Category: Physics Notes PPT

We know that all planets, asteroids, and comets in the solar system revolve around the Sun in approximately elliptical orbits. Thus as a result there are points in the orbital pathways when the heavenly body is farthest and nearest to the sun. Aphelion is when a planet, an asteroid, or a comet is most distant from the sun in its orbit. This is the aphelion definition in astronomy. This answers the question of what is aphelion. All planets in the solar system have an aphelion. The perihelion condition is the exact opposite. The tilt of the axis of the planet and the elliptical orbital pathways cause aphelion and perihelion.

Perihelion and Aphelion of the Earth

Perihelion is the point in the orbital pathway of earth where it is closest to the sun. The distance is approximately 91.4 million miles or 147 million kilometers. Aphelion on the other hand is the point in the orbit when the earth is farthest away from the sun. The distance is approximately 94.5 million miles or 152million kilometers. Aphelion occurs around July 4 about two weeks after the June Solstice. Perihelion occurs around January 3 after about two weeks of the December Solstice. The aphelion and perihelion occur around the same time every year. This 2021, aphelion of Earth was observed on July 5, at 6.27 P.M (Eastern Time) and perihelion of Earth was observed on January 2, at 8,52 A.M (Eastern Time). The precession of the perihelion events is the reason why the orbit is not a simple closed curve such as an ellipse. Milankovitch Cycles occur because of these events.

Earth’s orbital pathway around the sun cannot be described as a perfect circle. The orbital path is an elliptical one with an eccentricity of 0.017. Therefore the sun will not be at the center. According to the laws of Johannes Kepler, all planets in the Solar system have elliptical orbits with the Sun at one of the focal points. Now due to this reason at times, Earth will be closer to the sun and at times it will drift far away from the sun. Thus we can confirm that the elliptical orbit of the earth around the sun is the cause for aphelion and perihelion. Another cause for this perihelion and aphelion may be the 23.5-degree tilt of the axis of Earth. This tilt results in the changing of the seasons.

When the earth is closest to the sun i.e. during aphelion, the northern hemisphere has a winter season, and the southern hemisphere experiences the summer season. Thus it can be seen that the distance between the earth and the sun does cause any noticeable effect in the changing of the seasons. The minor effects of the difference in distances are overshadowed by the oceanic southern hemisphere and the continental northern hemisphere. Hence the change of the seasons is due to the rotation of the earth around its tilted axis. The tilt is measured to be 23.5 degrees. This is the reason for winter in the northern hemisphere in December – January and summer in the southern hemisphere as the Sun is farther south during this time. The part of the earth where sun rays fall slantingly experience winter whereas the parts where the sun rays fall directly experience the summer season.

Did You Know? 

• The words “ perihelion” and “ aphelion” are derived from ancient Greek, where “apo” means far, “peri” means close, and “helios” stands for the sun.

• All planets, comets, and asteroids in the solar system have approximately elliptical orbits and thus also have a perihelion and aphelion.

The radius of an atom of a chemical element is a measure of the atom’s size. The meaning of it is said as the typical distance which is from the center of the nucleus till the boundary of the atom which is surrounding the electrons. There are three widely used definitions which are used for atomic radius:they are the  ionic radius, Van der Waals radius, and covalent radius.

 

According to the definition these terms may be applied only to isolated atoms in condensed matter as well covalently which have bonding in molecules or even within ionized and excited states as well. And its value can also be obtained by the experimental measurements, or computed from models of theory. The radius value can even depend on the atom’s state.

 

It is said that the electrons do not have definite orbits or sharply defined ranges. The position of the molecules can be described as probability which has distributions that gradually taper off as one that moves away from the nucleus. And that too without a sharp cutoff. In condensed molecules and matter the cloud of electrons of the atoms usually overlap to some extent, and some of the electrons can even roam over a large region encompassing two or even more atoms.

 

In most of the definitions of the radii of isolated atoms which are neutral atoms range between 30 and 300 pm  that is trillionths. Or even between 0.3 and 3 ångströms. The radius of atoms is more than 10,000 times the radius of its nucleus that is 1–10 pm and less than 1/1000 of the wavelength of visible light that is 400–700 nm.

 

Covalent Radius

Here letter r covalent is defined as =  ½  that is the internuclear distance between two bonded atoms. The internuclear distance which is between two bonded atoms is called the bond length. 

 

Van Der Waals Radius

It is one the distance which is half the distance between the nuclei of two similar non-bonded isolated atoms or even two adjacent identical atoms belonging to two neighboring molecules of an element which are in the solid-state. The weakest forces which are also known as the van der wall magnitude of the radius are dependent on the packing of the atoms when the element is in the solid-state.

 

An example of the internuclear that is the distance which is between two adjacent atoms of chlorine in the solid-state which is 360 pm. So the Van der Waals radius of the chlorine atom is said to be 180 pm.

 

Metallic Radius

A crystal contains positive kernel ions which are arranged in a pattern which is definite in a sea of mobile electrons which are valence.The force of attraction which is between electrons that are basically mobile and the positive kernels is also called the metallic bond. It is said to be one of the half internuclear distances which is between the two adjacent metal ions in the lattice metallic. In a metallic lattice the valence electrons are mobile or we can say they are free to move  therefore they are only weakly attracted by the metal ions or kernels.

 

In a bond-like covalent bond, there is a pair of electrons which is strongly attracted by the nuclei of two atoms. That is why a metallic radius is always longer than its covalent radius. 

 

General Trends in Atomic Radii in the Elements of the Periodic Table

• The way the atomic radius varies with increasing atomic number is referred to here as the general trends. This trend can be explained by the arrangement of electrons in fixed shells around the nucleus of an atom. The general rule is that shells fill in  the order of increasing radius, since the negatively charged electrons are attracted by the positively charged protons in the nucleus. As the atomic numbers increase(and therefore the total number of protons) along each row of the periodic table, the additional electrons go into the same outermost shell; whose radius gradually contracts, due to the increasing nuclear charge. 

• In elements such as that of a noble gas, the outermost shell of the atom is completely filled; therefore, the additional electron of the next alkali metal enters into the next outer shell, which explains the sudden increase in the atomic radius.

• Thus we notice that for an atom in the periodic table,  increasing charge in the nucleus is partially counterbalanced by the increasing number of electrons in its orbit, a phenomenon that is called the “shielding effect”. This effect accounts for the size of atoms which gradually increases down each column in the periodic table. 

• However, there are few notable exceptions. They are the d-block contraction and the f-block contraction (also known as lanthanide contraction). Lanthanide contraction refers to the much smaller size of the 5d block of elements than one would expect which happens due to the poor shielding of the 4f electrons.

• As a thumb rule, the atomic radii decrease across the periods as the total protons in the nucleus increases. There is greater attraction experienced by the orbiting electrons, which draws them closer to the protons, decreasing the size of the atom. Therefore, the atomic radius decreases. 

• Down the groups, atomic radius increases because there are more energy levels and hence a greater space between protons and electrons. In addition to this, electron shielding effect is also observed which causes attraction to decrease and the remaining  (valence) electrons can go farther away from the positively charged nucleus. This causes the size, or atomic radius, to increase.

 

Explanation

The shells which are present are generally  filled in order of radius which is increasing since the negatively charged electrons are attracted by the positively charged protons in the nucleus. The additional electrons go into the same shell which is the outermost shell whose radius contracts graduall. And this happens mostly due to the increasing nuclear charge. In a noble gas if we keenly observe, the outermost shell is completely filled and therefore the additional electron of the next alkali metal will go into the next outer shell for the increase in the atomic radius.

 

This explains why the size of atoms usually increases down each column. There is one notable exception for this and is known as the lanthanide contraction that is the 5d block of elements which are much smaller than one would expect which is due to the weak shielding of the 4f electrons.

 

Notes

The Difference between experimental and empirical data: “Empirical data basically means that they are originating  or we can say they are based on observation or experience that are relying on observation or experience alone often without due regard for system and theory data”. It basically means that we measure it through physical observation and a lot of experiments which are generating the same results. Note that the values are not calculated by a formula. But, often the empirical results then become an equation of estimation. Experimental data which are on the other hand are only based on theories.

Bohr’s theory of atomic spectra says that an isolated atom possesses discrete energy levels and the energy of an electron depends on the orbit it is revolving in. However, isolated atoms don’t exist practically, but in crystals. 

Let’s take a single Silicon (Si) atom, the energy of the first electron is – 13.6 eV. Now, taking the second Si atom, the energy in its hidden electron is also – 13.6 eV, and it remains the same at n = 1. However, when atoms combine to form a crystal, the energy of electrons doesn’t remain the same. For that, we need to create energy bands in solids. Now, let’s understand the band theory of solids.

Band Theory of Solids

In crystals, electrons come close to each other (Approx. 2 to 3 Å closer) to have the following interactions with:

In crystals, each atom has a unique position. Hence, each electron has the following unique properties:

A straight line of the energy level splits into 1023 energy lines or levels within a width of 1 eV. These lines are so close to each other that they appear as energy bands (of crystals). These energy lines are continuous, and the difference between each is 10-23 eV.

Suppose we have a Sodium metal, where 1 mole of Na atoms has 6.022 x 1023atoms. Now, we break it into two pieces; the electron in each piece possesses different positions and interactions.

Here, the energy of an outer electron will be unique in each energy line, and this slight difference will be because each electron has a unique position and interaction. 

Now, let’s see energy bands in solids by taking an example of Na.

Energy Bands in Solids

In this context, we’ll study the band structure of solids.

We know that the electron configuration of Na = 1s22s22p63s1. Energy bands of 1s, 2s, 2p, and 3p, are shown below:

                                 

In the upper band, i.e. 3s having electrons is the valence band, and the energy level above it, having no electrons, is the conduction band. Here, we can discern that there’s no forbidden energy gap in conductor. Now, let’s take examples of Silicon.

Let’s take a Silicon crystal having ‘n’ mole of Silicon atoms. We know that the electronic configuration of Si = 1s22s22p63s23p2. The number of electrons in the outer energy level = 4n and maximum electrons  = 8, i.e. 2 from 3s and 6 from 3p.

Similarly, the number of outer energy levels available in Si-atom = 8 

Therefore, in a crystal, there are 8n (2n from 3s and 6n from 3p) electrons, where n = 10-23. We can see that out of 8n energy levels, 4n is filled, and 4n is vacant at zero Kelvin. 

                                            

If we look at this graph, initially, there are 2n and 6n electrons in 2n and 6n state, respectively. The interaction between outer electrons increases gradually, the energy level expands, and the time comes when both of these overlap. 

Now, it becomes hard to determine which state (2n & 6n) an electron belongs. Eventually, the distance between the atom nullifies and crystal forms.

During the mixing of energy levels (hybridization) of 2n and 6n state, the electrons from 2n state migrate to 6n, as they prefer to stay in the lower state. 

Now, after the crystal formation, we have two 4n states (8n = 4n + 4n), where the lower 4n state has filled 4 electrons, and the upper 4n state has zero electrons. The lower one is the valence band, and the upper one is the conduction band, which may/may not have electrons; however, there is a FEG or forbidden energy gap in semiconductor, i.e. Silicon. The energy band structure will be:

Energy Gap in Insulator

If we look at the energy band diagram of an insulator such as a Diamond, the energy gap, or FEG (Eg = 6 eV)) is larger. Though the valence band is completely filled (as per Pauli’s principle); due to a large gap between the valence band (Ev) and the conduction band (Ec), these electrons can’t transfer to the conduction band.

                           

Since electron movement isn’t possible here, that’s why electric conductions in these materials become impossible. 

Below you can see the energy bands in different solids:

Energy Bands in Conductors Semiconductors and Insulators

      

The enormous number of molecules in even a small amount of dilute gas results in simplification rather than compilation, as one would imagine. The explanation for this is that in most studies of gas behaviour and properties, only statistical averages are found, and statistical methods are very reliable when large numbers are involved. Only a few properties of gases, such as pressure, density, temperature, internal energy, viscosity, heat conductivity, and diffusivity, are important when compared to the number of molecules involved. (Electric and magnetic fields may be used to reveal more subtle properties, but they are of secondary importance.) 

Is it Easy to Figure it?

The fact that these properties are not mutually exclusive is remarkable. If you know the first two, you can figure out the rest. That is to say, specifying only two properties for a given gas—usually temperature and density or temperature and pressure—fixes all the others. Thus, if the density and the temperature of CO2 are specified, the element can have only one possible pressure, one internal energy, one viscosity, and so on. These other properties must either be measured or estimated from the known properties of the molecules themselves in order to be determined. The ultimate aim of statistical mechanics and kinetic theory is to perform such calculations, and dilute gases are the case where the most progress has been achieved.

Equilibrium Properties

Ideal Gas Equation of State

Apart from its low density as compared to liquids and solids, a dilute gas’s most noticeable Behaviour and properties are its high elastic behaviour of solids or compressibility and large volume expansion when heated. Both dilute gases have almost identical properties. Almost all of these gases can be correctly represented using the universal equation of state- pv=RT.

Since all real gases deviate slightly from this expression, it is referred to as the ideal, or perfect, gas equation of state. These deviations become less important as the density of the gas decreases. The pressure is p, the volume per mole is v, the universal gas constant is R, and the absolute thermodynamic temperature is T. If the volume is more than 10 times the critical volume, the expression is accurate to within a few per cent; the accuracy improves as the volume increases. In both high and low temperatures, the expression ultimately fails due to ionisation at high temperatures and condensation to a liquid or solid at low temperatures.

Internal Energy

Internal energy is a property or state function in thermodynamics that determines the energy of a material in the absence of capillary effects and external magnetic, electric, and other fields. The value of the energy, like any other state function, is determined by the state of the material rather than the existence of the processes that led to that state. The work is proportional to the change in internal energy when a system changes state as a result of a phase in which only work is involved, according to the first law of thermodynamics. If both heat and function are involved in a system’s change of state, the change in internal energy is equal to the heat supplied to the system minus the work performed by the system, according to the rule.

Transport Properties

The three major transport Behaviour and properties, viscosity, heat conductivity, and diffusivity, are summarised below. The transfer of momentum, energy, and the matter is represented by these properties.

Viscosity 

Viscosity is a form of internal friction found in all ordinary fluids. A constant force is required to keep a fluid flowing, just as a constant force is required to keep a solid body moving in the face of friction, also known as the viscoelastic behaviour of polymers. 

Heat Conduction

A flow of energy through a fluid may occur if a temperature differential is preserved through the fluid. According to Fourier’s law, the energy flow is proportional to the temperature differential, with the heat conductivity or thermal conductivity of the fluid, aka, λ. Energy may be transported by mechanisms other than conduction, such as convection and radiation; it is thought that these can be omitted or modified in this case.

Diffusivity

Diffusion is a mass transfer phenomenon that causes a species’ chemical behaviour distribution in space to become more uniform over time. A chemical dissolved in a liquid or a part of a gas mixture, such as oxygen in air, is referred to as a species in this case.

Fun Fact

What is the composition of matter? Atoms are the building blocks of all matter. Atoms are the tiniest particles in the universe. They’re so tiny that they can’t be seen with the naked eye or even a normal microscope. A million atoms make up a typical sheet of paper. A scanning tunnelling microscope (STM), which uses electricity to map atoms, has been developed by science to classify atoms. More on atoms will be discussed later, but first, let’s review the three states of matter.

Introduction

Languages are one of the most important things in human life that helps one not only to express but add feelings to their words. There are different modes and languages to talk or express feelings.one of those is braille language or code. In this language characters are represented by patterns of raised dots that are felt with the finger tip.This is used by  the people who are blind or physically impared. People can read it by eyes (which are not physically impared or blind). We do not designate braille as a language, but rather by a code.

What is Braille?

It is basically codes written on the paper in the form of raised dots which can easily be seen by normal people and can be touched and feeled by impared or blind people.

This code is not just restricted to one language but it can be inscripted in many more languages  for example  chinese, english, hindi etc.

It’s even written in the native language of people so that everyone can access  education. English braille is a specific code used in US, american edition, however from 2016 unified english braille code  became the main code for reading material, a code used in seven other speaking companies.

Find Out What Braille is?

As we know that it’s a system of touch reading and writing for the visually impaired . Equivalent punctuation that marks and provides punctuation marks and provides symbols to show letters grouping. It’s written from left to right by moving fingers on the letters, and the reading process involves both hands and index fingers. 125 words per min is the average reading speed but greater speed is 200 words per minute.

This code gives a broad range of reading material that includes recreational and educational ,financial statements and hotel reviews. They can also access their hobbies like music scores, hymnals, playing cards and board games.

What is Braille Communication?

The Braille system is a tactile writing system for visually impared people, Traditionally it was embossed on the paper. But now they can use the computer screen also and other electronic supporters by using a refreshable braille display. They can also use  original slate and stylus or they can use braille writer for typing  e.g. braille notetaker or a computer which prints braille embossers. 

Louis Braille a Frenchmen  is the creator of this braille code .He lost his  eyesight in a childhood accident. When he was in the age of 14 he had discovered code for french alphabets as an improvement on night writing then he started including musical notations in 1829. In 1837 a second revision was published in the modern era. It was the first small binary form of writing developed in the  modern era.

What is Braille Code? 

It is a code which enables blind or visually challenged people to read and write through touching the dots.

Its written in raised dotted form on the paper with cells of upto six dots in a 3*2 configuration. 

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The position of the dots are identified by the numbers from 1 to 6. Using one or more of these dots, 64 combinations are possible. An alphabet letter, number punctuation marks or even a whole word can be represented as a single cell. How the dots are numbered and how cells look like is illustrated by braille alphabet and number pages.

Few of the Alphabets

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What Language is Braille ?

Though it is said that braille is a language, a code for blind, visually impared, and is said to be after its inventor’s name Louis Braille. It is not a different language than one’s own languages e.g. we can study it in Chinese, French, Detch, German, English, Hindi etc Even we can learn it in our native languages.

it’s derived from the latin alphabet albeit indirectly . the upper four dot position occupied by first ten alphabets from a to j ⠁⠃⠉⠙⠑⠋⠛⠓⠊⠚  .these stand from 1 to 10 .though these dots have no obvious orders  the cell with the fewest dots are assigned to the first three letters abc=123.(⠁⠃⠉).

What is Braille for the Blinds?

Everyone doesn’t have this gift to experience, there are few exceptions like the visually impared or blind. A man called Louis Braille had discovered this whole. We can easily and shortly read something very easily due to the gift of vision. We can easily watch all beautiful colours present in the universe and near us but thinking about those who do  language for blinds to access education and knowledge.

What are Braille Dots Called?

 It looks like this for letters  

 [Image to be added Soon]

It is embodied on the sheets and it is read by both the hands and the index finger tips.

An uncontracted braille is described as when every letter and every word is expressed in braille. Many newly blinded people find it uncomfortable to understand. 

There are around 180 letters which are circumscribed in 75 letters only. These are the shortcuts which reduce the volume of paper needed and it becomes easy for the people to understand it quickly.

What is in Braille?

There are many different symbols which can  be used as shortcuts and can reduce lode on paper also. Six letters are inside one rectangular box. There are no different letters in braille language for capital letters, However, by placing dot 6 in a cell we can achieve the same. Numbers are made by using the first ten alphabets of numbers that are produced by signs or dots 3-4-5-6.

There are many reasons why blindness happens, few by accidents and few by disease but the  major reason is when there is a disturbance in the path of light in the eye also known as reflective errors. However there were remedies for these diseases also such as magnifying glasses , telescopes etc.

A rigid body is usually defined as a hard solid object with a definite shape and size. However, in reality, bodies can be compressed, stretched, and bent. Also, the appreciably rigid steel bar can be deformed with the application of a sufficiently large external force on it. It implies that solid bodies are not perfectly rigid. A solid body has a definite shape and size. For changing or deforming the shape or size of a body, an external force is needed. By stretching a helical spring or gently pulling its ends, the length increases slightly. Furthermore, when you leave the ends of the spring, it comes back to its original shape and size. The property of a body by which it tends to regain its original size and shape when the applied force is removed is what we refer to as elasticity, and the deformation caused is called elastic deformation. However, if we apply an external force to a lump of putty or mud, they won’t regain their previous shape as they do not tend to do so, and get permanently deformed. Such kinds of substances are called plastic, and the property is known as plasticity.

The elastic behaviour of materials or the property of elasticity plays a significant role in engineering design. For instance, while designing a building, having some knowledge of the elastic properties of materials like concrete, steel, etc is essential. The same holds for the design of bridges, automobiles, rope ways, etc.

Stress-strain Curve

The relationship between stress and strain for a given material under tensile stress can be proved with the help of an experiment. In a standard test of tensile properties, a test cylinder or wire is stretched by an external force. The fractional change in length or strain and the applied external force needed to cause the strain are recorded. The applied external force is gradually increased in steps, and the change in length is also recorded. A graph is plotted between the stress (which is equal in magnitude to the applied external force per unit surface area) and the strain produced. A typical graph for metal is shown below.

The stress-strain curves vary from one material to the other. The stress-strain curves help us in understanding how a given material deforms with an increase in the load. From the graph, we can see and find that in the region between points O and A, the curve is linear. In this region, Hooke’s law is followed and obeyed. The body regains its original dimensions when the applied external force is removed. In this region, the solid body behaves as an elastic body. Moving ahead, in the region between points A and B, stress and strain are not directly proportional. Nevertheless, the body still tends to return to its original dimension when the load is removed. The point B in the curve is called yield point (also referred to as the elastic limit), and the corresponding stress is called yield strength (σy) of the material. If the load increases further, the stress shall also exceed the yield strength, and the strain increases rapidly, even for very little change in the stress. The portion of the curve between points B and D shows the same.

When the load is removed, say at some point C, between B and D, the body does not regain its original shape and size. In such a case, even when the stress is 0, the strain is not 0. The material is said to then have a permanent set. The deformation is known as plastic deformation. The point D on the graph refers to the ultimate tensile strength of the material. Beyond point D, additional strain is produced even by a reduced applied external force, and fracture occurs at point E. If the ultimate strength and fracture between points D and E are close, the material is referred to as brittle. If they are quite far apart, the material is referred to as ductile. The stress-strain behaviour varies from one material to another. For instance, rubber can be pulled several times, and it shall still return to its original shape. Although the elastic region is large enough, the material does not follow Hooke’s law in most of the regions. Secondly, there is no well-defined plastic region. The substances like rubber, which can be stretched to cause large strains, are known as elastomers.

Elastic Moduli 

The proportional region, within the elastic limit of the stress-strain curve (region OA in the above figure), is of utmost importance for both structural and manufacturing engineering designs. The ratio of stress and strain, known as modulus of elasticity, is found to be a significant characteristic or property of the material.

Bulk Modulus 

We already know and have seen as well that when a body is submerged in a fluid, it undergoes or experiences hydraulic stress, which is equal in magnitude to the hydraulic pressure. The same leads to a decrease in the volume of the body and produces a strain known as volume strain.

Bulk Modulus is defined as the ratio of hydraulic stress to the corresponding hydraulic strain. It is denoted by symbol B, and can be expressed as: 

B = [frac{-p}{(frac{∆V}{V})}]

The negative sign in the formula indicates that as the pressure increases, the volume decreases. To be specific, if p or pressure is positive, then ∆V or the change in volume is negative. Hence, for a system in equilibrium, the value of bulk modulus or B is always positive. The SI unit of the bulk modulus is the same as that of pressure that is N m2 or Pa. The bulk moduli of a few common materials are specified in the table below:

The reciprocal of the bulk modulus or ‘B’ is known as compressibility and is denoted by the symbol k. It is defined or expressed as the fractional change in volume per unit increase in pressure. 

k = ([frac{1}{B}]) = – ([frac{1}{∆p}]) × ([frac{∆V}{V}])

It can be seen from the data given in the table that the bulk moduli for solid bodies are much larger than it is for liquids, which are again much larger than the bulk modulus for gases like air.

Therefore, the solid bodies are the least compressible, whereas gases are the most compressible. Also, gases are somewhere around a million times more compressible than solids. 

Gases have large compressibility, which vary with both pressure and temperature. The incompressibility of the solids is primarily due to the tight coupling between the ne
ighbouring atoms. The molecules in liquids are also bound with their neighbours, but not as strong as in the case of solids. Molecules in gases are very poorly coupled to their neighbouring atoms.