Category: Physics Notes PPT

How to define astronomical unit? Astronomers use astronomical units – or AU – to represent the distance of the solar system. We can say that one astronomical unit (AU) outlines the mean distance between the Earth and our Sun for general reference. An AU is nearly 93 million miles (150 million km). It’s approximately eight light minutes. The definition of AU also means distances in astronomical units to pre-eminent solar system objects. The astronomical unit is applied primarily for measuring distances around other stars or within the Solar System. 

It is also an essential element in the definition of another unit of astronomical length, the parsec. The astronomical unit is quite instrumental in formulating and understanding the distance between stellar objects and is crucial in the calculations and computation involving astronomical problems. One astronomical unit is equal to 92955807 miles.

Astronomical Unit Definition 

According to the prevailing astronomical convention, 1 astronomical unit is equal to 149,597,870.7 kilometres (or 92,955,807 miles). As the earth orbits the sun with a varying orbital distance, we need to consider the average distance, therefore, one astronomical unit is the average distance between the Earth and the Sun. In other words, the Earth and the Sun mid-distance varies in a single year. The varying distance between the earth and the sun is maximum at the aphelion ( 152,100,000 km or 94,500,000 miles or 1.016 AUs) and the minimum at the perihelion (147,095,000 km or 91,401,000 miles or 0,983 AUs).

1 astronomical unit value = 149597870700 metres (exactly)

  ≈ 92955807 miles

  ≈ 499.00478384 light-seconds

  ≈ 4.8481368×10⁻⁶ parsecs

  ≈ 1.5812507×10⁻⁵ light-years

The speed of light can be represented in terms of astronomical units. As we know  299792458 m/s is the speed of light which is equal to precisely 299792458 × 86400 ÷ 149597870700 or about 173.144632674240 AU/d, some 60 parts per trillion less than the 2009 estimate.

Development of Astronomical Unit

The earliest documented example of astronomers calculating the distance between the Earth and the Sun dates back to Classical Antiquity. In the 3rd century BCE, Greek mathematician Aristarchus of Samos imputed that the distance was estimated to be between 18 and 20 times the distance between the Earth and the Moon.

According to the oldest Chinese mathematical writing, Zhoubi Suanjing the 1st century BCE treatise also estimates the distance between the Earth and Sun. According to the anonymous exposition, the distance is calculated by conducting geometric measures of the length of noontime shadows formed by objects aligned at specific distances. However, the predictions were based on the belief that the Earth was flat.

By the 19th century, ascertainments of the speed of light and the constant deviation of light resulted in the first direct measurement of the Earth-Sun distance in kilometres. By 1903, for the first time, the term “astronomical unit” emerged. Developments in precision have always been a key to developing astronomical understanding. Throughout the twentieth century, measurements became more precise and ever more reliant on accurate observation of the effects described by Einstein’s theory of relativity and upon the analytical tools it used. 

Astronomical Unit Modern Usage

The astronomical unit finds great applicability in the measurement of the stellar distance of extraterrestrial objects. It can be used to calculate the heliocentric distance of an asteroid or measure the distance of a planet’s orbiting moon. In the solar system, it finds usage in the development of mathematical and numerical methods for computational purposes. Also, it can be used in general to measure the distance between planetary systems and understand the extent of gaseous clouds around planets. However, an astronomical unit is an inept way of measuring distance when it comes to interstellar objects. For interstellar purposes, it is best to use measures such as light-years and parsec. While fabricating a numerical model of the Solar System, the astronomical unit proffers a relevant scale that minimizes floating-point calculations errors.

The number of component particles, usually molecules, atoms or ions that are present in the amount of material given by one mole is called as the Avogadro’s number. It is the proportionality aspect that relates the molar mass of a material to the mass of a sample. It is represented by the symbol N_A or L, and has the value is 6.022140857×1023 mol⁻¹in the International System of Units (SI).

This number is also called as Loschmidt constant in German works. The Loschmidt constant was later redefined as the number of molecules in 12 grams of the isotope carbon-12 (¹²C), and still later comprehensive to relate amounts of material to their molecular weight. The Avogadro number is a dimensionless number and has the same arithmetical value of the Avogadro constant when given in basic units. Indifference to Avogadro constant has the measurement of the reciprocal amount of material. The Avogadro constant can also be written or said as 0.6023… mL⋅mol−1⋅Å−3, which can be used to change from volume per atom in cubic angstroms to molar volume in milliliters per mole. Incomplete revisions in the base set of SI units required redefinitions of the ideas of chemical quantity. 

Originated on the calculation made through the middle of 2018 which measured the value for the Avogadro constant of N_A = 6.022140758(62) ×1023 mol−1, the redefinition of SI components is planned to take effect on 20 May 2019. The value of the constant will be fixed to precisely 6.02214076×1023 mol.

History

The Scientist Amedeo Avogadro was the one, in 1811, first projected that the volume of a gas (at a specified pressure and temperature) is proportional to the number of molecules irrespective of the nature of the gas. The French physicist Jean Perrin in 1909 suggested naming the constant in memory of Avogadro. Perrin won Nobel Prize in 1926 in Physics, mainly for his work in shaping the Avogadro constant by some different approaches.

The value of the Avogadro constant was first designated by Johann Josef Loschmidt, who estimated that the average diameter of the atom in the air by a technique that is equal to calculating the number of particles in a given volume of gas during 1865. This latter value, the number density n0 of particles in an ideal gas, is now known as the Loschmidt constant and is connected to the Avogadro constant, N_A. 

[{displaystyle n_{0}={frac {p_{0}N_{rm {A}}}{RT_{0}}},}]Where R is the gas constant, p0 is the pressure, and T0 is the absolute temperature. The connection with Loschmidt is the source of the symbol L which is sometimes used for the Avogadro constant, and German-language literature can refer to both constants by the similar name, the only difference is the units of measurement.

Precise determinations of the Avogadro constant need the calculation of a single quantity on both the molecular and macroscopic scales using the similar unit of measurement. This was made possible for the first time when American physicist Robert Millikan calculated the charge on an electron in 1910. The electric charge/mole of electrons is a constant known as the Faraday constant and had been known since 1834 when Michael Faraday circulated his works on electrolysis. By splitting the charge on a mole of electrons by the charge on a solo electron, the value of the Avogadro number is obtained. Since 1910, new-fangled calculations have more precisely determined the values for the Faraday constant and the basic charge. 

While it is unusual to use units of amount of material other than the mole, the Avogadro constant can also be conveyed by pound-mole and ounce-mole.[{displaystyle F=N_{text{A}}e=96,485.33289(59) {{text{C}}{cdot }{text{mol}}^{-1}}.,}]

The Avogadro constant also arrives into the definition of the unified atomic mass unit, u,

1u = [frac{M_{u}}{N_{A}}] 1.660539(20) x 10-27 Kg 

Given Mu is the molar mass constant.

Measurement

Coulometry

The initial accurate method to calculate the value of the Avogadro constant was founded on coulometry. The standard is to calculate the Faraday constant, F, which is the electric charge followed by one mole of electrons, and split by the elementary charge, e, to get the Avogadro constant.

[{displaystyle N_{text{A}}={frac {F}{e}}}]NA= F/e

The typical experiment of Bower and Davis at NIST depends on dissolving silver metal far from the anode of an electrolysis cell while going through a constant electric current, I for an identified time t. If m is the mass of silver lost from the anode and Ar the atomic weight of silver, then the Faraday constant is shown by:

[{displaystyle F={frac {A_{rm {r}}M_{rm {u}}It}{m}}.}]F = A_rM_u It / m

The NIST scientists formulated a method in order to compensate for silver lost by mechanical causes from the anode and shown an isotope analysis of the silver used to regulate its atomic weight.  F90 = 96485.39(13) C/mol is the conventional Faraday constant, which resembles a value for the Avogadro constant of 6.0221449(78) × 1023 mol−1: both the values have a relative regular uncertainty of 1.3 × 10−6.

Electron Mass Measurement

Data for Science and Technology (CODATA) Committee publishes values for physical constants for global use. It regulates the Avogadro constant from the proportion of the molar mass of the electron A_r(e)M_u to the rest mass of the electron me:

[{displaystyle N_{rm {A}}={frac {A_{rm {r}}({rm {e}})M_{rm {u}}}{m_{rm {e}}}}.}]N_A = A_r (e) M_u / me

The relative atomic mass of the electron, Ar(e), is a directly calculated quantity, and the molar mass constant, Mu, is a known constant in the SI. The electron rest mass, however, is measured from other measured constants:

[{displaystyle m_{rm {e}}={frac {2R_{infty }h}{calpha ^{2}}}.}]m_c = 2R_∞ h / Cά²

International Avogadro Coordination

The assignment of Avogadro project is part of the efforts to redefine the kilogram in expressions of a universal physical constant, fairly than the International Prototype Kilogram, and balances the measurements of the Planck constant using Kibble balances. Current definitions of the International System of Units (SI) state that a calculation of the Avogadro constant is a secondary measurement of the Planck constant:

[{displaystyle h={frac {calpha ^{2}A_{rm {r}}({rm {e}})M_{rm {u}}}{2R_{infty }N_{rm {A}}}}.}]

The calculation uses highly polished balls of silicon with a weight of one kilogram. Balls are used to make simpler the measurement of the size (and hence the
density) and to reduce the effect of the oxide coating that certainly forms on the surface. The first calculation used the balls of silicon with natural isotopic composition and had a relative uncertainty of 3.1×10−7. These first outcomes were also inconsistent with values of the Planck constant resulting from Kibble balance calculation, although the source of the inconsistency is now believed to be known.

The diameter measurements on the balls are repeatable to within 0.3 nm, and the uncertainty in the quantity is 3 µg. Full outcomes from these determinations were predictable in late 2010. Their research paper, circulated in January 2011, potted the result of the IAC and presented a calculation of the Avogadro constant to be 6.02214078(18) ×1023 mol−1.

It is to be noted that the bodies which are charged bodies in a system of charges that are very small as compared to the distance which is between them are treated as point charges. Very often we deal with systems where the influence of many systems is taken into consideration. To calculate the final effect in such cases that we need to subtract and add these charges from one another. 

To simplify the operations which are involved, it is very necessary that we study the properties of charges which are point. In this topic and section we will learn about three such point properties of charges, the electric charge additivity of the charge, the electric charge conservation and at the quantization of charge which is electric charge.

Conservation of Electric Charge

If we look at the principle of conservation of charges we can notice that the charges are neither destroyed nor created, they are transferred from one body to the other body as well. If we take an example of two objects one has some charge and the other one has no charge which are made to come in contact with each other. 

The transfer of charge is from the object which is possessing some charge to the other object which is possessing no charge until and the charge is equally distributed over the whole system as well. 

Here if we see so we can notice that no charge is lost or created and is only transferred from the one which is possessing an excess of charge to the other possessing.

Electric Charge

An Electric charge can be defined as it is the physical property of matter that can experience a force when it is placed in an electromagnetic field. There are basically two types of electric charge that are negative and  positive that are commonly carried by electrons and protons respectively. 

The like charges are the charges which repel each other and unlike charges are the charges which attract each other. An object that is having an absence of charges which are net is referred to as neutral charges. The very early knowledge of how the substances which are charged interact is now called classical electrodynamics and still accurate for problems which really do not require consideration of effects of quantum.

An Electric charge is said to be a conserved property, the net charge which is of an isolated system, the amount of charge which is positive charge minus the amount of charge which is negative charge cannot change. Electric charge can be  carried out by particles which are subatomic. 

If there are electrons which are more than protons in a piece of matter, then it will have a negative charge for sure and  if there are fewer it will have a positive charge. And if there are an equal number of the charges then it will be neutral. Then it is said that the Charge is quantized. 

It comes in multiple which are  integer of individual that have small units which are called the elementary charge that is e and about 1.602×10−19 coulombs is its value that is considered as the smallest charge which freely exist that is the particles called quarks have smaller charges that are multiples of ⅓  e. 

But they are only found in combination and one more point here is that they are always combined to form particles with integer charge. The proton has a charge of positive that is +e and the electron has a charge of negative which is  −e.

Overview of the Topic

The fundamental property Charge of forms or of matter that exhibit replushion or electrostatic attraction in the presence of other matter. The electric charges which are is a characteristic property of many subatomic particles. The free standing charges of particles are integer multiples of the elementary charge that is e, we can say that electric charge value is quantized.

Scientist Michael Faraday in his electrolysis experiments was the first man to specifically note the nature of the discrete electric charge. Physicist Robert Millikan’s who did the oil drop experiment demonstrated this fact directly and along with that he measured the elementary charge. 

It has been discovered that one type of particles that are quicks and that have fractional charges of either −1/3 or +2/3 

but. it is duly believed that they always occur in multiples of integral charge which can also be said as free-standing quarks that have never been observed.

By the process of convection we can notice that the charge of an electron is negative, that is denoted by −e, while that of a proton is positive that is denoted by +e. The particles which are Charged particles whose charges have the same sign repel one another. 

And particles whose charges have always been different signs are the ones which attract. The law of Coulomb’s quantifies the force of electrostatic which is between two particles by asserting that the force is directly proportional to the product of their charges, and that is inversely proportional to the square of the distance which is between them. The antiparticle charge is equal to that of the corresponding particle but along with opposite signs.

Units 

The SI or we can also call it as the derived unit of quantity of electric charge is the coulomb that is denoted by the symbol: C. In the particle which is of modern practice, we can observe that the phrase “amount of charge” is used instead of “quantity of charge”. The symbols which are lowercase symbols that are q are often used to denote a quantity of electricity or charge. The charge of amount 1 electron  is an elementary charge which  is defined as a fundamental constant in the SI units system.

The gas or energy obtained as a result of the breakdown of organic matter is called biogas. As the name implies, bio is related to living beings and gas is the state of matter which is emitted on decomposition.

So, when you look for biogas meaning, note that you are aware that this is a form of energy that can be obtained naturally. Similar to other resources such as air, water, etc., biogas is also a significant source of energy.

All you have to do is trap this energy for utilisation in the desired areas. Therefore, students while studying this chapter need to be cautious about multiple aspects of biogas. Starting from how it is obtained to its advantages and disadvantages, along with its application in real life – everything is explained in detail below.

Biomass and Bioenergy

Biogas or bioenergy is obtained from biomass which consists of decaying animal waste, crop residues, household solid waste, food waste, agricultural waste, and other similar by-products. The gas emitted on the decomposition of such matter is what is meant by biogas. 

Look at the diagram below for your reference.

The image above shows the complete step by step process of the formation of biogas.

This obtained biogas contain gases like methane, carbon dioxide, small amounts of hydrogen, oxygen, nitrogen, etc. Besides, it also contains tiny portions of heavy metals, alkaline earth metals, and even alkali metals.  

What are the Advantages of Biogas?

Although biogas seems to be useful in all dimensions, it might be hard to believe there are both advantages and disadvantages of biogas. Here is a list of both the features for your understanding.

Advantages offered by Biogas are as Follows –

• It is environmentally friendly and does not contribute to pollution.

• A renewable source of energy since waste production is constant.

• Reduces land fillings significantly by decomposing them.

• A cost-effective option of getting access to a significant amount of energy.

• Establishment of a biogas plant leads to employment of innumerable people.

The Disadvantages of Biogas are Listed as Follows –

• Traces of impurities remain even after multiple layers of purification.

• Cannot be utilised or tapped for large scale production.

• Presence of methane and oxygen make it hazardous and prone to explosion and inflammation.

Therefore, the above list of advantages and disadvantages of biogas plants or biogas as a source of energy provides a detailed explanation why this is an important topic. While students must know about both the advantages and disadvantages of biogas plants, they should also have a clear idea of its origin. 

Biogas and Biogas Plant

The biogas plants are more like a miniature version of massive power generating plants that we generally see. There is a round-shaped dome-like structure which has an inlet to let in the organic wastes. These wastes are the primary sources of energy for a biogas plant, as already mentioned in biogas meaning. 

Refer to the picture below, which shows a real-life biogas plant.

The plant shown in this above picture is a comparatively smaller unit than conventional power plants. This is one of the major limitations of biogas plants which has restricted its universal use as a major contributor to energy creation. 

For more information on biogas meaning, you can refer to our online study programs. There you can access top-notch learning materials for a clear understanding. Additionally, you may also download our app for an enriched learning experience and easy access to short notes on biogas and other related topics.

Physics, Bragg’s law or we can say the Wulff–Bragg’s condition, it’s a special case of diffraction of Laue, this whole thing gives the angles for coherent and incoherent scattering from a lattice crystal. When the X-rays are incident on an atom and they make the cloud of electronic movement. As any electromagnetic wave does. 

These movement charges which reradiate waves with the frequency which is same and even slightly due to an effect of variety. This whole phenomenon is known as Rayleigh scattering or even we can see elastic scattering. The scattered waves can be scattered but this scattering which is secondary is assumed to be negligible.

A process which is similar occurs upon scattering neutron waves which are from the nuclei or we can say by a coherent spin interaction with an electron which are unpaired. The wave which is the resulting interference pattern is the basis of diffraction analysis. This analysis is also known as Bragg diffraction.

History 

In 1913 Bragg diffraction which is also called as the Bragg formulation of X-ray diffraction was first proposed by Lawrence Bragg and his father William Henry Bragg in response to discovery of crystalline solids. Finally, they found that these crystals which are present at wavelengths of certain specific and incident angles that produce a reflected effect type of  radiation which is intense.

Sir Lawrence Bragg explained in his thesis this result by modeling the crystal as a set of parallel discrete planes which are separated by a constant parameter which is denoted as d. It was proposed that the ray of incident that is X-ray radiation would be producing a Bragg peak if their reflections of planes interfere every time. Interference is constructive in nature when there is a shifting phase which is a multiple of 2π that is this condition which can be expressed by law of Bragg’s. This confirmed the existence of particles which are real although it is very simple at the atomic scale, as well as it provides a powerful tool for study of crystals in the form of X-ray and diffraction of neutrons.

Sir Lawrence Bragg along with his father who was named William Henry Bragg in 1915 were awarded with the Nobel Prize in physics for their work in determining crystal structures which are beginning with  ZnS, NaCl.

Conditions 

The conditions for Bragg diffraction occur when radiation along with a wavelength is comparable to atomic spacings, that is scattered in a fashion which is specular by the atoms of a crystalline system. And at times it also undergoes constructive interference. For a solid which is crystalline the waves are scattered from lattice planes which are later separated by the interplanar distance which is denoted as d. Wave gets scattered at that time the interference constructively remains in phase since the difference between the path and length which are of the two waves is equal to an integer multiple of the wavelength. And we should also note that this differs from the convention in Snell’s law where θ is measured from the normal of the surface. The constructive effect of destructive interference is because of the effect of reflection in successive crystallographic planes that is h, k, l of the crystalline lattice as described by sir Miller notation earlier.

Applications 

In X-ray diffraction which is also called as the XRD is the interplanar which is spacing d-spacing of a crystal is used for characterization and  identification purposes. Incident ray wavelength that is the X-ray is known and measurement is made of the incident angle denoted as: Θ at which constructive interference occurs at a point. An unknown given crystal is expected to have many plates which are rational of atoms in its structure and therefore, the collection of the “reflections” of all the planes can be used uniquely to identify an crystal which is unknown. Crystals in general with high symmetry that is isometric systems which tend to have relatively few atomic planes, on the other hand crystals with low symmetry that is in the monoclinic system and triclinic systems tend to have a very large number of possible atomic planes in their structures.

In wavelength case the dispersive spectrometry that is WDS or X-ray fluorescence spectroscopy denoted by XRF, crystals of known d-spaces are used for analyzing crystals in the spectrometer. The position of the sample which is mentioned and the detector which is fixed in these applications has the position of angle which is of the reflecting crystal is with Bragg’s law so that a particular wavelength of interest can be directed as a detector for quantitative analysis. Every element which is present in the Periodic Table has an energy which is a discrete difference which is between the orbital “shells” that is . K, L, M, in such a manner that every element will produce X-rays of a fixed wavelength.

The capacitor is an electric component that has the ability to store energy in the form of electrical charges that creates a potential difference, which is a static voltage, much like a small rechargeable battery. 

The most basic design of a capacitor consists of two parallel conductors (Metallic plate), separated with a dielectric material.  When a voltage source is attached across the capacitor, the capacitor plate gets charged up. The metallic plate attached to the positive terminal will be positively charged, and the plate attached to the negative terminal will be negatively charged. 

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Capacitor Symbols

Types of Capacitors

1. Film Capacitors: Film capacitors are the ones that use plastic film as the dielectric medium. They are available in nearly any value and voltages up to 1500 volts. They range from 10% to 0.01% in any tolerance. Additionally, film condensers arrive in a combination of shapes and case styles. There are two types of film condensers, radial type lead, and axial type lead.

2. Ceramic Capacitors: Ceramic capacitors are the ones that use ceramic as the dielectric material. It is used in high-frequency circuits such as audio to RF. In ceramic capacitors, one can develop both high capacitance and low capacitance by altering the thickness of the ceramic disc.

3. Electrolytic Capacitors: Electrolytic capacitors are the ones that use the oxide layer as the dielectric material. It has a wide tolerance capacity. There are mainly two types of electrolytic capacitors, tantalum, and aluminum. They are available with working voltages of up to approximately 500V, but the maximum capacitance values are not available at high voltage, and higher temperature units are available but are rare.

4. Variable Capacitor: Variable capacitors mostly use air as the dielectric medium. A Variable Capacitor is one whose capacitance can be mechanically adjusted several times. For example, this form of the capacitor is used to set the resonance frequency in LC circuits to change the radio to match impedance in antenna tuner devices.

Define the Capacitance of a Capacitor

The accumulation of charges in the conductors causes a potential difference across the capacitor. The amount of charge accumulated is called the charge holding capacity of the capacitor. This charge holding capacity is what is known as capacitance. The accumulated charge in the capacitor is directly proportional to the voltage developed across the capacitor:

Q ∝V 

Q = C/V

C = Q/V 

C is the constant of proportionality, also called the capacitance of a capacitor. The unit of capacitance is Farad(F) – 1 coulomb per volt. 

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The value of capacitance depends upon the physical features, area of the capacitor plates ‘A’, distance between the plates ‘d’, and the permittivity of the dielectric medium ‘ε’.

[C = varepsilon times frac{A}{d}]

Energy of Capacitor

The energy is stored in joules and is equal to half of the capacitance times the square of the capacitor’s voltage. 

[E = C times frac{V^2}{2}]

Capacitor in Series

The total capacitance of the capacitors connected in series C1, C2, C3,.. :

[frac{1}{C_{Total}}] = [frac{1}{C_{1}}] + [frac{1}{C_{2}}] + [frac{1}{C_{3}}] + …

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Capacitor in Parallel

The total capacitance of the capacitors connected in parallel  C1, C2, C3,.. :

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CTotal = C1+C2+C3+…

Factors affecting Capacitance

• Surface Area: The surface area of the two plates affects the capacitance value. Higher the value of the surface area, the higher the capacitance. 

• Distance: The distance between the plates affects the value of the capacitance. Lower the value of distance, the higher the capacitance. 

• Dielectric Medium: The type of material separating the two plates called “the dielectric.” The higher the dielectric’s permittivity, the higher the capacitance value.

Uses of a Capacitor

The capacitors have both electrical and electronic applications. They are used for several things such as filters, energy storage systems, engine starters, signal processing devices, etc. 

• Capacitors are used for storing energy, which can be used by the device for temporary power outages whenever they need additional power. 

• Capacitors are used for blocking DC current after getting fully charged and yet allow the AC current to pass through the circuit of a circuit. 

• Capacitors are used as sensor for several things like measuring humidity, fuel levels, mechanical strain, etc. 

• Capacitors can be used in a time-dependent circuit. This could be connected to any LED or loudspeaker system, and it’s likely that any flashing light/regular beeping uses a timing capacitor.

Fun Facts

• Capacitors with high capacitance are made up of material with high dielectric constant. 

• A Capacitor can take up and temporarily store energy from a circuit. Then, the capacitor will return the energy to the circuit later.

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