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विज्ञान में नई सोच अन्तर्विरोध और विरोधाभासों से ही विकसित होती है

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विज्ञान में नई सोच अन्तर्विरोध और विरोधाभासों से ही विकसित होती है हम विरोधाभास ऐसे कथन, ऐसे विचार या ऐसी घटना को कहते हैं जो सामान्य बुद्धि के विरुद्ध होता है। विरोधाभास कई तरह के होते हैं कुछ अन्तर्विरोध के सूचक होते हैं तो कुछ तर्कशास्त्रीय विरोधाभास होते हैं। कुछ भी हो विरोधाभास एक तरह से अन्तर्विरोध ही हैं। विज्ञान का अब तक का इतिहास बतलाता है कि विरोधाभास उस विचार श्रंखला को तोड़ देते हैं जिसका समाज आदी हो जाता है और हमें विवश करते हैं कि हम हर अस्पष्ट और असामान्य बात से मुंह मोड़ लें और बात को गहराई में जाकर देखें।  विज्ञान में ऐसे अनेक तर्कशास्त्रीय विरोधाभास होते हैं जो नपेतुले होते हैं, जिनके बारे में यह कहना कठिन होता है कि ये सत्य हैं या असत्य। इस प्रकार के विचित्र तर्कों को वाक्छल या सोफिज्म कहते हैं। एक व्यक्ति ने घोषणा की  कि मैँ जो कुछ भी बोलता हूँ, झूठ बोलता हूँ। इसका मतलब है कि  उसने इस बार भी झूठ बोला। लेकिन इस विरोधाभास में निष्कर्ष निकलता है कि उसने इस बार उसने खुद के बारे में सच कहा है। लेकिन इस आदमी की बात यदि सच है तो उसने झूठ ही कहा है।  इटली में 15 वीं शताब्दी म
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Magnetic Properties Of Solids

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Magnetic properties of Solids- e magnetic properties of different materials are studied in terms of their magnetic moments which arise due to the orbital motion and spinning motion of the electrons.  As electron is a charge particle, its orbital motion produces a small magnetic field along the axis of rotation and its spinning motion produces a small magnetic Field along the spin axis. Since magnetic moment is a vector quantity, the net magnetic moment is represented by an arrow. Based on the behavior in the external magnetic field, the solids are divided into following classes-  (i) Diamagnetic substances - Substances which are weakly repelled by the external magnetic field are called diamagnetic substances and the properties is called diamagnetism. Example – TiO2, NaCl, H2O and C6H6 etc. This properties is shown only by those substances which contain fully filled orbitals. i.e. no unpaired electron is present. The magnetic moment possessed by an electron with
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Crystal Defects or Crystal Imperfections

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Crystal Defects or Imperfections- Any departure from perfectly ordered arrangement of atoms in crystal is called crystal defects or imperfection. Schottky, International and Anti structure are three basic types of point secrets. In additional three hybrid types of de devta can aise from combination of two of basic types. Frankel effect is more common in tonic solid.  It is not possible to explain many properties of solids such as electrical conductivity  and mechanical strength on the basis of structure alone . Hence defects not only modify the properties but also impart some other properties of solids.   Point Defect- The defect caused by missing or misplaced atoms or ions in an ionic crystal is called point defects. It is always found in ionic solids. It is of following types- (1)Stoichoimetric Defects- If defects in crystal are such that the ratio between the cations and anions remains the same as represented by molecular formula, the defects are called sto
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Structure of Some Ionic Compounds

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Relation between nearest neighbour distance and radius of atom, Concept of Radius ratio

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Relationship between the nearest neighbour distance (d), edge of the unit cell (a) and the radius of the atom (r) (1)Simple cubic unit cell- Distance between nearest neighbour (d) = AB = a Hence for simple cubic (SC)  d = a   and r = a/2 (2)Face centred cubic unit cell-    Distance between nearest neighbour (d) =  AC (Because spheres at the face diagonal are touching each other)    But from  ∆ ABC      AC2 = AB2 + BC2                       Hence        d = a2 + a2                                  d =  2a2                             d =  √2a                             d =a/ √2   Since atomic radius (r = d/2)                                      r=  AC/2 = a/2√2                                                                    Hence for face centred cubic (FCC)  d =a√2         and   r =  a/2√2 (3) Body centred cubic unit cell- The distance between nearest neighbour (d) = 1/2 CD  Since all the spheres at the corners touch the central sphere, so CD
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Tertahadral & Octahedral Voids, HCP & CCP

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Concepts of Voids, HCP & CCP Arrangements Density of unit cell- Tetrahedral and Octahedral void-  Tetrahedral Void-                                                                              A simple triangular void in a crystal which is surrounded by four spheres is called tetrahedral void. A tetrahedral void is developed when triangular voids have contact with one sphere either in the upper layer or in the lower layer. Tetrahedral void means the tetrahedral arrangement of spheres.                                            .     Characteristics of tetrahedral void- (i) Ratio of radii of void and constituent particle is constant.   r/R = 0.225 (ii) Co-ordination number  of particle present in the void is 4 (iii) Each constituent particle makes two tetrahedron with three spheres above and three spheres below (iv) No. of tetrahedral voids    = 2 ×No. of atoms    = 2× octahedral voids Relationship B/W  radius of void (r) and radius o
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Crystal System & Bravais Lattices

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Crystal system and Bravais lattices -   Crystal system and Bravais lattices - Based upon the dimensions of the unit cells (i.e. length a, b, and c and the angles (α , β and γ ) there are seven types of unit cells. These are also called crystal systems are crystal habits because any crystalline solid must belong to any one of the unit cells. “At first sight there seems to be infinite number of shapes of crystals. However careful examination of several thousand crystals of various substances has revealed that only seven possible symmetries are possible. The seven different combinations of symmetry elements are called crystal systems.”  These crystal systems differ in the length of the unit cell edges (a, b and c) and angles ( α, β and γ ) between the unit cell The arrangement of particles in the study of crystal was first given by German Scientist M. Frankenheim in 1844. Classification on the basis of geometrical consideration-  In 1848 A. Bravais studied
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