Category: Physics Notes PPT

While studying crystallography, understanding crystal planes are of high importance. Miller Indices are the mathematical representation of the crystal planes. The concept of Miller Indices was introduced in the early 1839s by the British mineralogist and physicist William Hallowes Miller. This method was also historically known as the Millerian system and the indices as Millerian or the Miller Indices. 

The orientation and direction of a surface or a crystal plane may be defined by considering how the crystal plane intersects the main crystallographic axes of the solid. The use of a set of rules leads to the assignment of the Miller Indices (hkl) a set of integers that quantify the intercepts and thus may be used to uniquely identify the plane or surface. In this article, Miller Indices are explained in detail along with some solved examples for a better understanding.

Crystallographic Planes

We know that crystal lattices are the infinite array of points arranged periodically in space. These points can be joined together by drawing a straight line and by extending these lines in the three-dimension we notice that they appear to be a set of crystal planes or Crystallographic Planes. The crystal lattices are constructed by the set of parallel lines known as the Crystallographic Planes.

The lattice points have different mechanical, electrical, or optical properties in different directions, this will make the study of crystal structure difficult. To overcome this difficulty, we will choose a set of crystal planes such that the properties of the crystal lattice remain unchanged in the direction of the crystal plane. In order to choose specific crystal planes, a famous mineralogist William Hallowes Miller introduced a method known as the Miller Indices. Basically, Miller Indices are the mathematical representation of the set of parallel Crystallographic Planes.

Miller Indices Definition

After joining the crystal lattice points by straight lines, those straight lines were assumed to be the set of parallel crystal planes extending them in three-dimensional geometry. The problem that arose was the explanation of the orientation and direction of these planes. Miller evolved a method to designate the orientation and direction of the set of parallel planes with respect to the coordinate system by numbers h, k, and l (integers) known as the Miller Indices. The planes represented by the hkl Miller Indices are also known as the hkl planes.

Therefore, the Miller Indices definition can be stated as the mathematical representation of the crystallographic planes in three dimensions.

Construction of Miller Planes

Let us understand the steps involved in the construction of Miller Planes one by one. To construct the Miller Indices and the Miller Plane we follow the following method:

Step 1:

Consider a point or an atom as the origin, construct a three-coordinate axis and find the intercepts of the planes along the coordinate axis.

Step 2:

Measure the distance or the length of the intercepts from the origin in multiples of the lattice constant.

Step 3:

Consider the reciprocal of the intercepts. Reduce the reciprocals of the intercepts into the smallest set of integers in the same ratio by multiplying with their LCM.

Step 4:

Enclose the smallest set of integers in parentheses and hence we found the Miller indices that explain the crystal plane mathematically.

Rules for Miller Indices

• Determine the intercepts (a,b,c) of the planes along the crystallographic axes, in terms of unit cell dimensions.

• Consider the reciprocal of the intercepts measured.

• Clear the fractions, and reduce them to the lowest terms in the same ratio by considering the LCM.

• If a hkl plane has a negative intercept, the negative number is denoted by a bar (  ̅) above the number.

• Never alter or change the negative numbers. For example, do not divide -3,-3, -3 by -1 to get 3,3,3.

• If the crystal plane is parallel to an axis, its intercept is zero and they will meet each other at infinity. 

• The three indices are enclosed in parenthesis, hkl and known as the hkl indices. A family of planes is represented by hkl and this is the Miller index notation.

General Principles of Miller Indices

• If a Miller index is zero, then it indicates that the given plane is parallel to that axis.

• The smaller a Miller index is, it will be more nearly parallel to the plane of the axis.

• The larger a Miller index, it will be more nearly perpendicular to the plane of that axis.

• Multiplying or dividing a Miller index by a constant has no effect on the orientation of the plane. 

• When the integers used in the Miller indices contain more than one digit, the indices must be separated by commas to avoid confusions. E.g. (3,10,13)

• By changing the signs of the indices 3 planes, we obtain a plane located at the same distance on the other side of the origin.

Examples

1. Determine the Miller Indices of Simple Cubic Unit Cell Plane 1,[infty],[infty].

Ans:

Given that we have a plane 1,[infty],[infty] our aim is to determine the Miller indices for the given set of the plane. We know that we have a set of rules for determining the miller indices and they are as follows:

Step 1:

Consider the given plane 1,[infty],[infty].

Step 2:

Take reciprocals of the intercepts,

[frac{1}{1}], [frac{1}{infty}], [frac{1}{infty}]

Step 3:

Take LCM of these fractions to reduce them into the smallest set of integers.

1,0,0

Therefore, the miller indices for the given plane is 1,0,0.

2. Determine the Miller Indices for the Plane 1,[infty],1 

Ans:

Given that we have a plane 1,[infty],1, our aim is to determine the Miller indices for the given set of the plane. We know that we have a set of rules for determining the miller indices and they are as follows:

Step 1:

Consider the given plane 1,[infty],1.

Step 2:

Take reciprocals of the intercepts,

[frac{1}{1}], [frac{1}{infty}], [frac{1}{1}]

Step 3:

Take LCM of these fractions to reduce them into the smallest set of integers.

1,0,1

Therefore, the miller indices for the given plane is 101.

3. Determine the Miller Indices for the Plane ½,1,[infty]  

Ans:

Given that w
e have a plane ½,1,[infty], our aim is to determine the Miller indices for the given set of the plane. We know that we have a set of rules for determining the miller indices and they are as follows:

Step 1:

Consider the given plane ½,1,[infty].

Step 2:

Take reciprocals of the intercepts,

[frac{1}{frac{1}{2}}], [frac{1}{1}], [frac{1}{infty}] 

Step 3:

Take LCM of these fractions to reduce them into the smallest set of integers.

2,1,0

Therefore, the miller indices for the given plane is 2,1,0.

4. Determine the Miller Indices for the Plane −1,[infty],½

Ans:

Given that we have a plane −1,[infty],½, our aim is to determine the Miller indices for the given set of the plane. We know that we have a set of rules for determining the miller indices and they are as follows:

Step 1:

Consider the given plane −1,[infty],½.

Step 2:

Take reciprocals of the intercepts,

[frac{1}{-1}], [frac{1}{infty}], [frac{1}{frac{1}{2}}]

Step 3:

Take LCM of these fractions to reduce them into the smallest set of integers.

−1,0,2

Therefore, the miller indices for the given plane is 1,0,2.

Important Features of Miller Indices

Some important features of Miller indices have been mentioned below as:

1. A plane that is parallel to in the least one of the coordinate axes comes with an intercept of infinity ([infty]) and consequently, the Miller index for the said axis becomes zero.

2. All of the similarly spaced parallel planes having a specific alignment come with the same index number (h k I).

3. Miller indices don’t only give the definition of the specific plane but a combination of many parallel planes.

4. Only the ratio of indices is considered important over everything else. The planes do not matter.

5. A plane fleeting over the origin is defined in comparison to a parallel plane that has non­zero intercepts.

6. Altogether the parallel equally far planes consist of the same Miller indices. Therefore, the Miller indices are used in relation to a set of parallel planes.

7. A plane that is parallel to anyone out of the many coordinate axes comes with an intercept of infinity.

8. If the Miller indices relating to two planes comes with the same ratio, for example, 844 and 422 or 211, then the planes can be proved as parallel to each other.

9. If h k I am the Miller indices relating to a plane, then the plane will divide or cut the axes into a/h, b/k, and c/l equivalent sections individually.

10. If the integers that are being used in the Miller indices comprise more than one single digit, the indices must be parted by commas for precision, for example (3, 11, 12).

11. In a family the crystal directions are not necessary to be parallel to each other. Likewise, not all members in a family of planes are supposed to be parallel to each other.

12. By altering the signs of entirely each one of the indices of a crystal direction, we find the antiparallel or conflicting direction. By altering the signs of each and every one of the indices of a plane, we get a plane that is situated at a similar distance on the other side of its origin.

After the experimental confirmation of Rutherford’s scattering theory in about the year 1913, the one-to-one relationship or link of an atom with its atomic number Z was proven by the work of Henry Moseley from the year 1887 to 1915. 

Henry Moseley used the structure of Bohr’s atomic model to determine the energy radiated by an electron when it migrates from low-level orbitals. This energy released during migration has a strong dependence on an atomic number ‘Z’ so that by measuring the energy of the X-rays characteristic of any element, its atomic number Z can be confidently determined. 

Moseley Periodic Law

Here, we will measure the x-ray spectra of a number of elements and also identify several unknown elements by looking at their characteristics, viz: X-ray spectra.

Moseley’s law was discovered and published by an English Physicist named Henry Moseley. This law is an empirical law that concerns the characteristics of X-rays emitted by atoms.

The frequency v of X-ray emitted by an atom is related to its atomic number ‘Z’ by the following formula:

v =(a−b)−−−−−− [sqrt{(a-b)}]        …..(1)

Here,

a and b = are constants. We also call these constants proportionality and screening or shielding constants.

Equation (1) is Moseley’s X-ray Characteristic formula and here the two physical constants ‘a’ and ‘b’ are independent constants of an element; however, these two depend on the X-ray series.

For a ‘k’ series, the value of a and b is:

a = [frac{3RC}{4}]−−−−−−[sqrt{frac{3RC}{4}}]

and

b = 1 

Where,

R = Rydberg’s constant

c = speed of light

For the L series, the value of a and b is as follows:

a = [frac{5RC}{36}]———– [sqrt{frac{5RC}{36}}],

and

b  = 7.4

The relation between a and b is determined by experiments using Henry Moseley’s law and the graph for this relationship is as follows:

The line intersecting in the graph at the Z-axis shows that Z = b, where b is 1 for K series elements and 7.4 for elements in L series.

Moseley Law Statement

A simple idea is that the effective charge of the nucleus decreases by 1 when it is being screened by an unpaired electron that persists behind in the K-shell.

Moseley X-Ray Experiment

X-ray spectrometers are the fundamental foundation-stones of the process of X-ray crystallography. 

The working by Moseley by employing X-ray spectrometers is as follows:

A glass-bulb electron tube was used, inside this evacuated tube, electrons were fired at a metallic substance, which was a sample of the pure element in his work.

The firing of electrons on a metallic substance caused the ionization of electrons from the inner electron shells of the element. The rebound of electrons into the holes in the inner shells then caused the emission of X-ray photons leaving out the tube in a semi-beam, through an opening in the external X-ray shielding. 

Now, these radiated X-rays were then diffracted by a standardized salt crystal, with angular results emitting in the form of photographic lines by the exposure of an X-ray film fixed at the outside the vacuum tube at a known distance. 

Next, Moseley employed the application of Bragg’s law after initial guesswork of the mean distances between atoms in the metallic crystal, based on its density next leading to calculate the wavelength of the emitted X-rays.

Analysis of Moseley’s Experiment

To Determine the following things:

• Firstly, we must confirm Moseley’s law with six known samples of elements. Since the energy is the characteristic X-ray (according to Moseley), which is proportional to (Z – n and channel number N is directly proportional to E, then N is proportional to (Z – n). Therefore, N kZ = − bg n. 

• Draw a graph plotting N vs. Z for the six known samples. Obtaining the best values of k and n can be observed from this graph. Now, look at your spectra carefully and think about what the uncertainties in your data are. Devise a reasonable method for determining the uncertainties in n and k.

• Determine Z for the unknowns by comparing the peak position for each with your results from the six known samples and also determine the uncertainty associated with your findings.

So, this is how we can determine the atomic number of a material; by observing the X-ray characteristic of an element. 

Moseley’s Law and a Basic Introduction

Moseley’s law is used to understand the emitted x-rays by the atoms. This law was derived and published by Henry Moseley. He used this law to determine the energy exerted by an atom. Atoms are the smallest particle that exists. And to find the energy that is exerted by the atom, Moseley’s law is used. It is an empirical law that determines the atomic number. 

Students can find more information about Moseley’s law on the website. It has all free downloadable content that students can use and study. It is important to practice all the formulas with example questions to get a better understanding of the law. This law is very important as it created the basis of the periodic table and also helped in discovering new elements that were previously unknown to the scientists. 

Statement of the Moseley’s Law

The statement of moseley’s law is: “The square root of the frequency of the x-ray emitted by an atom is proportional to its atomic number”. New elements were also found because of this law. This law came to existence because when Henry Moseley was studying graphs, he found a strange relationship between the lines and the atomic number. This law also helped with organizing the elements on the periodic table based on atomic numbers rather than atomic mass. 

The formula for Moseley’s law is ν=a(Z–b)…(1) 

Importance of Moseley’s law 

Moseley’s law is very important because it proved that atomic numbers are more necessary than atomic mass and it is because of this reason that the entire periodic table was changed based on the element’s atomic number. This law also helped with discovering new elements and explained the property of elements way better. 

In 1914, Moseley also published a paper where he spoke about three unknown elements between two others and because of all his experiments and data, we now have more information about how to study elements. He also found that the K lines were related to the atomic number and later found the formula by which the approximated relationship between them could be calculated. 

The formula which is called Moseley’s Law is: 

V = A . (Z – b)²

In this case, 

Energy is one of the most important entities in our universe. We perform many day to day activities. Think, what causes humans to do all the daily activities? This capacity or ability of a body or system to do work is referred to as energy. 

Energy is thus a qualitative property that needs to be transferred to another object in order to make it work or function. Energy can neither be created nor destroyed. It can only be transferred or converted from one form to another. As energy exists in multiple forms, it is hard to find a single elaborate definition of it. Energy can be chemical, thermal, mechanical, electrical, nuclear and light etc. 

The SI unit of energy is Joule (J), which is defined as the energy spent in making an object move through a distance of 1 m, against a supplied force of 1 newton. We will now discuss a few sources of energy in this article below.

Types of Natural Sources of Energy

Energy sources are of two types:

1. Renewable energy sources

2. Non-renewable sources

Renewable Sources of Energy

The sources of energy present on the earth that can get replenished, or recharged without getting exhausted (running out) are called renewable sources of energy. Renewable energy sources are available on a daily or seasonal basis. Renewable sources are clean and do not cause any pollution to the environment. For example: sun, wind and water etc.

The sun is a very essential source of renewable energy in our life. Our sun is a star i.e. its light is internally produced, it does not reflect the light of any other star or body. It is the basic source of heat and light for the entire living world and the source of energy for all ecosystems. Its thermal heat can be used for passively heating buildings and water. Its natural light (daylight) contributes immensely to the reduction of artificial light needed to light our buildings. It is useful for plants to grow. Sun can provide electrical energy with the help of photovoltaic cells (PV Cells), which are made up of silicon or any other material that transforms sunlight into electricity. Solar panels absorb the sunlight and store it in a solar battery. Solar panels convert solar energy into usable electricity by the photovoltaic effect. Solar energy is also used as solar thermal energy.

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Wind energy is an environment friendly and abundantly available source of energy.  Windmills are used to harness the wind potential. Wind rotates the turbine’s blades, which feeds an electric generator and produces electricity. The turbine makes use of kinetic energy of wind and converts it into mechanical energy. The generator can convert mechanical energy into electricity. Mechanical energy can also be used directly for specific tasks such as pumping water etc.

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Water or hydel energy is the energy derived from the flowing water. Electricity produced by the flow of water using dams is called hydroelectricity. In this process, a hydel dam captures energy from the moving water of the river. This water is made to fall from a great height. The falling water rotates the turbine, which feeds the generator. The dam operators control the flow of water and the amount of electricity produced.

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Non-Renewable Sources of Energy

Non-renewable energy sources are those which are present in a limited quantity. They are exhaustible, and will run out if not used judiciously. These sources cause pollution to the environment because carbon is the main element present in fossil fuels such as coal and petroleum. Most sources of non-renewable energy are fossil fuels. Fossil fuels were created as the remains of terrestrial and marine flora and fauna that decayed millions of years ago and got buried in layers under huge amounts of pressure and heat. Most fossil fuels are burnt to produce energy and electricity. Coal is also a fossil fuel.

Fossil fuels are a valuable source of energy. They can also be stored, piped, or shipped anywhere in the world.

Coal is a black coloured rock-like fuel. We burn coal to get energy. Coal is widely used as a domestic fuel to make food. When coal is burnt, it releases harmful smoke. Coal is essentially formed as a result of decayed vegetation. There are four stages in the formation of coal- peat, lignite, bituminous and anthracite. Coal mainly contains carbon, hydrogen and oxygen. 

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Petroleum is a liquid fossil fuel composed of a variety of hydrocarbons. It is a very useful energy source. However, the petroleum that is drilled out from oil wells is crude oil. It has to be refined through a process called fractional distillation, where different hydrocarbons separate to form different fractions. Petrol, kerosene, paraffin, diesel are some of its fractions.  Petrol is used as a fuel in vehicles. Petroleum and its products are used not just for transport but also to manufacture many different products such as plastics, tyres and synthetic materials such as polyester. It is a reliable & portable source of energy. However, the burning of both coal and petroleum is harmful to the environment.

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We know that sound is a form of energy. Sound is a mechanical wave and the study of sound starts with the properties of sound waves and the types of sound waves. Basically, the sound is generated in the form of a wave or vibration. Human ears are extremely sensitive to sound waves ranging from 20Hz to 20KHz, known as audible sound range. There are many categories of acoustical sound such as pleasant sound, unpleasant sound, music, noise, soft, loud, etc. 

Now, noise is also a type of sound, it is really important to distinguish between what we mean by noise and what is sound. Noise is a type of sound and it can be explained or defined as a type of sound that can be unpleasant, unwanted, annoying or too loud for human ears. Noise acoustics will help us in understanding what is noise and how it can be reduced. In this article, we will discuss noise and noise acoustics by understanding how noise is produced and different types of noises.

Noise Acoustics

We know that human ears are highly sensitive and excellent at recognizing noise. Generally, noise is a kind of unpleasant and annoying tone of sound that causes mild to major discomfort or sometimes it may lead to irritation. These noise sound vibrations are capable of piercing through the ground noise that accompanies our lives. When it comes to the measuring of the various sorts of noise, we would like to duplicate how the human ear identifies and recognizes any kind of noise to urge an accurate interpretation of its impact. 

Thus, generally, in noise acoustics, we use something called the A-weighted frequency, which is considered to be much more sensitive between the frequencies 500 Hz and 6 kHz range. Depending on these frequency range there are four different types of noises, as listed below:

• Continuous noise

• Intermittent noise

• Impulsive noise

• Low-frequency noise

Let’s discuss the four sorts of noise one by one as follows:

1. Continuous Noise:

According to the name of the type of noise, we can say it is a kind of noise that is produced continuously. The specimens used or any sample of continuous noise are all mainly caused due to the machines that run continuously with no breaks in between, just like while riding a car we hear the sound of functioning parts especially such as the sound of an engine. The main source of continuous noise could be the production factories, we have seen that in factories large machinery produce continuous noise such that barely we can hear anything else.

2. Intermittent Noise:

• The intermittent noises are such sound frequencies that are not produced continuously. At the same time, the intermittent noises are produced continuously but with particular intermediate breaks.

• The best day to day illustration and example of the intermittent noises are the drilling machines, which we would have seen during the destruction or construction of any kind of building. The drilling machines are used to drill the ground and these machines reproduce unbearable sound.

• Another best and relative example of intermittent noise is drilling machines employed by a carpenter or the dentist.

3. Impulsive Noise:

• The impulsive noise is a kind of noise characterized by a background level of audible range up to 40dB in less than a half-second with a duration of 1 second.

• Impulsive noises mainly include almost all unwanted, unpleasant and instantaneous sharp sounds.

• The best examples of impulsive noises are bomb explosions that are terrifying and unbearable, the perimeter of weapons, and so on.

4. Low-Frequency Noise:

• The low-frequency noises are generally produced from the items available in our surroundings in our everyday life. The low-frequency noise is one of the complicated types of noise to scale back, and even if it is measured in a silent room still it would register sound levels around only 30-40 decibels.

• The low-frequency noise can be noticed in an office setting, this noise might have been produced from heating or ventilation. In domestic cases, it will arise from the ticking on a timepiece or wall clock. Usually, we can not even recognize these sorts of noises unless we direct our attention towards them.

So, these are the various types of noises and what is the meaning of noise physics. In analogue electronics and network theory, the word noise refers to those random, unpredictable, and undesirable signals, or mutations in signals, that cover the specified and desired information and the content. At the same time noise in the radio signal transmission seems to be as a static wave and in television signals as snow. depending on the complexity levels, the noises are subdivided into white noise and pink noise. Let us have a look at these two one-by-ones.

A. White Noise:

The white noise may be referred to as a complex signal or sound wave that incorporates the whole range of audible frequencies, all of which possess equal intensity. White noise is identical to white light, which contains merely equal intensities of all frequencies of light present in nature. A good approximation to white noise is that the static waves found in between the radio stations on the FM band.

B. Pink Noise:

The pink noise includes all the frequencies of the audible spectrum but with an intensity that will considerably decrease with increases in frequency at a rate of three decibels per octave. This decrease in frequency roughly corresponds there to acoustic (non-electronic) musical instruments or ensembles. Thus, the pink noise has been used in checking the listening rooms and particularly for auditoriums for his or her acoustic characteristics and parameters, such as reverberation time, sound-absorbing, and undesirable resonance behaviour which are the most important parameters in noise acoustics. It can also be used in audio equalizers to supply a linear intensity versus frequency response within the available listening environment.

Any kind of noise can be eliminated by providing the rooms with sound proof walls or by sound blocking. These days acousticcurtains are constructing the building by keeping the acoustic soundproofing walls for the buildings and auditoriums.

Did You Know?

1. The Maximum Loudest Sound the Earth Has Ever Produced: 

The loudest natural sound or the noise on Earth are produced by erupting volcanoes. In the year 1883, the volcano eruption that took place on Krakatoa is considered to be the loudest noise that had bee
n produced on Earth. 

2. The Noisiest City in the World: 

According to the recent survey and the research conducted by City Quiet, the top three noisiest cities in the entire world are Mumbai (India), Kolkata (India) and Cairo (Egypt). These cities are also subjected to maximum noise pollution due to the same reason.

3. The Loudest Animal on Earth: 

Even though we have heard that the call of a blue whale reaches 188 decibels, which is even louder than a jet engine or any grenade explosion, yet the loudest animal on Earth is the sperm whale whose communicative signals have been measured about up to 230 dB.

4. We have to consider an important fact that the root and main source of noise in urban environments: According to the survey and research of a European Environment Agency (EEA) briefing ‘Managing exposure to noise in Europe’, the transport sector is a major reason for noise pollution. Road traffic is the predominant noise source affecting approximately around 100 million people in the 33 member countries of the EEA.

Basically, the physical density would be the ratio of mass to the volume, and optical density measures the speed of light while passing through an optically dense medium. 

 

The optical density is a property of a transparent material that measures the speed of the light through the material. The extent to which any optically dense medium bends transmitted light rays towards or away from the normal is called the optical density.  

 

The light passing via an optically dense medium bends towards the normal and if the same light passes via any rarer medium such as air, it bends away from the normal.

 

Optical Density

Now, let us understand the phenomenon of optical density and its effect on the light passing via a medium by comparing the two media.

 

Consider two mediums: glass and air. When a beam of light passes from air to glass. The speed of the light decreases in the glass. It tells us that the glass is optically denser than air.

 

Which means,

 

If the same light passes from glass to air. The speed of light increases. 

Which means,

 

What is Transmittance?

The transmittance of a medium or a material is defined as the constituent of the light that moves via the other side of the medium or the ratio of the light energy falling on it to the light transmitted through it. When light passes through any medium, it can be transmitted, reflected, or absorbed.

 

The transmittance of the light can be defined as the ratio of the intensity of incident light (Io) to the amount of intensity (Ia)  passing through the medium. It is denoted by T.

 

Where,

 

The transmittance has no unit.

The ratio of radiant flux transmitted by the material (Φt) to the radiant flux (Φi) received by that surface is known as the Transmittance (T).

 

Transmittance Formula

 

Here, the radiant flux is the radiant energy emitted, reflected, transmitted, or received, per unit time. Its unit is Watt and the SI unit is Joule per second (J/s)

 

Optical Density formula

An optical density is defined as an equation given by, 

 

The optical density of any medium is defined as the logarithmic ratio of the intensity of incident light (Io) to the intensity of the transmitted light (It) passing through that medium. 

The O.D value for absorbance can be computed by the formula given by,

O.D. Value

 

Where, Io is the intensity of visible light incident upon a small area of the film and It, the intensity of light transmitted by that region. T% is the percentage of transmission.

 

The Relation Between Optical Density and Absorbance

The optical density and absorbance both measure the absorption of light when that light passes through an optical medium however they both are not the same.

 

Optical density measures the ability of an object to slow or delay the transmission of light. It measures the speed of light via a substance which is affected mainly by the wavelength of the given light wave.

 

Absorbance, in a wave motion, is the transfer of the energy of a wave to matter as the wave passes via it. If there is only a fragmental absorption of energy, the medium is said to be lucid to that particular radiation, but, if all the energy is lost, the medium is said to be opaque. Therefore, absorption of light occurs more in an optically dense medium.

 

Absorption Unit

The absorption unit is basically used in ultraviolet-visible spectroscopy where AU is a dimensionless quantity denoted by AU. 

Absorption of any material is taken as A given by,

Where Φ t is the radiant flux transmitted by that material and, Φ i is the radiant flux received by that material. T is the transmittance.

 

How does Concentration Influence Optical Density?

Since optical density can influence the speed of light due to optical absorption, it is quite evident that the concentration can also influence the optical density of the matter. If the optical density of the material is higher in value then it will decrease the speed of light and this causes the light to change its motion. Due to the slower speed of light, it will bend. Optical density is influenced by the concentration of light due to optical absorption. With increased concentration, the optical density of the matter will also increase.

The Significance of Optical Density

The concept of optical density helps the students to understand the speed of light transmission. The concept of optical density helps students to understand why the speed of light decreases when passing through a particular substance and the importance of the wavelength of the light transmitted through the medium. This is an important concept of physics that explains a lot of phenomena involving light emission and transmission.

Difference between Optical Density and Absorbance

Optical density measures the degree of the angle to which a particular medium slows down the speed of the transmitted light. Absorbance measures the capacity of a particular object or a medium to absorb the transmitted light that is of a specific wavelength. The concept of optical density takes both the phenomenon into account, that is the absorption of the light of a specific wavelength and the amount of light that is scattering.

The Best Way to Understand the Concept of Optical Density

The best way to understand the concept of physics is to take practical examples and analyse them on the basis of the knowledge of a particular topic. The concept of optical density explains what are the influential factors that can change the course of the lig
ht and can even lower the speed of the transmitted light. There are some practical examples that we can find around ourselves. The students can consider these items to understand the concepts of physics. Optical density takes the absorption of light by a particular medium, the scattering of the lights of different wavelengths, and the refractive index into account.

All these associated concepts can be understood by the students if they are provided with proper examples. Different types of objects can influence the speed of the light and its motion depending on the mass or the optical density, and the power of absorption. The concept can also help the students to establish relationships between the optical density, refractive index, and the speed of the light. The more the refractive index is, the more will be the optical density of a particular matter and will affect the speed of the light inversely.

The students can also refer to various reference books and textbooks prescribed by CBSE to understand various concepts of Physics. The subject-specific NCERT books are available on the website of for free. The NCERT books of physics, chemistry and biology are available on the website along with the other revision notes that can help the students to memorize the important facts that they have already learned.

How does the Intensity of a Particular Medium Influence the Speed of Light?

When light passes through a denser medium it has to face more particles and due to the absorption of the different wavelengths of the light, the speed of the light decreases. For example, when light passes through the medium of air, the frequency of the wavelength and the speed will not be affected by the medium. But when light passes through the medium of water or glass, the speed of the light decreases gradually.

In Physics, parity is a feature that is significant in describing a physical system using quantum mechanics. It usually has to do with the symmetry of the wave function that represents a system of fundamental particles. A parity transformation is a type of mirror image that substitutes such a system. In mathematical terms, the system’s spatial coordinates are inverted through the origin point; that is, the coordinates x, y, and z are substituted with x, y, and z. In general, a system is said to have even parity if it is identical to the original system following a parity transformation. Its parity is odd if the final formulation is the inverse of the original. Physical observables that are dependent on the square of the wave function are unaffected by parity. The overall parity of a complex system is the product of the parties of its constituents.

Conservation of Parity

A Physics principle says that two mirror images of each other, such as left-spinning and right-spinning particles, should act the same. The idea does not apply to subatomic particle interactions that are weak.

Fundamental Particles Sign

In the study of basic particles, there have been some remarkable breakthroughs in recent years. One of the outcomes has been the appearance of a new language and a huge number of new symbols in scientific writing. Specific types of particles are designated by symbols such as,, and. Others have been used to characterize only phenomenological behaviour (e.g.,). Various authors have given different names to the same particle or assigned different meanings to the same symbol. The meaning of a sign can sometimes alter throughout time. To offer an example, the Greek letter was originally employed to denote a heavy meson that stopped in the emulsion and then decayed, resulting in a single ionising particle. Later, the Latin letter K was substituted for the Greek letter as a code for the above-mentioned phenomenological description.

While the letter took on a more concrete physical meaning: a hefty meson that decays into one charged and two neutral particles. The letter K is also often used to represent any charged particle that is heavier than a -meson but lighter than a proton and whose method of disintegration is unclear. Another example is the neutral particle with a mass of roughly 1,000 m e that decays into two -mesons, which has been given numerous names such as v0, V 20, and V 40, although some authors have used the letter V 20 to identify any V0-particle other than the so-called V 10. Parity is also known as Multiplicative Quantum Number. Parity is a useful concept in both Nuclear Physics and Quantum Mechanics. Parity helps us explain the type of stationary wave function (either symmetric or asymmetric) that subatomic particles, like neutrons, electrons, or protons have.

In simple words, parity is the reflection of coordinates about the origin. For instance, the wave functions of x, y, and z are ψx, y, z.

 

Here, the wave function, ψ explains the stationary state of any particle, and x, y, z are the functions of the position.

Further, the parity is the transpose of  x, y, z as;

x  →  – x…..(1)

y  →  – y ….(2)

z  →   – z….(3)

To understand parity in particle Physics in detail, view this page till the end.

Conservation of Parity in Particle Physics

Now, let’s understand the parity conservation in particle Physics from the above three equations:

Assume that there is a three-axis coordinate system with x, y, and as coordinates. 

A point P lying on the coordinate plane has a position of P (x, y, z). Suppose that we shift the position of P to another point that is at its mirror image.    

Now, the coordinates of this point become P (- x, –  y, – z), i.e., the transpose of the original coordinates. We call this practice the transformation or reflection about the origin.

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So, the changes we have made above are called Parity.

Certainly, we can state the definition of Parity into words:

Parity Definition

Above all, Parity is the reflection of the coordinates in a plane around the origin. Furthermore, parity helps us define the stationary state of the wave function.  

Further, parity can be explained in simple terms as;

Parity Particle in Physics

Now, let’s say, a parity operator “UP,” where “U” is the operator and “P” is parity.

Further, this  parity operator must follow the below property:

                        UP2  ….(a)

Similarly, the unity operator property is:

                  UP*  UPt =1……(b)

Indeed, the above equation (b) says that the product of the operator and the transpose of an operator is always unity.

Now, comparing equations (1) and (2), we get:

As a matter of fact, the transpose of an operator becomes equal to the operator itself, we call this property the Hermitian Property or Hermitian Operator.

Points to Note:

• The value of parity operator UP must be one.

• Also, the parity operator must be a unitary operator.

So, when the above two conditions are equal, we get what we call the “Hermitian Operator.” Besides, the condition of the Hermitian operator says that all its eigenvalues are real. Now, let’s understand the Parity of Elementary Particle:

Parity of Elementary Particle

Let’s say, a wave function  ψx, y, z  =  ψ(R), where the function “R = x, y, z.” 

Furthermore, when the wave function  is operated in the following manner, we get an eigenvalue “P;” 

                    UPψ(R)  = P  ψ(R)……(c)

Additionally, operating the function, we may or may not get the same function.  However, in the above case, the function is the same, i.e., ψ(R).           

Now, again operating the above equation (c) with a parity operator as;

                UP(UPψ(R)) =  UP(P ψ(R)) …..(d)

We know that the eigenvalue is always real and constant, so taking “P” out from equation (d), we have:          

               UP(UP< span>ψ(R)) =   P  . UP(ψ(R))

As we know from equation (c), UPψ(R)  = P  ψ(R), putting the same in equation (e), we get:

                  UP(UPψ(R)) =   P . P  ψ(R)

So, 

                  UP2 ψ(R) =  P2 ψ(R)

Since P is an eigenvalue and P2 = 1,therefore,

The above equation (f) has two meanings, let’s understand these:

P = + 1

P =  – 1

What is the Significance of a Parity Operator?

Now, let’s see what even and odd parity is.

Considering a function, ψx, y, z on transposing, forms ψ– x, – y, – z.

On doing the transpose of ψ– x, – y, – z, we get “ψx, y, z“ again, which means, it is an even function.

However, if we get (- ψx, y, z ) in place of (ψx, y, z), it is an odd function.

When the sign of function remains the same, it is an even parity, i.e., (+ ψx, y, z).

Furthermore, when the sign of function remains the same, it is an odd parity, 

i.e., (- ψx, y, z ).

Parity Signs Explained

Let’s suppose that we change the coordinates of the stationary state of the particle.

However, on changing if we get the same function, it is an even parity, such as (ψ– x, – y, – z) remains (+ ψx, y, z) after a change. We call this function the symmetric function.

Moreover, if we get a different function, i.e., from (ψ– x, – y, – z) to ((+ ψx, y, z) after a change. We call this function an asymmetric function.