Wave Properties and Units of Measure

Wave Properties and Units of Measure

• Amplitude (A) represents the maximum displacement of a wave from its equilibrium (zero) position, measured in meters (m).
• Wavelength (λ) indicates the distance between two consecutive points in the same phase, such as the distance between two wave crests or troughs, measured in meters (m).
• Frequency (f) defines the number of oscillations or waves passing a given point per second, measured in Hertz (Hz), where 1 Hz = 1 s⁻¹ (one oscillation per second).
• Period (T) is the time it takes for a complete oscillation or wave to pass a given point, measured in seconds (s).
• Wave speed (v) represents the speed at which the wave propagates through a medium, measured in meters per second (m/s), and can be calculated using the formula v = λ · f, where λ is the wavelength and f is the frequency.
• Displacement (y) is the distance a point on the wave has from its equilibrium position at a given time, measured in meters (m).
• Equilibrium position is the position of a point on the wave when it is not affected by the wave (zero point); in a mechanical wave, particles in the medium oscillate around this position.
• Phase describes the position of a point on the wave in its oscillation relative to other points; two points are in phase if they have the same displacement and move in the same direction.
• Energy (E) characterizes the energy waves transport; for electromagnetic waves (like light), the energy of a photon is given by E = h · f, where f is frequency and h is Planck's constant (6.63·10⁻³⁴ js), measured in Joules (J).
• Intensity (I) is defined as the power per unit area that the wave transfers, measured in Watts per square meter (W/m²).

Wave Speed

• Wave speed (v) refers to the rate at which a wave propagates through a medium.
• It is measured in meters per second (m/s).
• It can be calculated using the formula v = λ · f, where λ is the wavelength in meters (m), and f is the frequency in Hertz (Hz).
• For sound waves in air, the speed is approximately 340 m/s.
• For electromagnetic waves like light in a vacuum, wave speed is a universal constant: c = 299,792,458 m/s ≈ 3.0 · 10⁸ m/s.
• Wave speed depends on both the wavelength and frequency of the wave.

Calculating Frequency from Wavelength for Light

• The frequency (f) of light (or any EM wave) can be found if the wavelength (λ) is known using the formula f = c / λ.
• Here, f is the frequency in Hertz (Hz), c is the speed of light in a vacuum (3.0 × 10⁸ m/s), and λ is the wavelength in meters (m).
• The speed of light (c) in a vacuum is a constant, approximately 3.0 × 10⁸ m/s.
• Wavelength (λ) is the distance between two consecutive wave crests or troughs, measured in meters (m).
• Frequency (f) represents the number of waves passing a given point per second, measured in Hertz (Hz).
• For example, if light waves have a wavelength of 401 nm (nanometers), the frequency can be calculated as follows:
• Convert the wavelength to meters: 401 nm = 401 × 10⁻⁹ m.
• Use the formula: f = (3.0 × 10⁸ m/s) / (401 × 10⁻⁹ m).
• Calculate the frequency: f ≈ 7.48 × 10¹⁴ Hz.
• Light with a wavelength of 401 nm has a frequency of approximately 7.48 × 10¹⁴ Hz.

Properties of Light Waves

• Wavelength (λ) is the distance between consecutive wave crests or troughs in light waves, measured in meters (m), but often in nanometers (nm) for visible light; for example, visible light ranges from 400 nm to 750 nm.
• Frequency (f) is the number of waves that pass a given point per second, measured in Hertz (Hz), where 1 Hz = 1 s⁻¹; it is related to wavelength by the formula f = c / λ, where c is the speed of light in a vacuum (3.0 × 10⁸ m/s).
• Wave speed (v) is the rate at which the light wave propagates, and in a vacuum, this speed is a constant, approximately 3.0 × 10⁸ m/s, measured in meters per second (m/s).
• Amplitude (A) is the maximum displacement of the light wave, indicating how strong the light is, and it measured in meters (m), but often is related to the intensity (power per unit area).
• Intensity (I) represents the power per unit area that the light wave transfers, measured in Watts per square meter (W/m²); the intensity is proportional to the square of the amplitude.
• Phase: describes the position of a point on the light wave in its oscillation relative to other points; two light waves are in phase if they have the same displacement and move in the same direction.
• Polarization describes the direction of the electric and magnetic fields in the light wave; light can be polarized in a specific direction or be unpolarized.
• Energy (E) characterizes the energy that light waves transfer; for a photon (a quantum of light), the energy is given by E = h · f, where h is Planck's constant (6.63 × 10⁻³⁴ js) and f is the frequency, measured in Joules (J).
• Interference occurs when light waves interact with each other, leading to constructive or destructive interference depending on the phase difference between the waves.
• Diffraction happens when light waves bend around obstacles and spread out when passing through small openings.

Radiation

• Radiation transfers energy through waves or particles at high speed.
• Electromagnetic radiation consists of waves of electric and magnetic fields; examples include visible light, radio waves, microwaves, infrared radiation, ultraviolet radiation, X-rays, and gamma rays; it can travel through a vacuum.
• Particle radiation consists of high-energy particles, such as electrons, protons, or alpha particles; examples include radioactive decay (alpha, beta, and gamma radiation) and neutron radiation.
• Radiation can originate from a radiation source, like the sun, which emits electromagnetic radiation (solar radiation).
• Radiation can be ionizing, meaning it can remove electrons from atoms (e.g., X-rays or gamma radiation).

Examples of Radiation

• Visible light: Wavelengths between 400 nm and 750 nm are visible to the human eye.
• Infrared radiation: Heat radiation emitted from warm objects.
• Ultraviolet radiation: Causes sunburn and comes from the sun.
• Radio waves: Used for communication, such as in radio and TV.
• Alpha radiation: Consists of helium nuclei (two protons and two neutrons) emitted from radioactive materials.
• Beta radiation: Consists of electrons or positrons emitted from radioactive materials.
• Gamma radiation: High-energy EM radiation emitted from radioactive materials.
• Radiation transfers energy from one place to another.
• For EM radiation, the energy per photon is given by E = h · f.
• E is the energy in Joules (J), h is Planck's constant (6.63 × 10⁻³⁴ js), and f is the frequency in Hertz (Hz).

Radiated Power

• Radiated power refers to the amount of energy per unit time emitted by a radiation source through radiation (such as light, heat radiation, or other EM radiation).
• The definition of radiated power is the power (energy per second) a source emits in the form of radiation, measured in Watts (W), where 1 W = 1 Joule per second (J/s).
• The total radiated power from the sun is approximately 3.83 × 10²⁶ W, which means the sun emits 3.83 × 10²⁶ Joules of energy every second, and a human at rest radiates about 45 W in the form of heat radiation (infrared radiation).
• Radiated power (P) can be calculated using the Stefan-Boltzmann law: P = σ · A · T⁴.
• P is radiated power (W), σ is the Stefan-Boltzmann constant (5.67 × 10⁻⁸ W / m² K⁴), A is the surface area of the radiating source (m²), and T is the temperature of the radiating source in Kelvin (K).
• The sun has a radius of 6.96 × 10⁸ m, so its surface area is A = 4πr² = 4π × (6.96 × 10⁸m)² ≈ 6.09 × 10¹⁸ m².
• The sun's surface temperature is approximately 5800 K.
• Radiated power (P) is: P = σ · A · T⁴ = 5.67 × 10⁻⁸ × 6.09 × 10¹⁸ × 5800⁴ ≈ 3.83 × 10²⁶ W.
• Radiated power is the energy per second emitted by a source as radiation, measured in Watts (W), where 1 W = 1 J/s, and it can be calculated for heat radiation using the Stefan-Boltzmann law (P = σ × A × T⁴).
• The sun radiates 3.83 × 10²⁶ W, and a human radiates approximately 45 W.

Radiation Density

• Radiation density is a measure of how much energy an object or surface emits as radiation per unit area and per unit time, valuable for quantifying radiation from an object, particularly heat radiation from black bodies.

• Radiation density (U) is defined as the power per unit area emitted by an object through radiation, measured in Watts per square meter (W/m²).

• Formula to calculate radiation density: U = P/A = σ × T⁴.

• U is the radiation density (W/m²), P is the total radiated power (W), A is the surface area of the object (m²), and for a black body, the radiation density can also be computed using Stefan-Boltzmann's law: U = σ × T⁴.

• Et menneske:

• A person sitting at rest radiates approximately 45 W.

• The surface area of an average human body is about 1.7 m².

• So, the radiation density is: U = P/A = 45 W / 1.7 m² ≈ 26 W/m².

• Sola:

• The sun has a radiated power of 3.83 × 10²⁶ W and a radius of 6.96 × 10⁸ m.

• The surface area of the sun is approximately 6.09 × 10¹⁸ m².

• So, the radiation density is: U = P/A = 3.83 × 10²⁶ W / 6.09 × 10¹⁸ m² ≈ 6.29 × 10⁷ W/m².

• Examples of radiation density:a human has a radiation density of approximately 26 W/m²; the sun has a radiation density of approximately 6.29 × 10⁷ W/m².

Black Body

• A black body is a theoretical or ideal object that absorbs all incoming electromagnetic radiation (light, heat radiation, etc.) without reflecting any.
• Black bodies are perfect absorbers of radiation and are described as an important model in physics to understand radiation and energy.
• Black bodies are objects that absorb all radiation that hits them, regardless of wavelength or angle of incidence, and even though they absorb all radiation, they also emit radiation (called thermal radiation) depending on their temperature.
• The color of a black body depends on its temperature; if it is hot enough, it emits visible light and appears white or blue.

Properties of Black Bodies

• Perfect absorber: Absorbs all radiation, without transmission or reflection (passage).
• Perfect emitter: Emits radiation depending on temperature, following Planck's radiation law and Stefan-Boltzmann's law.
• Temperature-dependent radiation: Radiation depends on temperature; higher temperatures produce more energy and shorter wavelengths.
• The sun can be considered an approximate black body because it absorbs and emits radiation similarly to an ideal black body, and stars are also examples of black bodies because they emit radiation following the laws for black-body radiation.

Radiation Laws for Black Bodies

• Planck's Radiation Law: Describes how the intensity of radiation varies with wavelength and temperature, showing that radiation has a maximum intensity at a specific wavelength depending on temperature.
• Stefan-Boltzmann's Law: Describes the total radiated power per unit area from a black body as U = σ · T⁴, where U is radiation density (W/m²), σ is the Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m² K⁴), and T is the temperature in Kelvin (K).
• Wien's Displacement Law: Describes the relationship between the temperature of a black body and the wavelength at which the radiation is most intense: λtopp * T = a, where λtopp is the wavelength for maximum radiation (m), T is the temperature (K), and a is a constant (2.90 × 10⁻³ mK).

Examples of Laws

• For the sun, with a surface temperature of approximately 5800 K, and a wavelength for maximum radiation: (λtopp ≈ 500 nm)(λtopp = a / T = (2.90 × 10⁻³ mK) / 5800 K ≈ 500 nm), falling within the visible spectrum; this explains why the sun appears yellow/white.
• A black body is a theoretical object that absorbs all radiation and emits radiation depending on its temperature. that follows Planck's radiation law, Stefan-Boltzmann's law, and Wien's displacement law.
• Significance: Black bodies are a fundamental model in physics for understanding radiation, energy, and temperature.
• Black-body radiation is the EM radiation emitted by a black body due to its temperature and an important model for understanding how objects emit energy in the form of radiation, especially heat radiation.
• The radiation only depends on the temperature of the black body, not the material or surface, with a characteristic spectrum (wavelength distribution) that follows Planck's radiation law.

Changes to blackbody radiation

• When the temperature of a black body rises, the profile of the radiation pattern changes with Wavelength for radiation intensity increases and shifts toward shorter wavelengths. This is Wien's law.

Changes to radiation amounts

• The total Radiation emitted by a blackbody increases. It is proportional to its 4th power of temperature, according to Stephen-Boltzmanns law.
• There is also a change in colour: When the temperature is raised to a blackbody, the perceived colour emissions is also changed. When temperatures are low the blackbody emits predominantly Infra-red rays, not visible, a low temperatures as the temperature rises, there is a change to its visible colour, at first read, the orange, yellow white and even blue high temperatures

Summary:

The total radiation effect that a blackbody emits increases with a rising temperature as for Stephen Boltzmann's law and formula.

• Blackbody shifts the range of highest radiation intensity toward a shorter ranges with an increase in temperature for Wanes law.
• Planck curvature the amount of radiation is as a result, is asymmetrical with high dependence. A rise temperature has had high radiation levels for a reduction of the wavelength in temperature.
• A peak for ultra-violet rays or visible radiation will lead to a curve that is skewed and tilted Low temperatures will lead the blackbody mostly radiating from infra-red waves, that is caused with a curve more skewed and tilled.
• Radiation levels will increase when temperatures rise, resulting in more energy emissions overall.

Examplies of Blackbodys

1. Sol a sun can be considered the natural approximation and has its temperature around 5800 kelvins
2. A star may be treated as a black body and the radiation comes about by the laws of blackbody radiation and radiation depends on levels of surface temperature. Blue stars have hotter temperatures and colder star are more predominantly red.

Are there non-blackbodys that emit radiation

All objects emit radiation however back body objects have radiation in tangent with Planck's law. Which is an expression that is relative to Stephen boltzmann, so the black body objects are nearly equal

• All obtects at zero come in the form of a heat emitting material, most do if energy is high enough. For most black body objects. There's a good range.

• All objects that emit radiation all depend on various materials. Black body objects. Can absorb all radiation, whilst all other objects, either transfer part of all the radiation, the material, the surface and other factors.

• A person at most levels, release radiation for example , radiation in form of heat .

Luminous intensity

Is a measurements of light that emits and is essential for explaining, what and how light radiates.

An Atom

• An atom is the smallest unit of an element that retains its chemical properties.
• Atoms consist of positively charged protons and uncharged neutrons forming in the nucleus, tiny, negatively charged electrons orbit the nucleus.
• Atom consists mostly of a nucleus. Tiny electrons reside in the atomic range
• An atom is considered to have the nucleus centered, for the proton and neutron to connect. Mass and extreme amounts a small if compared, is how we can define the structure is defined.

Atom numbers

1. Is the atom atomic number which defines the identity of an atom
2. Mass total: Sum of atomic range, for instance call but 12 consists of 6 protons equals 12 total.

Examples

• Hydrogen is the simplest
• atom with a Rutherford Atomic structure has electrons that rotate.
• A tomes are extremely short with a hydrogen ray has an average of 5-11 m
• There are short if compared to other objects. 7 and 10 -7 m are short of compressed hydrogen atoms, is like covering it's breadths with hair strands

Atom History.

Democritus was to first assume objects and atoms and 1800 has developed a tomb, to believe. And to be more precise. I 1911 Ernest Rutherford proposed a new Tom and the structure with alpha range in the atoms.

The Rutherford Model

Rutherford is one of multiple elements for the atom and has a positive nucleus Electrons move along like planets, although there's a lot of mass and tome Is sorted short of being empty. With the Rutherford version, there's small if not strong in the middle element and tomes with an alpha

Limitations of Rutherford Atomic Models

There are some negative features the models like and some are that do not consider all atomic structure there seems to be a slight and that most electrons rotate, electrons are to always have a short and then that should always happen

Quantum theories for Adams

• Bohr is the most famous, his is an electric range that is strong and constant and to be on top with that.
• There is wave actions in atoms, electrons or orbital ranges, these come in all forms for instance s ,p d anf F orbital and the electron has quantum numbers to see that. These are a few quantum that has been expressed.

What model for understanding comes in handy

1. Bohr has a Tom model that helps connect to physics. With this is described as strong in levels of light as is connected with models. And helps develop

Kinetic Theory

Links atoms and physics close to each other and helps make sense. That tomes our core in the Tom’s core. That most have been a part for our time in life for a kinetic base and how they are.

Forms

• Constant guess parties that the are 2, Boltzmann constant and temperature is the unit to express for calvin.

In short.

This base describes for all the tomes and what's on this realm . kinetic is very central to see the existence with quantum and physic.

Rutherford model

• Thomas has developed what the current model consists and was expressed on the end of the 1800s and described the Tom has a constant atom. And positive element and had certain issues.
• Ruth had made these ideas and how those would create better versions of atoms and positive elements Like and Tom is short and can be explained very quickly and how these interact

Rutherford model , why did the old model fall off

• If there's any small issues inside the electrical waves, then electron ranges can move along with the inner core. This can be for electrical ways that can't prevent electrons to prevent electricity from falling inwards by electrical ranges

Wanes with Rutherford Model

• The classic atomic way, has helped to expand atoms. And in an exact form with is very clear to be correct. He had also mentioned about electro ranges and made them the core the electrical part that it all was. For these there some strong reasons to believe in it all and see how tomes interact.

A wave in nature.

And that atomes can move across and for both the electric to all and that the electron would need have exact energy levels.

What the short version is of electrons in the system that there's lots of energy what for the atom the follow to be in check then that’s what follows.

What's a photon

It contains all the base for radiation in waves, radiation for short distances is what they contain so they move in a constant form.

• These atoms can move and not have a force to prevent all their ranges. And wave duality for light helps show this.

Quantisied

Which there are several that come in to effect and are to always have light and constant rays.

• Each element for it. , light and all that and then those are to have those energy to then that .

What we say the things and to always keep them checked.

All systems contain items and that can help to follow all. Light rays, help electron ways to have their rays

Bohr Atomic Structure

And electrons always follow in some form for hydrogen form If electrons are to be checked the form has to be stable of force

1. Light should move at all forces for and all has to always follow if there's any atom, for an electrical wave.

Energy

With all electrical components a wave the have to have energy

Short. Bohr are all waves. So these have to all follow the rules

All of this what they have, is all that there is for the atoms

To express in waves. And the rules to do it

Electrons should do it's part and never have any force , these most if not follow and never to not have this.

Which has been the issue of all old models.

The force to never prevent their constant waves is all that needs to come about them

For electrical ways . the most easy will be hydrogen which the electron can come about . and no force can prevent all to have such forms of atoms.

A lot of times there's electrical waves where . light can be in use for an electrical element.

In these instances radiation can be constant waves that are to have most times be seen.

Short of all items and what tomes need and the rules to follow what it all entails.

There must have been a force for all forms of light to never be prevented.

There Is a way for light and all ways to see some form of radiation with light and there are several factors to what comes to play.