Refraction in a raindrop

An important optical effect that explains how raindrops produce rainbows is refraction.

Refraction refers to the way that electromagnetic radiation (light) changes speed and direction as it travels across the interface between one transparent medium and another.

  • As light travels from a fast medium such as air to a slow medium such as water it bends toward the normal and slows down.
  • As light passes from a slower medium such as water to a faster medium such as air it bends away from the normal and speeds up.
  • In a diagram illustrating optical phenomena like refraction or reflection in a raindrop, the normal is a line drawn from the surface of a raindrop to its centre.
  • The speed at which light travels through a given medium is expressed by its refractive index (also called the index of refraction).
  • If we want to know in which direction light will bend at the boundary between transparent media we need to know:
    • Which is the faster, less optically dense (rare) medium with the smaller refractive index.
    • Which is the slower, more optically dense medium with the higher refractive index.
  • The degree to which refraction causes light to change direction is dealt with by Snell’s law.
  • Snell’s law considers the relationship between the angle of incidence, the angle of refraction and the refractive indices (plural of index) of the media on both sides of the boundary. If three of the four variables are known, then Snell’s law can calculate the fourth.
More about refraction in a raindrop
  • Light rays (streams of photons) undergo refraction twice when they encounter a raindrop, once as they enter, then again as they leave.
  • Once inside a raindrop, a given photon may reflect off the inside surface of a raindrop several times, but on each refraction, some light crosses the boundary back and undergoes refraction as it escapes into the surrounding air.
  • Some photons never escape, instead, they are absorbed when they strike electrons within a raindrop, releasing heat that can causes evaporation.

Saturation

Saturation refers to the perceived difference between one colour and another in terms of its purity and vividness. The hue of a vivid colour appears to be at full strength and can leave an after-image of its complementary colour as an observer looks away.

  • A fully saturated colour appears bright and vibrant because it has a single strong dominant hue.
  • A freshly cut tomato is a good example of a saturated colour with a strong red hue.
  • A saturated colour is a unique spectral colour produced by a single wavelength (or a narrow band of wavelengths) of light.
  • A fully saturated colour (100%) is the purest version of a hue.
  • Unsaturated colours (0-10%) can appear:
    • Misty or milky the nearer they are to white.
    • Dull and washed out as their hue disappears leaving achromatic grey tones.
About saturation & wavelength
  • Saturation is one of the three primary properties of colour, alongside hue and brightness.
    • A colour looks saturated when made by a single or a small range of wavelengths.
    • A colour made by one wavelength of light is often referred to as a pure spectral colour.
    • Unsaturated colours appear faded due to a wider range of wavelengths.
    • Saturation is linked to the complexity of light.
Light complexity
  • Light complexity, linked to saturation, refers to the quantity and range of wavelengths of light used to create a colour.
    • Spectral colours are simple because they consist of just one wavelength of light.
    • Bands of colour are relatively simple because they are composed of a continuous range of wavelengths.
    • Non-spectral colours can be produced from a mix of many wavelengths from different parts of the spectrum, making them the most complex.
  • In reality, colours are often produced by complex combinations of wavelengths.
  • The greater the number and spread of wavelengths across the visible spectrum present in a colour, the lower the saturation.
  • The human eye can perceive millions of different colours due to the complex interactions of wavelengths and the eye’s colour receptors.
About saturation and colour models
About the HSB colour model

The HSB colour model is an additive colour model used to mix light (subtractive colour models are used to mix pigments and inks).

  • The main difference between the HSB colour model and the RGB colour model is how colours are represented and managed in software and applications.
  • The HSB model represents colours based on hue, saturation, and brightness, whereas the RGB model mixes red, green, and blue light to create colours.
  • HSB is popular because it provides a user-friendly way to select and modify colours when using applications like Adobe Creative Cloud for design, photography, or web development.
  • On HSB colour wheels, saturation typically increases from the centre towards the edge.

In the HSB colour model:

  • Hue refers to the perceived difference between colours and is usually described using names such as red, yellow, green, or blue.
    • Hue can be measured as a location on an HSB colour wheel and expressed as a degree between 0 and 360.
  • Saturation refers to the vividness of a colour compared to an unsaturated colour.
    • Saturation is measured between a fully saturated colour (100%) and an unsaturated colour (0%)that appear either:
      • Dull and washed out until all colour disappears, leaving only a monochromatic grey tone (0%).
      • Misty or milky the nearer they are to white.
    • On many HSB colour wheels, saturation decreases from the edge to the centre.
  • Brightness refers to the perceived difference in the appearance of colours under ideal sunlit conditions compared to poor lighting conditions where a hue’s vitality is lost.
    • Brightness can be measured as a percentage from 100% to 0%.
    • As the brightness of a fully saturated hue decreases, it appears progressively darker and achromatic.
  • Saturation refers to the perceived difference between one colour and another in terms of its purity and vividness.
  • The hue of a vivid colour appears to be at full strength and can leave an after-image of its complementary colour as an observer looks away.
  • A fully saturated colour appears bright and vibrant because it has a single strong dominant hue.
  • A freshly cut tomato is a good example of a saturated colour with a strong red hue.
  • A saturated colour is a unique spectral colour produced by a single wavelength (or a narrow band of wavelengths) of light.
  • A fully saturated colour (100%) is the purest version of a hue.
  • Unsaturated colours (0-10%) can appear:
    • Misty or milky the nearer they are to white.
    • Dull and washed out as their hue disappears leaving achromatic grey tones.

Saturation & colour

About saturation & wavelength
  • Saturation is one of the three primary properties of colour, alongside hue and brightness.
    • A colour looks saturated when made by a single or a small range of wavelengths.
    • A colour made by one wavelength of light is often referred to as a pure spectral colour.
    • Unsaturated colours appear faded due to a wider range of wavelengths.
    • Saturation is linked to the complexity of light.
Light complexity
  • Light complexity, linked to saturation, refers to the quantity and range of wavelengths of light used to create a colour.
    • Spectral colours are simple because they consist of just one wavelength of light.
    • Bands of colour are relatively simple because they are composed of a continuous range of wavelengths.
    • Non-spectral colours can be produced from a mix of many wavelengths from different parts of the spectrum, making them the most complex.
  • In reality, colours are often produced by complex combinations of wavelengths.
  • The greater the number and spread of wavelengths across the visible spectrum present in a colour, the lower the saturation.
  • The human eye can perceive millions of different colours due to the complex interactions of wavelengths and the eye’s colour receptors.

Saturation & colour models

About saturation and colour models

Scattering

Scattering happens when light waves interact with particles or irregularities in a medium, causing the light to change direction.

  • When light encounters obstacles, such as molecules in the atmosphere or imperfections in a surface, it can undergo various processes.
  • These include reflection, where the light bounces back like a mirror, as well as refraction, diffraction, and absorption, where the light is bent, spread out, or absorbed by the material.
  • Scattering plays a  role in various natural phenomena, such as the colour of the sky, the appearance of clouds, and the shimmering of water surfaces.

Scattering does not take place:

  • When parallel rays of light reflect off a smooth, flat surface like a mirror, producing a distortion-free reflection.
  • When parallel rays of light reflect off a smooth convex surface (although the reflection appears magnified).
  • When parallel rays of light reflect off a smooth concave surface (although the reflection typically appears smaller and inverted).
  • When parallel rays of light pass through translucent materials containing dissolved substances like dyes.
About regular scattering
  • Regular scattering happens when light bounces off a smooth, curved surface in a predictable way, creating a clear and undistorted image.
  • Think about a spoon in a glass of water. The smooth, curved surface of the spoon predictably bends the light, making the spoon appear slightly bent or magnified. This is an example of regular scattering.
  • Regular scattering often occurs when parallel rays of light hit smooth, transparent objects like raindrops or prisms. In these cases, the light bends (refracts) in a predictable way depending on the angle it hits the object and the materials involved.
  • This predictable bending can sometimes separate white light into its component colours, creating a rainbow effect known as chromatic dispersion.
  • On a microscopic level, all types of scattering follow the laws of reflection and refraction (Snell’s law).
  • Let’s look at two cases of regular scattering in more detail:
    • When parallel rays of light with a single wavelength strike and enter an object like a raindrop or prism, their path depends on the initial point of impact, the refractive indices of air and water, and the object’s surface properties.
    • When parallel rays of incident light with a single wavelength meet the curved surface of a transparent medium at various points, the different angles at which they strike the surface and experience deflection mainly determine how they scatter as they exit the medium.
About random scattering
Random scattering
  • Random scattering occurs when a material, due to irregularities or imperfections on its surface, reflects or transmits light rays in various unpredictable directions.
  • This scattering can produce a variety of effects:
    • Reflected light may appear hazy or lack detail, or there may be no clear reflection at all.
    • When light passes through sheets of glass with irregular yet smooth surfaces, random scattering distorts the view of the world beyond, making the image blurry and confused.
    • A reflection that is free of the effects of random scattering is called a specular reflection. Mirrors generally produce specular reflections.
Diffuse light
  • Diffuse light is a specific type of random scattering that occurs when light bounces off rough or uneven surfaces.
  • In these cases, the light scatters in all directions, creating a soft, even glow.
  • The overall structure and composition of a material can also cause diffuse light.
  • This happens when light travels through a medium that contains foreign materials, suspended particles, or has an irregular internal structure or variations in density.
  • Translucent materials containing dissolved substances, however, typically don’t cause random scattering because the particles are too small.
  • On a microscopic scale, all objects adhere to the law of reflection; however, when surface irregularities are larger than the wavelength of light, the light undergoes scattering leading to diffusion.
About scattering in raindrops
  • Scattering in raindrops obeys the laws of both reflection and refraction, commonly referred to as Snell’s law. Here are three related descriptions of what causes scattering when visible light strikes a raindrop:
    • When light of a specific wavelength strikes the surface and enters a raindrop its subsequent path depends upon the point of impact, and the refractive indices of water and air.
    • When rays of light of a single wavelength strike a raindrop at different points, scattering is primarily determined by the angles at which they enter the droplet.
    • The interaction between refraction and chromatic dispersion gives rise to the appearance of rainbow colours when parallel white light rays strike various points on the surface of a raindrop.

Scattering

Scattering takes place when streams of photons (or waves of light) are deflected in different directions.  In this resource, the term is used to refer to the different forms of deviation produced by diffusion, dispersion, interference patterns, reflection and refraction as well as by the composition and surface properties of different media.

Regular scattering
  • When light of a particular wavelength strikes the surface and enters a raindrop its subsequent path depends upon the point of impact, the refractive indices of air and water and the surface properties of the droplet.
  • For incident rays of a single wavelength striking the surface of a single droplet at different points,  it is the different angles at which they enter the droplet that are the chief determinant of the way they scatter as they exit the droplet. In this case.
  • For incident rays of a white light striking the surface of a single droplet at different points, it is the combined effects of the different angles at which they enter the droplet along with the effects of chromatic dispersion (causing the separation of white light into spectral colours) that determine the form of scattering.
  • Chromatic dispersion refers to the way that light, under certain conditions, separates into its component wavelengths and the colours corresponding with each wavelength become visible to a human observer.
  • Regular scattering is not random and obeys the law of reflection and refraction (Snell’s law).
Random scattering
  • In optics, diffusion results from any material that scatters light during transmission or reflection producing softened effects without sharp detail.
  • Objects produce diffuse reflections when light bounces off a rough or uneven surface and scatters in all directions.
  • Transparent and translucent materials transmit diffuse light unless their surfaces are perfectly flat and their interiors are free of foreign material.
  • All objects obey the law of reflection on a microscopic level, but if the irregularities on the surface of an object are larger than the wavelength of light, the light undergoes diffusion.
  • A reflection that is free of the effects of diffusion is called a specular reflection.
  • In the case of raindrops, random scattering can result from:
    • Atmospheric conditions affecting incident sunlight.
    • Turbulence distorting the shape of raindrops.
    • Light being reflected off the surface of multiple raindrops, one after another, before reaching an observer.

Scattering

Scattering takes place when streams of photons (or waves of light) are deflected in different directions.  In this resource, the term is used to refer to the different forms of deviation produced by diffusion, dispersion, interference patterns, reflection and refraction as well as by the composition and surface properties of different media.

Regular scattering
  • When light of a particular wavelength strikes the surface and enters a raindrop its subsequent path depends upon the point of impact, the refractive indices of air and water and the surface properties of the droplet.
  • For incident rays of a single wavelength striking the surface of a single droplet at different points,  it is the different angles at which they enter the droplet that are the chief determinant of the way they scatter as they exit the droplet. In this case.
  • For incident rays of a white light striking the surface of a single droplet at different points, it is the combined effects of the different angles at which they enter the droplet along with the effects of chromatic dispersion (causing the separation of white light into spectral colours) that determine the form of scattering.
  • Chromatic dispersion refers to the way that light, under certain conditions, separates into its component wavelengths and the colours corresponding with each wavelength become visible to a human observer.
  • Regular scattering is not random and obeys the law of reflection and refraction (Snell’s law).
Random scattering
  • In optics, diffusion results from any material that scatters light during transmission or reflection producing softened effects without sharp detail.
  • Objects produce diffuse reflections when light bounces off a rough or uneven surface and scatters in all directions.
  • Transparent and translucent materials transmit diffuse light unless their surfaces are perfectly flat and their interiors are free of foreign material.
  • All objects obey the law of reflection on a microscopic level, but if the irregularities on the surface of an object are larger than the wavelength of light, the light undergoes diffusion.
  • A reflection that is free of the effects of diffusion is called a specular reflection.
  • In the case of raindrops, random scattering can result from:
    • Atmospheric conditions affecting incident sunlight.
    • Turbulence distorting the shape of raindrops.
    • Light being reflected off the surface of multiple raindrops, one after another, before reaching an observer.

Definition

Explanation

Summary

About sections (temp)

References

Scattering: physics

About scattering in physics
Rayleigh scattering
Mie scattering
Non-selective scattering
Tyndall effect
    • Tyndall effect is another phenomenon related to scattering, where light is scattered by colloidal particles, causing them to become visible in a transparent medium.
    • Colloidal particles are small solid particles or liquid droplets that are dispersed within a medium, typically a liquid or a gas.

Scattering: Raindrops

About scattering in raindrops
  • Scattering in raindrops obeys the laws of both reflection and refraction, commonly referred to as Snell’s law. Here are three related descriptions of what causes scattering when visible light strikes a raindrop:
    • When light of a specific wavelength strikes the surface and enters a raindrop its subsequent path depends upon the point of impact, and the refractive indices of water and air.
    • When rays of light of a single wavelength strike a raindrop at different points, scattering is primarily determined by the angles at which they enter the droplet.
    • The interaction between refraction and chromatic dispersion gives rise to the appearance of rainbow colours when parallel white light rays strike various points on the surface of a raindrop.

Scattering: Random

About random scattering
Random scattering
  • Random scattering occurs when a material, due to irregularities or imperfections on its surface, reflects or transmits light rays in various unpredictable directions.
  • This scattering can produce a variety of effects:
    • Reflected light may appear hazy or lack detail, or there may be no clear reflection at all.
    • When light passes through sheets of glass with irregular yet smooth surfaces, random scattering distorts the view of the world beyond, making the image blurry and confused.
    • A reflection that is free of the effects of random scattering is called a specular reflection. Mirrors generally produce specular reflections.
Diffuse light
  • Diffuse light is a specific type of random scattering that occurs when light bounces off rough or uneven surfaces.
  • In these cases, the light scatters in all directions, creating a soft, even glow.
  • The overall structure and composition of a material can also cause diffuse light.
  • This happens when light travels through a medium that contains foreign materials, suspended particles, or has an irregular internal structure or variations in density.
  • Translucent materials containing dissolved substances, however, typically don’t cause random scattering because the particles are too small.
  • On a microscopic scale, all objects adhere to the law of reflection; however, when surface irregularities are larger than the wavelength of light, the light undergoes scattering leading to diffusion.

Scattering: Regular

About regular scattering
  • Regular scattering happens when light bounces off a smooth, curved surface in a predictable way, creating a clear and undistorted image.
  • Think about a spoon in a glass of water. The smooth, curved surface of the spoon predictably bends the light, making the spoon appear slightly bent or magnified. This is an example of regular scattering.
  • Regular scattering often occurs when parallel rays of light hit smooth, transparent objects like raindrops or prisms. In these cases, the light bends (refracts) in a predictable way depending on the angle it hits the object and the materials involved.
  • This predictable bending can sometimes separate white light into its component colours, creating a rainbow effect known as chromatic dispersion.
  • On a microscopic level, all types of scattering follow the laws of reflection and refraction (Snell’s law).
  • Let’s look at two cases of regular scattering in more detail:
    • When parallel rays of light with a single wavelength strike and enter an object like a raindrop or prism, their path depends on the initial point of impact, the refractive indices of air and water, and the object’s surface properties.
    • When parallel rays of incident light with a single wavelength meet the curved surface of a transparent medium at various points, the different angles at which they strike the surface and experience deflection mainly determine how they scatter as they exit the medium.

Scotopic curve

A scotopic curve is a graphical representation of the sensitivity of the human eye to light under low-light conditions, such as at night or in very dimly lit environments.

  • A scotopic curve is like a line graph that shows how sensitive the human eye is to light under low-light conditions.
  • A scotopic curve is an important way to understand night vision.
  • The curve shows the minimum amount of light needed for the eye to detect light at different colours and their corresponding wavelengths.
  • This information comes from the response of our rod cells, which are more active in low light than the cones that dominate in bright light.
  • Unlike the photopic curve, which peaks at around green-yellow light, the scotopic curve peaks at blue-green light, which means our eyes are most sensitive to these colours in low light.
  • It’s interesting to note that scotopic and photopic curves use different units to measure light.
    • The photopic curve uses a unit similar to overall brightness.
    • The scotopic curve uses a unit related to light intensity per unit area (such as brightness per square degree).
  • A scotopic curve is a graphical representation of the sensitivity of the human eye to light under low-light conditions, such as at night or in very dimly lit environments.
  • A scotopic curve is like a line graph that shows how sensitive the human eye is to light under low-light conditions.
  • A scotopic curve is an important way to understand night vision.
  • The curve shows the minimum amount of light needed for the eye to detect light at different colours and their corresponding wavelengths.
  • This information comes from the response of our rod cells, which are more active in low light than the cones that dominate in bright light.

Secondary colour

A secondary colour is made by mixing two primary colours in equal parts within a particular colour model. The colour space can be from an additive colour model using different light wavelengths or a subtractive model using pigments or dyes.

  • Secondary colours in additive colour models differ from spectral colours in a rainbow.
  • The RGB colour model can create a vast range of colours.
  • When all three primary (or secondary) colours are mixed together in equal proportions, the result is white.
  • Because the RGB colour model involves adding different wavelengths of light together (additive colour), the resulting colour often appears lighter to a viewer than its components.
  • In subtractive colour models, like the CMYK model used for printing, the primary colours are cyan (C), magenta (M), and yellow (Y) plus black (K) which is used to produce darker shadows.
  • A secondary colour is made by mixing two primary colours in equal parts within a particular colour model. The colour space can be from an additive colour model using different light wavelengths or a subtractive model using pigments or dyes.
  • Secondary colours in additive colour models differ from spectral colours in a rainbow.
    • A spectral colour is made by a single wavelength or a small range of wavelengths in the visible spectrum.
    • A secondary colour within an additive model (such as the RGB colour model) comes from overlapping light wavelengths from three distinctly different parts of the visible spectrum.
    • For humans, the best additive primary colours of light are red, green, and blue.
  • The RGB colour model can create a vast range of colours.
  • When all three primary (or secondary) colours are mixed together in equal proportions, the result is white.

Secondary colour

secondary colour is a colour made by mixing two primary colours in a given colour space. The colour space may be produced by an additive colour model that involves mixing different wavelengths of light or by a subtractive colour model that involves mixing pigments or dyes.

Secondary rainbow

A secondary rainbow is formed when sunlight undergoes two internal reflections within water droplets, creating an arc with colours reversed from the primary rainbow (violet on the outside, red on the inside). It appears larger and fainter due to light loss during the second reflection and a broader spread of wavelengths.

  • rainbow is an optical effect produced by illuminated droplets of water. Rainbows are caused by reflectionrefraction and dispersion of light in individual droplets and results in the appearance of an arc of spectral colours.
  • A secondary rainbow appears when sunlight is refracted as it enters raindrops, reflects twice off the inside surface, is refracted again as it escapes back into the air, and then travels towards an observer.
  • A secondary rainbow always appears alongside a primary rainbow and forms a larger arc with the colours reversed.
  • A secondary rainbow has violet on the outside and red on the inside of the bow.
  • When both primary and secondary bows are visible they are often referred to as a double rainbow.
  • A secondary rainbow forms at an angle of between approx. 50.40 to 53.40 to its centre as seen from the point of view of the observer.
  • A secondary bow is never as bright as a primary bow because:
    • Light is lost during the second reflection as a proportion escapes through the surface back into the air.
    • A secondary bow is broader than a primary bow because the second reflection allows dispersing wavelengths to spread more widely.
Secondary rainbow properties
  • The centre of a rainbow is always on an imaginary straight line (the axis of the rainbow) that starts at the centre of the Sun behind you, passes through the back of your head, out through your eyes and extends in a straight line into the distance.
  • The centre-point of a rainbow is sometimes called the anti-solar point. ‘Anti’, because it is opposite the Sun with respect to the observer.
  • The axis of a rainbow is an imaginary line passing through the light source, the eyes of an observer and the centre-point of the bow.
  • The space between a primary and secondary rainbow is called Alexander’s band.
Related diagrams

Each diagram below can be viewed on its own page with a full explanation.

  • A secondary rainbow is formed when sunlight undergoes two internal reflections within water droplets, creating an arc with colours reversed from the primary rainbow (violet on the outside, red on the inside). It appears larger and fainter due to light loss during the second reflection and a broader spread of wavelengths.
  • A secondary rainbow appears when sunlight is refracted as it enters raindrops, reflects twice off the inside surface, is refracted again as it escapes back into the air, and then travels towards an observer.
  • A secondary rainbow always appears alongside a primary rainbow and forms a larger arc with the colours reversed.
  • A secondary rainbow has violet on the outside and red on the inside of the bow.
  • When both primary and secondary bows are visible they are often referred to as a double rainbow.
  • A secondary rainbow forms at an angle of between approx. 50.40 to 53.40 to its centre as seen from the point of view of the observer.

Secondary rainbow

A secondary rainbow appears when sunlight is refracted as it enters raindrops, reflects twice off the inside surface, is refracted again as it escapes back into the air, and then travels towards an observer.

  • A secondary rainbow always appears alongside a primary rainbow and forms a larger arc with the colours reversed.
  • A secondary rainbow has violet on the outside and red on the inside of the bow.
  • When both primary and secondary bows are visible they are often referred to as a double rainbow.
  • A secondary rainbow forms at an angle of between approx. 50.40 to 53.40 to its centre as seen from the point of view of the observer.
  • A secondary bow is never as bright as a primary bow because:
    • Light is lost during the second reflection as a proportion escapes through the surface back into the air.
    • A secondary bow is broader than a primary bow because the second reflection allows dispersing wavelengths to spread more widely.
Remember that:
  • The axis of a rainbow is an imaginary line passing through the light source, the eyes of an observer and the centre-point of the bow.
  • The space between a primary and secondary rainbow is called Alexander’s band.

Seeing colour

About seeing colour
  • When an observer asks themselves what colour something is, they might refer to:
    • Spectral colours and use names commonly associated with rainbows (ROYGBV)
    • An extended vocabulary of colour names such as dark red, vermilion, golden yellow, lemon yellow, pale yellow, greenish-yellow, chartreuse, leaf green or light green.
    • A specific colour model such as RGB, CMYK or HSB
    • A family of colours such as warm or cool colours
    • Tints or shades of colours
    • A palette of colours they have selected or are working with.

Seeing in colour

About seeing in colour
  • When an observer considers the colour of something, they might refer to:
    • Spectral colours and use names commonly associated with rainbows (ROYGBV).
    • A specific colour model such as RGB, CMYK or HSB.
    • A family of colours such as warm or cool colours.
    • Tints or shades of colours.
    • A palette of colours they have selected or are working with.
    • A broader vocabulary of colour names, such as dark red, vermilion, golden yellow, lemon yellow, pale yellow, greenish-yellow, chartreuse, leaf green, or light green.

Shells & orbitals

About shells & orbitals
Shells

Think of shells as regions around the nucleus where electrons are most likely to be found. These regions are like “zones” or “areas” within the atom, organized according to their energy levels.
Shells are labelled using letters (K, L, M, N, etc.) starting from the nucleus outwards. Each shell has a specific energy, with the K shell being closest to the nucleus and having the lowest energy, followed by L, M, and so on.
Imagine them as concentric circles around the nucleus, with outer shells being like bigger “orbits” further away.

Orbitals

Within each shell, electrons occupy specific orbitals, which are subregions of probability where an electron is most likely to be found. These orbitals are like specific “paths” or “locations” within each shell.
While the shell gives a general region, the orbital pinpoints the specific area where the electron spends most of its time.
Each shell can hold a specific number of electrons depending on its shape and energy level.

Connecting Shells and Orbitals to Energy Levels

Each shell and orbital has a unique energy level. Electrons in lower shells (closer to the nucleus) and orbitals have lower energy levels than those in higher shells and orbitals. This is because they experience a stronger attraction from the positively charged nucleus, holding them closer and requiring more energy to escape.
Electron transitions typically happen between orbitals in different shells or within the same shell but with different energy levels. When an electron absorbs energy, it jumps to a higher-energy orbital (excitation). When it releases energy, it moves to a lower-energy orbital (de-excitation).

Example

Imagine a carbon atom with six electrons. Two electrons are in the lowest energy K shell (1s orbital). The remaining four electrons occupy the L shell, two in the lower-energy 2s orbital and two in the slightly higher-energy 2p orbitals.
When a carbon atom absorbs light, one of the electrons in the 2s orbital might get excited and jump to an empty 2p orbital, moving to a higher energy level within the same shell.

Key Points

Shells and orbitals are ways to visualize the location and energy levels of electrons around the nucleus.
Electrons occupy specific orbitals within shells, with each shell having a unique energy level.
Electron transitions involve movement between orbitals, driven by absorption or release of energy.

Sine

In math, sine (sin) is a trigonometric function that relates an angle to a specific ratio in a right-angle triangle. The sine of an angle is defined as the ratio of the length of the side opposite the angle (opposite) to the length of the longest side of the triangle (hypotenuse).

  • The sine of an acute angle is defined in the context of a right-angled triangle, but can be applied to any angle using the unit circle.
  • In the context of angles and triangles, “acute” refers to an angle that is greater than 0 degrees and less than 90 degrees.
  • For any given angle, its sine is the ratio of the length of the side opposite that angle to the length of the longest side of the triangle (the hypotenuse).
  • The maths notation for sine is sin.
  • In math, sine (sin) is a trigonometric function that relates an angle to a specific ratio in a right-angle triangle. The sine of an angle is defined as the ratio of the length of the side opposite the angle (opposite) to the length of the longest side of the triangle (hypotenuse).
  • The sine of an acute angle is defined in the context of a right-angled triangle, but can be applied to any angle using the unit circle.
  • In the context of angles and triangles, “acute” refers to an angle that is greater than 0 degrees and less than 90 degrees.
  • For any given angle, its sine is the ratio of the length of the side opposite that angle to the length of the longest side of the triangle (the hypotenuse).
  • The maths notation for sine is sin.