Mirror formula is the relationship between object distance (u), image distance (v) and focal length. 1/v + 1/u = 1/f In Triangle ABC and Triangle A’B’C <A = <A’ = 900 <C =<C ( vert. opp. <s] Triangle ABC ~Triangle A’B’C [AA similarity] => AB /A’B’ = AC/A’C ----(I) Similarly, In Triangle ABC and A’B’C <A = <A’ = 900 <C =<C ( vert. opp. <s] Also, in Triangle ABC ~Triangle A’B’C [AA similarity] AB /A’B’ = AC/A’C ----(1) Similarly, In DFPE ~ A’B’F EP /A’B’ = PF/A’F AB /A’B’ = PF/A’F [ AB=EP] ----(II) From(i) &(ii) AC/A’C = PF/A’F => A’C/AC = A’F/PF => (CP-A’P)/(AP- CP) = (A’P – PF)/PF Now, PF = -f ; CP = 2PF = -2f ; AP = -u ; and A’P = -v Put these value in above relation: [(-2f) –(-v)] /(-u)-(-2f) = {(-v) –(-f) }/(-f) => uv = fv +uf => 1/f = 1/u + 1/v you may also see (a) Mirror formula (b) Mirror Formula
Derivation or Proof-of- the relation between focal length and radius of curvature(X) physics [R=2f] Consider a ray of light AB, parallel to the principal axis, incident on a spherical mirror at point B. The normal to the surface at point B is CB and CP = CB = R, is the radius of curvature. The ray AB, after reflection from mirror will pass through F (concave mirror) or will appear to diverge from F (convex mirror) From the figure, According to law of reflection,< i = <r <i = <q [Since, AB IICP] => <r= <q So, In D BCF, CF = BF ----(i) If the aperture of the mirror is small, B lies close to P, BF = PF (ii) From (i) and (ii) CF = FP Now, PC = PF + FC = 2 PF or R = 2f
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Atom: It is the smallest particle of an element which may or may not have independent existence. The atoms of certain elements such as hydrogen, oxygen, nitrogen, etc .do not have independent existence whereas atoms of helium, neon, argon, etc. do have independent existence. Thus we can say that all elements are composed of atoms. IUPAC (International Union of Pure and Applied Chemistry) approves names of elements. Many of the symbols are the first one or two letters of the element’s name in English. The first letter of a symbol is always written as a capital letter (uppercase) and the second letter as a small letter (lowercase) For example : (i) hydrogen, H (ii) aluminium, Al and not AL (iii) cobalt, Co and not CO. Symbols of some elements are formed from the first letter of the name and a letter, appearing later in the name. Examples are: (i) chlorine, Cl, (ii) zinc, Zn etc. Other symbols have been taken from the names of elements in Latin, German or Greek. For example, the symbol of iron is Fe from its Latin name ferrum, sodium is Na from natrium, potassium is K from kalium. Therefore, each element has a name and a unique chemical symbol. Molecule: A molecule is the smallest or the simplest structural unit of an element (or) a compound which contains one (or) more atoms. It retains the characteristics of an element. A molecule can exist freely and it is a combined form of bonded units whereas an atom is a singular smallest form of non bonded unit. Molecules are of two types, namely homo atomic molecules and hetero atomic molecules. Homo atomic molecules: These are the molecules which are made up of atoms of the same element. For example hydrogen gas consists of two atoms of hydrogen (H2).Similarly oxygen gas consists of two atoms of oxygen (O2). HETERO ATOMIC MOLECULES : The hetero atomic molecules are made up of atoms of different elements. They are also classified as diatomic, triatomic, or polyatomic molecules depending upon the number of atoms present. H2O, NH3, CH4, etc., are the examples for hetero atomic molecules. Atomicity: The number of atoms present in one molecule of an element is called the atomicity of an element. Depending upon the number of atoms in one molecule of an element, molecules are classified into monoatomic, diatomic, triatomic or poly atomic molecules containing one, two, three, or more than three atoms respectively. Mon atomic molecules: Helium (He) Neon (Ne) Metals Di atomic molecules: Hydrogen H2 Chlorine Cl2 Tri atomic molecules: Ozone (O3) Poly atomic molecules: phosphorous P4 Sulphur S8 Atomicity = Molecular Mass/Atomic mass MORE TO KNOW : Isotopes ⇒ These are the atoms of same element with same atomic number (Z) but different mass number (A). Example (17Cl35,17Cl37 ) Isobars ⇒ These are the Atoms of the different element with same mass number but different atomic number. Example (18Ar40, 20Ca 40 ) Isotones ⇒ These are the atoms of different elements with same number of neutrons Example : (6C13, 7N14 ) AVOGADRO’S HYPOTHESIS : Amedeo Avogadro put forward hypothesis and is based on the relation between number of molecules and volume of gases that is “volume of a gas at a given temperature and pressure is proportional to the number of particles”. Avogadro’s Law: Equal volumes of all gases under the same conditions of temperature and pressure. contain the equal number of molecules. TEST YOUR UNDERSTANDING SKILL (a) Find the atomicity of chlorine if its atomic mass is 35.5 and its molecular mass is 71 (b) Find the atomicity of ozone if its atomic mass is 16 and its molecular mass is 48 WHAT IS AN ION? An ion is a charged particle and can be negatively or positively charged. A negatively charged ion is called an ‘anion’ and the positively charged ion, a ‘cation’. For example, sodium chloride (NaCl). Its constituent particles are positively charged sodium ions (Na+) and negatively charged chloride ions (Cl–). Ions may consist of a single charged atom or a group of atoms that have a net charge on them. A group of atoms carrying a charge is known as a polyatomic ion e.g. Calcium oxide (Ca+2 O-2) RELATIVE ATOMIC MASS (RAM): Relative atomic mass of an element is the ratio of mass of one atom of element to the 1/12th part of mass of one atom of carbon. Relative atomic mass is a pure ratio and has no unit. If the atomic mass of an element is expressed in grams, it is known as gram atomic mass. e.g., Gram atomic mass of hydrogen = 1g ; Gram atomic mass of carbon = 12g Gram atomic mass of nitrogen = 14g ; Gram atomic mass of oxygen = 16g Atomic mass is expressed in atomic mass unit (amu). One atomic mass unit is defi ned as 1/12th part of the mass of one atom of carbon. Chemical Formulae: The chemical formula is a symbolic representation of a compound of its composition. Valency : The combining power (or capacity) of an element is known as its valency. Valency can be used to find out how the atoms of an element will combine with the atom(s) of another element to form a chemical compound. RELATIVE MOLECULAR MASS (RMM) : The relative molecular mass of an element or a compound is the ratio of mass of one molecule of the element or a compound to the mass of 1/12 th part of mass of one atom of carbon. Relative Molecular mass is a pure ratio and has no unit. If the molecular mass of a given substance is expressed in gram, it is known as gram molecular mass of that substance. Molecular mass is the sum of the masses of all the atoms present in one molecule of the compound or an element. Test your numerical skill : Problem: Find the gram molecular mass of water (H2O) Solution: Þ 2(H) = 2 x 1 = 2 and 1(O) = 1 x 16 = 16 Gram molecular mass of H2O = 2 + 16 = 18g Problem: Find the gram molecular mass of carbon dioxide Solution: Þ (CO2) 1(C) = 1 x 12 = 12 and 2(O) = 2 x 16 = 32 Gram molecular mass of CO2 = 12 + 32 = 44 g MOLE CONCEPT While performing a reaction, to know the number. of atoms (or) molecules involved, the concept of mole was introduced. The quantity of a substance is expressed in terms of mole. Definition of mole : Mole is defined as the amount of substance that contains as many specifi ed elementary particles as the number of atoms in 12g of carbon-12 isotope. One mole is also defined as the amount of substance which contains Avogadro number (6.023 x 1023) of particles. MORE TO KNOW Avogadro number: Number of atoms or molecules or ions present in one mole of a substance is called Avogadro number. Its value is 6.023 x 1023. Therefore, one mole of any substance = 6.023 x 1023 particles may be atoms, molecules, ions For e g. One mole of oxygen atoms represents 6.023 x 1023 atoms of oxygen and 5 moles of oxygen atoms contain 5 x 6.023x1023 atoms of oxygen. To find the number of moles, the following formulae are useful 1. When the mass of the substance is given: Use this formula : Number of moles = given mass/ atomic mass (a). Calculate the number of moles in (i) 81g of aluminium ii) 4.6g sodium (iii) 5.1g of Ammonia (iv) 90g of water (v) 2g of NaOH Solution: (i) Number of moles of aluminium = given mass of aluminium / atomic mass of aluminium = 81/27 = 3 moles of aluminium [Rest Question do yourself] (b) Calculate the mass of 0.5 mole of iron Solution: mass = atomic mass x number of moles = 55.9 x 0.5 = 27.95 g Do yourself : Find the mass of 2.5 mole of oxygen atoms [ Mass = molecular mass x number of moles] 2. Calculation of number of particles when the mass of the substance is given: Number of particles =( Avogadro number x given mass)/gram molecular mass Problem: Calculate the number. of molecules in 11g of CO2 Solution: gram molecular mass of CO2 = 44g Number of molecules = (6.023 x 1023 x 11) / 44 = 1.51 x 1023 molecules Do yourself: Calculate the number of molecules in 360g of glucose 3. Calculation of mass when number of particles of a substance is given: Mass of a substance = (gram molecular mass x number of particles)/6.023 x 1023 Problem: Calculate the mass of 18.069 x 1023 molecules of SO2 Solution: Gram molecular mass SO2 = 64gm The mass of 18.069 x 1023 molecules of SO2 = (64x18.069 x 1023)/ (6.023 x 1023) = 192 g Do yourself: (a) Calculate the mass of glucose in 2 x 1024 molecules (b) Calculate the mass of 12.046 x 1023 molecules in CaO 4. Calculation of number of moles when you are given number of molecules: Problem: Calculate the number moles for a substance containing 3.0115 x 1023 molecules in it. Solution: Number of moles = [Number of molecules/(6.023 x 1023)] = ( 3.0115 x 1023)/( 3.0115 x 1023) =0.5 moles Do yourself: (a) Calculate number of moles in 12.046x 1022 atoms of copper (b) Calculate the number of moles in 24.092 x 1022 molecules of water. Problem: Calculate the number of aluminum ions present in 0.051 g of aluminum oxide. (Hint: The mass of an ion is the same as that of an atom of the same element. Atomic mass of Al=27 u) Solution: Mass of the 1 mole of Al2 O3 = 2x27 + 3x16 = 102gm The number of ions present in 102 gm of aluminum oxide = 6.023 x 1023 ion The number of ions present in 0.051g of aluminum oxide= (6.023 x 1023 ion x 0.051g)/ 102 gm = 6.023 x 1023 ion x0.0005 = 3.0115 x 1020 ions In Al2 O3, Aluminium and oxygen are in ratio 2:3 So, The number of aluminum ions present(Al3+) in 0.051g of aluminum oxide = 2 x 3.0115 x 1020 ions =6.023 x 1020 ion DOWNLOAD FULL E-NOTES
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Open Text Material for Class IX DOWNLOAD Open Text Material for Class XI DOWNLOAD Additional for PSA PSA SAMPLE QUESTION PAPER FOR CLASS IX AND XI CLICK HERE SUPPORT MATERIAL WITH FOR PSA WITH ANSWER CLASS IX AND XI Problem Solving Assessment Question Paper 2013 : Class-IX Problem Solving Assessment Question Paper 2013 :Class XI Courtesy:CBSE The basic structural and functional unit of an organism The basic structural and functional unit of an organism is called cell. Cells are like bricks that are assembled to make a building. Similarly, cells are assembled to make the body of every organism. This is why cell are called the basic structural and functional unit of an organism. Discovery of cell: Robert Hooke in 1665 observed slices of cork (a part of the bark of a tree) under a simple magnifying device. He Robert Hooke observed under a microscope there are many partitioned boxes or compartments like a honeycomb. Hooke coined the term ‘cell’ for each box. A hen’s egg can be seen easily. Is it a cell or a group of cells? It is a single cell. A white blood cell (WBC) in human blood is another example of a single cell. How do scientists observe and study the living cells? Scientists used microscopes which magnify objects. Stains (dyes) are used to colour parts of the cell to study the detailed structure. Kinds of organism: Organisms which are made up of a single cell are called unicellular where as Organisms made up of more than one cell is called multicellular. Cell Theory : Cell Theory was elaborated by a German botanist Schleiden and Zoologist Schwann The Cell Theory states that: 1) All organisms are made up of one or more cells and the products of those cells. 2) All cells carry out life activities ( require energy, grow, have a limited size). 3) New cells arise only from other living cells by the process of cell division. Tissue: The group of cells that are similar in structure and functions is called tissue. like nervous tissue in animal and Vascular tissue in plant. Cells have different shape of Cells according to function they perform in body: Generally, cells are round, spherical or elongated (red blood) . Some cells are long and pointed at both ends. They exhibit spindle shape (muscle cells) . Cells sometimes are quite long. Some are branched like the nerve cell or a neuron. Guard cell in leaves are kidney shaped. White blood cells change their shape and move like amoeba. Which part of the cell gives it shape? Cell membrane provides shape to the cells of plants and animals. Cell wall is an additional covering over the cell membrane in plant cells. It gives shape and rigidity to cells. The size of cells in living organisms may vary . The smallest cell is 0.1 to 0.5 micrometre in bacteria. The largest cell measuring 170 mm ×130 mm, is the egg of an ostrich. Nerve cell is the longest cell and blood cells are the smallest cell in our body Cell Structure Protoplasm: The entire content of a living cell is known as protoplasm. It includes the cytoplasm and the nucleus. Protoplasm is called the living substance of the cell. Plasma membrane: The cytoplasm and nucleus are enclosed within the cell membrane together called the plasma membrane. Cell membrane: The outer boundary of the cell is the cell membrane. It is composed of proteins and carbohydrates. Functions of Cell membrane: The cell membrane gives shape to the cell. The cell membrane separates cells from one another and also the cell from the surrounding medium. The cell membrane is porous and allows the movement of substances or materials both inward and outward. This is why it is called selectively permeable membrane. Cell wall: There is also another thick additional covering of animal cell called the cell wall. This is because plant cell need protection against variations in temperature, high wind speed, atmospheric moisture, etc. Full E-Notes for CBSE & NCERT class 8th given below
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