average lifetime of a photon would be 3.

Photons cannot be stored or suspended in space. Once a photon is created and emitted by a source, it travels at this very high velocity until it interacts with and is absorbed by some material.

### Photon energy - Wikipedia

In its very short lifetime, the photon moves a small amount of energy from the source to the absorbing material. Physical Characteristics of a Photon Here we see the scales for the three quantities that are shown in relationship to the various types of radiation. The Electromagnetic Spectrum While it is possible to characterize any radiation by its photon energy, wavelength, or frequency, the common practice is to use different quantities for different types of radiations, as discussed below.

Photon Energy Since a photon is simply a unit of energy, its most important characteristic is the quantity of energy it contains.

Photon energies are usually specified in units of electron volts or appropriate multiples. If the various types of electromagnetic radiation were ordered with respect to photon energies, as shown above, the scale would show the electromagnetic spectrum. It is the energy of the individual photons that determines the type of electromagnetic radiation: An important aspect of photon energy is that it generally determines the penetrating ability of the radiation.

### Energy Transport and the Amplitude of a Wave

The lower energy x-ray photons are often referred to as soft radiation, whereas those at the higher-energy end of the spectrum would be so-called hard radiation. In most situations, high-energy hard x-radiation is more penetrating than the softer portion of the spectrum. If the individual units of energy, photons or particles, have energies that exceed the binding energy of electrons in the matter through which the radiation is passing, the radiation can interact, dislodge the electrons, and ionize the matter.

Frequency is a rate of vibration or oscillation. In this relationship, h is Planck's constant, which has a value of 6. Frequency is the most common quantity used to characterize radiations in the lower end, or the RF portion, of the electromagnetic spectrum and includes radiation used for radio and television broadcasts, microwave communications and cooking, and MRI.

For example, in MRI, protons emit signals with a frequency of Although, theoretically, x-radiation has an associated frequency, the concept is never used. The minimum radiation energy that can produce ionization varies from one material to another, depending on the specific electron binding energies.

Electron binding energy is discussed in more detail in Chapter 4. The ionization energies for many of the elements found in tissue range between 5 eV and 20 eV. Therefore, all radiations with energies exceeding these values are ionizing radiations.

Photon energy quantities are generally used to describe radiation with relatively high photon energy, such as x-ray, gamma, and cosmic radiation. Wavelength Various physical phenomena observed with electromagnetic radiation suggest that the radiation has certain wavelike properties.

This is also the distance the radiation moves forward during the period of one oscillation. Wavelength can be expressed in any unit of length. Radio and television signals have relatively long wavelengths that are usually expressed in meters.

For higher energy photons, such as light and x-ray, two smaller length units are used. In some literature, x-ray photon spectra are given in terms of wavelength rather than photon energy.

This causes the spectrum curve to have an entirely different appearance. By using the relationship given above, it is possible to convert a spectrum of one kind into the other. Since energy and wavelength are inversely related, the highest energy on the spectrum corresponds to the shortest wavelength. Wavelength is most frequently used to describe light. At one time it was used to describe x-radiation but that practice is now uncommon. Wavelength is often used to describe radio-type radiations.

General terms like "shortwave" and "microwave" refer to the wavelength characteristics of the radiation. An electron has a mass of 9. The question might be raised as to why such a small particle can be the foundation of our modern technology. Tremendous numbers of electrons are involved in most applications.

For example, when a watt light bulb is turned on, electrons race through the wires carrying energy to it at the rate of 5. In addition to its mass, each electron carries a 1-unit negative electrical charge. It is the charge of an electron that enables it to interact with other electrons and particles within atoms. Types of Energy Associated with Electrons Because an electron has both mass and electrical charge, it can possess energy of several types, as shown here.

It is the ability of an electron to take up, transport, and give up energy that makes it useful in the x-ray system. Rest Mass Energy Even when an electron is at rest and has no apparent motion, it still has energy.

In fact, according to the laws of physics, an object has some energy just because of its mass. Under certain conditions, mass can be converted into energy and vice versa. In this relationship, c is the speed of light. Although it is not possible with our present technology to convert most objects into energy, certain radioactive materials emit particles, called positrons, that can annihilate electrons.

When this happens, the electron's entire mass is converted into energy. According to Einstein's relationship, each electron will yield keV. This energy appears as a photon. The annihilation of positrons and electrons is the basis for positron emission tomography PET. Kinetic Energy Kinetic energy is associated with motion. It is the type of energy that a moving automobile or baseball has. When electrons are moving, they also have kinetic energy.

Generally, the quantity of kinetic energy an object has is related to its mass and velocity. For large objects, like baseballs and cars, the energy is proportional to the mass of the object and the square of the velocity. Doubling the velocity of such an object increases its kinetic energy by a factor of 4.