# Wavelengths and energy relationship to power

### Energy and Power of a Wave - Physics LibreTexts The greater the energy, the larger the frequency and the shorter (smaller) the wavelength. Given the relationship between wavelength and frequency — the. c = × m/s. 1 m = 1 × nm. 1 kJ = J example. Light with a wavelength of nm is green. Calculate the energy in joules for a green light photon. Energy takes many forms including light, sound and heat. Different colors of light are given by photons of various wavelengths. The relationship.

The total energy associated with a wavelength is the sum of the potential energy and the kinetic energy: If the velocity of the sinusoidal wave is constant, the time for one wavelength to pass by a point is equal to the period of the wave, which is also constant.

For a sinusoidal mechanical wave, the time-averaged power is therefore the energy associated with a wavelength divided by the period of the wave.

The tension in the string is When the string vibrator is turned on, it oscillates with a frequency of 60 Hz and produces a sinusoidal wave on the string with an amplitude of 4. What is the time-averaged power supplied to the wave by the string vibrator? Strategy The power supplied to the wave should equal the time-averaged power of the wave on the string.

The speed of the wave on the string can be derived from the linear mass density and the tension. The string oscillates with the same frequency as the string vibrator, from which we can find the angular frequency. Solution Begin with the equation of the time-averaged power of a sinusoidal wave on a string: We need to calculate the linear density to find the wave speed: This is true for most mechanical waves.

If either the angular frequency or the amplitude of the wave were doubled, the power would increase by a factor of four. The timeaveraged power of the wave on a string is also proportional to the speed of the sinusoidal wave on the string. If the speed were doubled, by increasing the tension by a factor of four, the power would also be doubled. Check Your Understanding The equations for the energy of the wave and the time-averaged power were derived for a sinusoidal wave on a string. In general, the energy of a mechanical wave and the power are proportional to the amplitude squared and to the angular frequency squared and therefore the frequency squared.

## 6.3 How is energy related to the wavelength of radiation?

Another important characteristic of waves is the intensity of the waves. Waves can also be concentrated or spread out. Waves from an earthquake, for example, spread out over a larger area as they move away from a source, so they do less damage the farther they get from the source.

Changing the area the waves cover has important effects. Light of a single wavelength behaved as if it consisted of separate particles, photons, all with the same energy, with each ejected electron being the result of a collision between one photon and one electron in the metal.

Greater intensity of light meant only that more photons were hitting the metal per second and more electrons were being ejected, not that there was more energy per photon. The energy of the outgoing electrons depended on the frequency of light used. The energy E of the incoming photons is directly proportional to the light frequency which can be written as, 2 in which h is a constant.

Max Planck first proposed this relationship between energy and frequency in as part of his study of the way in which heated solids emit radiation.

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For photons, the property most readily measured is their energy. The different colors of light for example, are thought of as representing photons of different energy.

The link between the particle theory and the wave theory lies in Planck's fundamental postulate of quantum theory given by equation 2. There is an inverse relation between the energy E, of the photon and the wavelength, 3 The energy E in equation 3 can be expressed in many units. In the analysis of art and in the description of light, the most convenient unit of energy to use is the electron volt, abbreviated eV. In terms of wavelength,in nanometers nmand energy Ein electronvolts evequation 3 can be expressed for light travelling in a vacuum as: The constants and numerical relations found in equations 3 and 4 are found from Planck's equation Eqn.

Visible light is composed of photons in the energy range of around 2 to 3 eV. Orange light with a wave length of nanometers is composed of photons with energy of 2 eV. The pathway electrons travel as they transfer energy from one point to another is a circuit. A basic electrical circuit is shown here. All circuits must contain at least two components or devices as shown. One component, designated here as the source, can convert energy from some other form and transfer it to the electrons. Batteries are good examples of electron energy sources.

The other component, designated here as a load, performs essentially the opposite function. As the electrons pass through the device they lose their energy as it is converted into some other form; a light bulb is a good example of a load in which its energy is converted into light and heat.

The energy source and load are connected with two conductors over which the electrons can freely move. The ideal conductor offers no resistance to the flow of the electrons. If the conductor offers significant resistance, the electrons lose some of their energy there. The lost energy is converted into heat.

Electrical circuits neither create nor destroy electrons. The electrons are always present within the conductive materials.

• Relation between Energy and Wavelength
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Energy is given to and taken from the electrons as they move around the circuit. The energy carried by the electrons is a form of potential energy.

## Photon energy

Even though the electrons are moving through the conductors, their velocity is not sufficient to give them significant kinetic energy. When electrons are moving through free space, they can carry significant kinetic energy, but they cannot when they are moving through solid conductors. In the typical electrical circuit, one conductor has higher potential energy than the other conductor. In principle, the energy source elevates the electrons to the higher potential energy level which they maintain until they give up the energy in passing through the load device.

The electrons at the lower potential level return to the energy source to repeat the process. The connection points terminals between the source and load devices and the conductors are designated as either positive or negative. The electrons exit the source at the negative terminal and enter the negative terminal of the load.

They then exit the positive terminal of the load device and enter the source at the positive terminal. In principle, the negative conductor contains the electrons at the high potential energy level. The positive conductor contains the electrons that have lost their energy and are returning to the source. In direct current DC circuits the polarities do not change. However, in alternating current AC circuits the polarity of the conductors is constantly alternating between negative and positive. However, by collective effort, electrons can transport a tremendous amount of energy. The amount of energy transferred by an electrical circuit depends on the quantity of electrons and the energy carried by each. We now consider these specific electrical quantities and their associated units. When an electrical circuit is in operation, electrons are continuously moving or flowing through the conductor. The number of electrons that move past a given point per second is referred to as the current. Since, in the typical circuit, the number of electrons per second is quite large, a more useful unit than this number is desirable.

The basic unit of current is the ampere A. One ampere is defined as the flow of 6. In x-ray machines, the current is typically a fraction of 1 A, and the milliampere mA is a more appropriate unit. As indicated here, a current of 1 mA is equal to the flow of 6. The current that flows through an x-ray tube is generally referred to as the "MA. When used as the unit, milliampere, it is written as mA. Electron Quantity and Charge In addition to the rate at which electrons are flowing through a circuit, i.

In x-ray work the most appropriate unit for specifying electron quantity is the milliampere-second mAs. Since a current of l mA is a flow of electrons per second, it follows that 1 mAs is a cluster of 6.

It should be recalled that all electrons carry a negative electrical charge of the same size. In some situations the quantity of electrons might be specified in terms of the total electrical charge. If extra electrons are added to an object, it is said to have acquired a negative charge. However, if some of the free electrons are removed from an object, a positive charge is created. In either case, the total charge on the object is directly proportional to the number of electrons moved.

Generally speaking, charge is a way of describing a quantity of electrons. The basic unit of charge is the coulomb Cwhich is equivalent to the total charge of 6.

We pointed out earlier that electrons could exist at different potential energy levels, because of either their different positions within the atom or their different locations within an electrical circuit. Consider the two wires or conductors shown here. Electron Potential Energy or Voltage The electrons contained in one of the conductors are at a higher potential energy level than the electrons in the other. Generally, the electrons in the negative conductor are considered to be at the higher energy level. An electrical quantity that indicates the difference in electron potential energy between two points within a circuit is the voltage, or potential difference, suggesting a difference in potential energy.

The unit used for voltage, or potential difference, is the volt. The difference in electron potential energy between two conductors is directly proportional to the voltage.

Each electron will have an energy difference of 1 eV for each volt.

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It is the quantity of energy that an electron gains or loses, depending on direction, when it moves between two points in a circuit that are 1 V apart. In the basic x-ray machine circuit the voltage is in the order of thousands of volts kilovolts and is often referred to as the KV. When used to mean the quantity, voltage or potential, it is written KV or KVp. When used as the unit, it is written as kV or kVp.

Electrical Power Power is the quantity that describes the rate at which energy is transferred. The power in an electrical circuit is proportional to the energy carried by each electron voltage and the rate of electron flow current.

Total Energy The amount of energy that an electrical circuit transfers depends on the voltage, current, and the duration time of the energy transfer. The fundamental unit of energy is the joule.

The basic circuit shown here is found in all x-ray machines. The power supply that gives energy to the electrons and pumps them through the circuit is discussed in a later Chapter. The voltage between the two conductors in the x-ray circuit is typically in the range of 30, V toV 30 kV to kVand in radiology this kilovoltage is generally adjustable and an appropriate value can be selected by the operator of the x-ray equipment.

In this circuit, the x-ray tube is the load. It is the place where the electrons lose their energy.

### Wavelegnth, Frequency and Energy Calculations

The energy lost by electrons in passing through an x-ray tube is converted into heat and x-ray energy. These are generally designated as direct current DC circuits.

A battery is an example of a power supply that produces a direct current. Some power supplies, however, produce voltages that constantly change with time. Since, in most circuits, the current is more or less proportional to the voltage, it also changes value.