writing chemical formulas

    We have to find the equation of the line using the following formula`(y-y1)/(y2-y1)`=`(x-x1)/(x2-x1)`    Here (x1,y1) and (x2,y2) are the given two points.  Substitute the given points in the above formula we have to get the equation of the line.Example:(1, 3) and (4, 8) write the equation of the line that passing through the given two points by Method - 1Solution:Here x1 = 1 and y1=3 and x2=4 and y2=8The formula for equation of the line is `(y-y1)/(y2-y1)`=`(x-x1)/(x2-x1)`Substitute the x1, y1, x2 and y2 values in the above equation we have to get, `(y-3)/(8-3)`=`(x-1)/(4-1)`Simplifying this we can get, 3y=5x+4This is the equation of the line that passes through the given two points.

binomial formula

Q. 6. Explain Stefan's law of thermal radiation. (1996,2000,01,04)Ans. Stefan's Law : This law states that the radiant energy '£' emitted from the unit area of surface of a perfect black-body in unit time is proportional to the 4th powerof the absolute temperature of the body. -i.e. Â£ oc T4 or £ = oT4 _Where c is a constant which is called Stefan's constant and its value is 5 • 67 x 10~8 j/m2-s-K4.Suppose that a black-body having absolute temperature T\ is surrounded by a black enclosure at absolute temperature Tz- The body will emit a7|4 joule energy per second per unit area of its surface. At the same time it will absorb <rlf joule energy per second per unit area from the surrounding atmosphere. Thus net energy emitted by unit area of the body in unit time will be£1-£2=o(rl4-T24)The rate of emission of radiant energy from the area A of a body with emissive power e, at the absolute temperature T is given byE = oT4eAQ. 7. Establish Newton's law of cooling from Stefan's law. (1996,2000,01,04)Ans. Newton's Law of Cooling : This law states that if the temperature difference between a body and its surrounding is small then rate of cooling of the body (or rate of loss of heat by the body) is proportional to the temperature difference between the body and surroundings.i.e. rate of loss of heat « temperature differenceDerivation of Newton's Law From Stefan's Law: Suppose that a body is placed in air for cooling. Let the absolute temperature of the body and that of surroundings be Ti and T. Let e be the emissive power of the body. Then according to Stefan's law the net rate of loss of heat by the body is given by.A£ = ae(Ti4-T4)Let Ti-T + t wheret = 7} -T > 0is smallthen AE = ce[(T + t)i-T4]= aeT4 jl + 4—.......j -1 (Using Binomial Expansion)t < T, hence ^ is very small, hence higher degrees of ^ are neglected.= 4oeT3fv Atmosphere is very big as compared to the body, hence its temperature remains almost constant.Hence, rate of heat loss oc t (temperature difference)Q. 8. Draw spectral distribution curves of black-body radiation and write the effect of rise in temperature on it. (1996,2001)Or Draw the curves between energy and wavelength at different temperatures of a black-body radiations and write the conclusions drawn from these curves. (2003)Ans. Spectral Distribution of Black-Body Radiation : A perfect black-body, when heated upto high temperature, emits radiation of all possible wavelengths, that is why it is called full radiator. In 1899, two scientists Lummer and Pringsheim studied the spectral energy distribution in black-body radiation at differenl temperatures. They heated the black-body at differenl temperatures and at each temperature they plotted the radiant energy, emitted at different wavelengths againsl wavelength. The general shape of these curves are shown in the fig. 13 -2.Following conclusions were drawn from these graphs:(i) At a given temperature, the radiant energy 'E\ emitted by the black-body at wavelength 'A.' first increases with the wavelength and attains a maxima at a certain wavelength and then goes on decreasing.(ii) At a given temperature, maximum energy is emitted at a certain wavelength which is denoted by Xm.(iii) As the temperature is increased, the energy 'Ex emitted at wavelength X is also increased for each wavelength.(iv) The product of absolute temperature T of black-body and wavelength X,„ at which maximum energy is emitted, is a constant.i.e. XmT = b (constant)This law is called Wein's displacement law and the constant 'b' is called Wein's constant.From this law we can observe that, at low temperatures the maximum energy is emitted at larger wavelengths, but as the temperature is increased more energy is emitted in shorter wavelengths and maximum energy peak is shifted towards shorter wavelengths (see graphs).(iv) The area under these curves increases with increasing temperature directly as the 4th power of the absolute temperature of the body. That means the total radiant energy (measured by the area under the curve) emitted by the body is directly proportional to 4th power of the absolute temperature.i.e. ExT4Thus Stefan's law is also verified by these curves.Q. 9. Explain Planck's hypothesis of radiation. Discuss its importance in modern physics. (1997,98,99)Or State Planck's hypothesis. (2004)Ans. Planck's Hypothesis: According to this hypothesis, emission or absorption of radiant energy is not continuous process but is takes place in the form of small packets of energy. Each such packet is called a photon or quanta. The energy associated with a photon of radiation having frequency v is hv. Here 'h' is a constant called Planck's constant. Thus we can conclude that energies emitted by a body can be hv, 2hv,3hv....(integer multiple of hv) but not in between.Classical mechanics and thermo-dynamics could not explain the spectral energy distribution in black-body radiation. Planck, used his hypothesis and derive a formula to explain the spectral energy distribution in black-body radiation and found it in close agreement with the results of Lummer and Pringsheim experiments. Further Einstein successfully explained photo-electric effect on the basis of Planck's hypothesis. In this way Planck's hypothesis gained recogni tion.Q. 10. Find the expression for kinetic mass and momentum of photon using Planck's hypothesis. (1999,2004)Ans. Momentum of Photon: According to Planck's hypothesis, the rest mass mo of photon is zero and each photon travels with the speed of light c.If v is the frequency of photon, then its energy will be E = hv. Further if m is the kinetic mass of photon then by mass energy relation, we haveE = mc2.2 ' hv h f v 1)E = hv = mc => m = = — '•' ~ = -c2 cX V c X):. Kinetic mass of photon m = ~= —v c2cXIf p is the linear momentum of photon, thenp = kinetic mass x velocityor p=mc or p = (v velocity = c)h hvor p = — = —c/v c (â– -• X = c/v)Momentum p = — = —y X c

in situ conservation

In situ conservation is the most appropriate method to maintain species of wild animals and plants in their natural habiats. This approach in-cludes protection of total ecosystems through a network of protected areasThe common natural habitats (protectedareas) that have been set for in situ conservation ofwild animals and plants include —1. National parks2. Wildlife sanctuaries3. Biosphere reserves4. Several wetlands, tnangrooves and coralreefs.5. Sacred grooves and Lakes.In situ conservation ilso includes the intro-duction of plants and ani mal species back intoagricultural, horticultural and animal husbandrypractices so that they are cultivated/reproduced fortheir reuse by the farmers/animal husbandrypeople. Farmers and horticulturists have beentraditionally maintaining large genetic diversity ofcrop plants/flowers by savir g seeds for next plant-ing season by a wide variety of indegenously developed practices. For example, tubers,rhizomes, bulbs and seeds of large variety of plant species ai e stored by the far ners/horticulturists fortheir cultivation in the next sieason. Similarly, native species of cattle, which are better adapted to dis-eases, drought and other adverse conditions, arebeing maintained by animal husbandry people.

heat of neutralization

The heat of neutralization of all strong acids and bases are the same in dilute solution. It can be explained easily on the basis of this theory. According to this theory, the strong acids and bases are completely ionised in solution. They combine to form a highly ionised salt and feebly ionised water and since in all cases water is formed, the heat produced should be same. Heat of neutralization is, in fact, the heat of formation of water from H+ and OH" ions, which is always the same irrespective of the nature of acids and bases.H+ + CI" + Na+ + OH" Na+ + CF + H20 + 13-7k calsor H+ + OH"—»H20 + 13-7 k cals

matrix division

A AEROBIC RESPIRATION oxidation of food in the presence of oxygen ANAEROBIC RESPIRATION oxidation of food in the absence of oxygep ANTIBIOTIC medicine that kills disease-causing bacteria ANUS opening at one end of the digestive tract through which undigested food leaves the body ATP (adenosine triphosphate) small molecule in a cell which can store, transfer or release energy AUTOTROPHS organisms that make their own food AXON long fibre thai extends from the cell body of a neuronB  BALL AN D SOCKET JOINT joint in which end of one bone is rounded, which fits into the hollow part of the other bone BERI BERI condition caused due to deficiency of vitamin B BOWMAN'S CAPSULE cup-shaped structure at one end of a nephron BRONCHUS {plural bronchi) thin pipe that branches off from the trachea to enter a lung C CAMBIUM lateral meristematic tissue that produces new xylem and phloem cells in a stem CARNIVORES animals that eat other animalsCELL BODY central part of a neuron CELL WALL structure in plant cell Outside the cell membrane CENTRIOLE organelle in animal cells which helps in cell division CHLOROPLASTplastid containing chlorophyll CHROMOPLAST plastid containing coloured pigments CHROMOSOME small, thread-like structure in the nucleus of a cell CISTERNAE flattened sac-like vesicles of endoplasmic reticulum and golgi bodiesCONNECTIVE TISSUE tissue that joins and supports different body parts CRISTAE folds of the inner membrane of mitochondrion CUTANEOUS RESPIRATION exchange of gases through the skin of animals CYTOPLASM jelly-like'substance that fills most of the cell D  DENDRITE short branched extension of a neuronDERMIS inner thick layer of the skin DIGESTION process of converting complex food into a simple, absorbable form E ENDOPLASMIC RETICULUM network of membranes in the cytoplasm EPIDERMIS outer layer of the skin EPITHELIAL TISSUE layer of cells that covers the external surface of the body and also forms the lining of the internal organs EXTEN50R muscle that contracts to straighten a part of the body F FLEXOR muscle that contracts and causes a part of the body to bend towards the bodyGGEOTROPiSM movement of plant parts in response to force of gravity GLAND organ that produces secretions GLIDING JOINT joint that allows sliding movement between two bonesH HAEMOGLOBIN red oxygen-carrying pigment in RBCs HERBIVORES animals that feed or plantsIHETEROTROPHS organisms that obtain food directly or indirectly from plantsINTERNAL RESPIRATION using oxygen to break down food and release energy in the bodyJJOINT place where two or more bones meet together in the skeletonkKIDNEY organ that filters wastes from the bloodL LACUNA tiny fluid-filled spaces in cartilagenous connective tissue LIGAMENT strong band of connective tissue that hold two or more bones at jointsLIVER organ that produces bile which helps in digestion LOCOMOTION movement of the entire body of the animal from one place to another LYMPH colourless fluid connective tissue; it surrounds cells of the bodyM MATRIX ground substance of connective tissue in which cells are presentMERISTEMATIC TISSUE plant tissue made up of cells that divide continuously MICROORGANISMS living organisms that can be seen only through a microscope MITOCHONDRION {plural mitochondria} rod-like organelle which helps get energy from food MUSCULAR SYSTEM system consisting of the muscles in the body MUSCULAR TISSUE animal tissue that forms the muscles in the body NNASTIC MOVEMENTS non-directional plant movements that occur in response to environmental stimuli NERVE bundle of nerve cells that carry messages throughout the body NEURON specialized cell that makes up the brain, spinal cord and nerves O OESOPHAGUS tube that leads from the mouth to stomach ORGAN part of an organism made up of one or more .types of tissues, which performs a specific function ORGAN SYSTEM group of organs that work togetherORGANELLE small structure found in the cytoplasm of a cellP PALISADE TISSUE parenchyma tissue in leaves containing chloroplastsPARENCHYMA plant tissue composed of simple cells with thin wailsPERMANENT TISSUE plant tissue made up of ceils that cannot dividePLASMA liquid part of blood in which the blood cells floatPROTOZOA group consisting of only single-celled animalsRRED BLOOD CELL cell that transports oxygenRESPIRATION process of taking in oxygen and using it,to release energy from foodRESPONSE reaction of an organism to a stimulus S SCAVENGERS animals that consume dead animals and dispose them SCLERENCHYMA hard and strong supporting tissue made up of dead and thick-walled cells SIEVE CELL elongated cell of phloem having minute pores SPECIES a group of living organisms which can breed among themselves SPIRILLA spiral-shaped bacteriaTTENDON connective tissue that joins skeletal muscles to bones TISSUE cells that have similar structure and perform similar functions TRACHEA tube passing through the neck that divides into two bronchi TRACHEID tube-like dead cell in xylem TRANSPIRATION loss of water from leaves through the stomataV VACUOLE sac-like organelle which stores food, water or wastesVASCULAR BUNDLE xylem and phloem tissues present togetherVASCULAR TISSUE permanent tissue in plants made up of xylem and phloemVERTEBRA smalt bone of a vertebral columnVESICLE small, round membranous structure in a cellVESSEL non-living part of xylem that, has tube-like ceils joined end to endW WARM BLOODED ANIMAL animal ' that has a constant body temperatureWHITE BLOOD CELL cell in blood that, fights disease-causing microorganisms xXYLEM complex vascular tissue that transports water and mineral salts

aldol condensation

(i) With hydroxylamine : Aldehydes and ketones react with hydroxylamine to give corresponding oximes containing (> C = N - OH) group. The reaction is carried in the presence of a base like NaOH.(a) Acetaldehyde with hydroxylamine gives acetaldoxime. h hI ________ICH3 - C = Jo + _H2]nOH ) CH3 - cf NOH + HzO *acetaldehyde acetaldoximeCH3 CH3 ....CH3 - c =€f +~H21NOH ) CH3 - c = NOH + H20i____.Z'i ; - acetone acetoxime (ii) With hydrazine : Aldehydes and ketones react with hydrazine to give corresponding hydrazones. h h 1 r-___„ * IH3C-C = jO + H2|- N-NH2-> H3C-C =N-NH2 + H2O acetaldehyde acetaldehyde hydrazone ch3 ch3 I .1 h3c - c =jo_ + JH2_j- n - nh2—> h3c - c = n - nh2 + h2oacetone acetone hydrazone(iii) With phenylhydrazine : Aldehydes and ketones react with phenylhydrazine to give the corresponding phenylhydrazone.(a) Acetaldehyde with phenylhydrazine gives acetaldehyde phenylhydrazone.H HI Ich3 - c = jo + H2j nnhc6h5 -4 ch3 - c = nnhc6h5 + h2oacetaldehyde acetaldehyde phenylhydrazone(b) Acetone with phenylhydrazine gives acetone phenylhydrazone.CH3 CH3I ICH3- C=iO + H^N -NH-CgHs —» CH3-C = N-NH_C6H5 +H20acetone acetone phenylhydrazone(iv) Aldol condensation : Aldehydes or ketones containing active a-hydrogen atom, i.e. hydrogen on the carbon atom adjacent to carbonyl group (a-carbon atom) give P-hydroxy aldehyde, i.e. aldol or p-hydroxy ketone respectively on warming with dilute solution of sodium hydroxide (10%) or sodium carbonate. This reaction is known as aldol condensation. Formaldehyde and benzaldehyde do not give this reaction as they have no a-hydrogen atom. Aldol contains an aldehydic group (-cho) and also alcoholic group (-oh). (Aid for aldehyde group and -ol for alcohol, hence the name aid + ol = aldol.)(a) This is an addition reaction. This addition takes place in such a way that a-carbon atom of one aldehyde molecule is attached to the carbonyl carbon of the second molecule and a-hydrogen of one aldehyde is attached to carbonyl oxygen of the other to give P-hydroxy aldehvde.Aldol loses one water molecule on heating with an acid to form unsaturated aldehyde.When aldol condensation takes place between two molecules of different aldehydes, then it is known as cross aldol condensation. h h I „ Na2C03 I „ch3ch2c =o+hch2c = o-> ch3ch2-cp-ch2-c = o| solution ( |h oh hpropionaldehyde acetaldehyde propionaldol(b) Certain ketones like acetone in presence of barium hydroxide or sodium hydroxide give diacetone alcohol (p-hydroxy ketone). CH3 H O CH3 H O I I II Ba(OH)2 J J II CH3 -C + H-c«-c-CH3---^ cha-pc-aC -C-CH3Oh oh hacetone acetone diacetone alcohol(4-hydroxy, 4 -methyl, pentan-2-one)

modern periodic table

Learn table of Pythagorean related trigonometric identities:cos2θ + sin2θ = 1sin θ = ± `sqrt(1 - cos^2 theta)`cos θ = ± `sqrt(1 - sin^2 theta)`sin θ = `1/(csc theta)`cos θ = `1/(sec theta)` tan θ = `1/(cot theta)`csc   θ = `1/(sin theta)` sec   θ = `1/(cos theta)`  cot   θ = `1/(tan theta)`1 + tan2θ = sec2θ1 + cot2θ = csc2θsin θ = ± `(tan theta)/(sqrt(1 + tan^2theta))`cos θ = ± `1/(sqrt(1 + tan^2theta))`tan θ = Â± `sqrt(sec^2 theta - 1)`csc θ = ± `(sqrt(1 + tan^2theta))/(tan theta)`    sec θ = ± `(sqrt(1 + tan^2theta))`cot θ =  ± `1/(sqrt(sec^2 theta - 1))`Learn table of symmetry related trigonometric identities:sin (-θ) = - sin θ       cos (-θ) = + cos θ      tan (-θ) = - tan θ   csc (-θ) = - csc θ  sec (-θ) = + sec θ      cot (-θ) = - cot θ     sin (∏ - θ) = + sin θcos (∏ - θ) = - cos θtan (∏ - θ) = - tan θcsc (∏ - θ) = + csc θsec (∏ - θ) = - sec θcot (∏ - θ) = - cot sin (`pi/2` - θ) = + cos θcos (`pi/2` - θ) = + sin θtan (`pi/2` - θ) = + cot θcsc (`pi/2` - θ) = + sec θsec (`pi/2` - θ) = + csc θcot (`pi/2` - θ) = + tan θLearn table of shifts and periodicity related trigonometric identities:sin (θ + `pi/2` ) = + cos θ cos (θ + `pi/2` ) = - sin θ tan (θ + `pi/2` ) = - cot θ   csc (θ + `pi/2` ) = + sec θsec (θ + `pi/2` ) = - csc θ     cot (θ + `pi/2` ) = - tan θ    sin (θ + ∏) = - sin θcos (θ + ∏) = - cos θtan (θ + ∏) = + tan θcsc (θ + ∏) = - csc θsec (θ + ∏) = - sec θcot (θ + ∏) = + cot θsin (θ + 2∏) = + cos θcos (θ + 2∏) = + sin θtan (θ + 2∏) = + cot θcsc (θ + 2∏) = + sec θsec (θ + 2∏) = + csc θcot (θ + 2∏) = + tan θ