परमाणु की सरंचना एक संक्षिप्त जानकारी

परमाणु की सरंचना एक संक्षिप्त जानकारी 

परमाणु तत्त्वों के रचनात्मक भाग होते हैं। ये तत्त्व के एेसे छोटे भाग हैं, जो रासायनिक क्रिया में भाग लेते हैं। प्रथम परमाणु सिद्धांत, जिसे जॉन डॉल्टन ने सन् 1808 में प्रतिपादित किया, के अनुसार परमाणु पदार्थ के एेसे सबसे छोटे कण होते हैं, जिन्हें और विभाजित नहीं किया जा सकता है। उन्नीसवीं शताब्दी के अंत में प्रयोगों द्वारा यह प्रमाणित हो गया कि परमाणु विभाज्य है तथा वह तीन मूल कणों (इलेक्ट्रॉन, प्रोटॉन तथा न्यूट्रॉन) द्वारा बना होता है। इन अव-परमाणविक कणों की खोज के बाद परमाणु की संरचना को स्पष्ट करने के लिए बहुत से परमाणु मॉडल प्रस्तुत किए गए।

सन् 1898 में थॉमसन ने कहा कि परमाणु एक समान धनात्मक विद्युत् आवेश वाला एक गोला होता है, जिस पर इलेक्ट्रॉन उपस्थित होते हैं। वह मॉडल, जिसमें परमाणु का द्रव्यमान पूरे परमाणु पर एक समान वितरित माना गया था, सन् 1909 में रदरफोर्ड के महत्त्वपूर्ण α-कण के प्रकीर्णन प्रयोग द्वारा गलत सिद्ध हुआ। रदरफोर्ड ने यह निष्कर्ष निकाला कि परमाणु के केंद्र में बहुत छोटे आकार का धनावेशित नाभिक होता है और इलेक्ट्रॉन इसके चारों ओर वृत्ताकार कक्षों में गति करते हैं। रदरफोर्ड मॉडल, जो सौरमंडल से मिलता-जुलता था, निश्चित रूप से डाल्टन मॉडल से बेहतर था, परंतु यह परमाणु की स्थिरता की, अर्थात् यह इस बात की व्याख्या नहीं कर पाया कि इलेक्ट्रॉन नाभिक में क्यों नहीं गिर जाते हैं? इसके अलावा यह परमाणु की इलेक्ट्रॉनिक संरचना, अर्थात् नाभिक के चारों ओर इलेक्ट्रॉनों के वितरण और उनकी ऊर्जा के बारे में कुछ नहीं बता सका। रदरफोर्ड मॉडल की इन कठिनाइयों को सन् 1913 में नील बोर ने हाइड्रोजन परमाणु के अपने मॉडल में दूर किया तथा यह प्रस्तावित किया कि नाभिक के चारों ओर वृत्ताकार कक्षों में इलेक्ट्रॉन गति करता है। केवल कुछ कक्षों का ही अस्तित्व हो सकता है तथा प्रत्येक कक्षा की निश्चित ऊर्जा होती है। बोर ने विभिन्न कक्षों में इलेक्ट्रॉन की ऊर्जा की गणना की और प्रत्येक कक्षा के लिए नाभिक और इलेक्ट्रॉन की दूरी का आकलन किया। हालाँकि बोर मॉडल हाइड्रोजन के स्पेक्ट्रम को संतोषपूर्वक स्पष्ट करता था, लेकिन यह बहु-इलेक्ट्रॉन परमाणुओं के स्पेक्ट्रमों की व्याख्या नहीं कर पाया। इसका कारण बहुत जल्द ही ज्ञात हो गया। बोर मॉडल में इलेक्ट्रॉन को नाभिक के चारों ओर एक निश्चित वृत्ताकार कक्षा में गति करते हुए आवेशित कण के रूप में माना गया था। इसमें उसके तरंग जैसे लक्षणों के बारे में नहीं सोचा गया था। एक कक्षा एक निश्चित पथ होता है और इस पथ को पूरी तरह तभी परिभाषित माना जा सकता है, जब एक ही समय पर इलेक्ट्रॉन की सही स्थिति और सही वेग ज्ञात हो। हाइज़ेनबर्ग  के ‘अनिश्चितता सिद्धांत’ के अनुसार एेसा संभव नहीं है। इस प्रकार हाइड्रोजन परमाणु का बोर मॉडल न केवल इलेक्ट्रॉन के दोहरे व्यवहार की उपेक्षा करता है, बल्कि हाइज़ेनबर्ग अनिश्चितता सिद्धांत का भी विरोध करता है।

सन् 1926 में इरविन श्रोडिंजर ने एक समीकरण दिया, जिसे ‘श्रोडिंजर समीकरण’ कहा जाता है। इसके द्वारा त्रिविम में इलेक्ट्रॉन के वितरण और परमाणुओं में अनुमत ऊर्जा स्तरों का वर्णन किया जा सकता है। यह समीकरण न केवल दे ब्रॉग्ली के तरंग-कण वाले दोहरे लक्षण की संकल्पना को ध्यान में रखता है, बल्कि हाइज़ेनबर्ग के ‘अनिश्चितता सिद्धांत’ के भी संगत है। जब इस समीकरण को हाइड्रोजन परमाणु में इलेक्ट्रॉन के लिए हल किया गया, तो इलेक्ट्रॉन के संभव ऊर्जा-स्तरों और संगत तरंग फलनों (जो गणितीय फलन होते हैं) के बारे में जानकारी प्राप्त हुई। ये क्वांटित ऊर्जा-स्तर और उनके संगत तरंग-फलन जो तीन क्वांटम संख्याओं– मुख्य क्वांटम संख्या n, दिगंशीय क्वांटम संख्या l, और चुंबकीय क्वांटम संख्या ml के द्वारा पहचाने जाते हैं, श्रोडिंजर समीकरण के हल के परिणामस्वरूप प्राप्त होते हैं। इन तीन क्वांटम संख्याओं के मानों पर प्रतिबंध भी श्रोडिंजर-समीकरण के हल से स्वतः प्राप्त होते हैं। हाइड्रोजन परमाणु का क्वांटम यांत्रिकीय मॉडल उसके स्पेक्ट्रम के सभी पहलुओं की व्याख्या करता है और उसके अतिरिक्त कुछ एेसी परिघटनाओं को भी समझाता है, जो बोर मॉडल द्वारा स्पष्ट नहीं हो सकीं।

परमाणु के क्वांटम यांत्रिकीय मॉडल के अनुसार बहु-इलेक्ट्रॉन परमाणुओं के इलेक्ट्रॉन-वितरण को कई कोशों में बाँटा गया है। ये कोश एक या अधिक उप-कोशों के बने हुए हो सकते हैं तथा इन उप-कोशों में एक या अधिक कक्षक हो सकते हैं, जिनमें इलेक्ट्रॉन उपस्थित होता है। हाइड्रोजन और हाइड्रोजन जैसे निकायों (उदाहरणार्थ– He+, Li2+ आदि) में किसी दिए गए कोश के सभी कक्षकों की समान ऊर्जा होती है, परंतु बहु-इलेक्ट्रॉन परमाणुओं में कक्षकों की ऊर्जा n और l के मानों पर निर्भर है। किसी कक्षक के लिए (n + l) का मान जितना कम होगा उसकी ऊर्जा भी उतनी ही कम होगी। यदि कोई दो कक्षकों का (n + l) मान समान है, तो उस कक्षक की ऊर्जा कम होगी, जिसके लिए n का मान कम है। किसी परमाणु में एेसे कई कक्षक संभव होते हैं, तथा उनमें ऊर्जा के बढ़ते क्रम में इलेक्ट्रॉन पाउली के अपवर्जन सिद्धांत (किसी परमाणु में किन्हीं दो इलेक्ट्रॉनों की चारों क्वांटम-संख्या का मान समान नहीं हो सकता है) और हुंड के अधिकतम बहुकता नियम (एक उपकोश के कक्षकों में इलेक्ट्रॉनों का युग्मन तब तक प्रारंभ नहीं होता, जब तक प्रत्येक कक्षक में एक-एक इलेक्ट्रॉन न आ आए) के आधार पर भरे जाते हैं। परमाणुओं की इलेक्ट्रॉनिक संरचना इन्हीं विचारों पर आधारित है।

A Concise Details About Structure of Atom

A Concise Details About Structure of Atom

Atoms are the building blocks of elements. They are the smallest parts of an element that chemically react. The first atomic theory, proposed by John Dalton in 1808, regarded atom as the ultimate indivisible particle of matter. Towards the end of the nineteenth century, it was proved experimentally that atoms are divisible and consist of three fundamental particles: electrons, protons and neutrons. The discovery of sub-atomic particles led to the proposal of various atomic models to explain the structure of atom.

Thomson in 1898 proposed that an atom consists of uniform sphere of positive electricity with electrons embedded into it. This model in which mass of the atom is considered to be evenly spread over the atom was proved wrong by Rutherford’s famous alpha-particle scattering experiment in 1909. Rutherford concluded that atom is made of a tiny positively charged nucleus, at its centre with electrons revolving around it in circular orbits. Rutherford model, which resembles the solar system, was no doubt an improvement over Thomson model but it could not account for the stability of the atom i.e., why the electron does not fall into the nucleus. Further, it was also silent about the electronic structure of atoms i.e., about the distribution and relative energies of electrons around the nucleus. The difficulties of the Rutherford model were overcome by Niels Bohr in 1913 in his model of the hydrogen atom. Bohr postulated that electron moves around the nucleus in circular orbits. Only certain orbits can exist and each orbit corresponds to a specific energy. Bohr calculated the energy of electron in various orbits and for each orbit predicted the distance between the electron and nucleus. Bohr model, though offering a satisfactory model for explaining the spectra of the hydrogen atom, could not explain the spectra of multi-electron atoms. The reason for this was soon discovered. In Bohr model, an electron is regarded as a charged particle moving in a well defined circular orbit about the nucleus. The wave character of the electron is ignored in Bohr’s theory. An orbit is a clearly defined path and this path can completely be defined only if both the exact position and the exact velocity of the electron at the same time are known. This is not possible according to the Heisenberg uncertainty principle. Bohr model of the hydrogen atom, therefore, not only ignores the dual behaviour of electron but also contradicts Heisenberg uncertainty principle. 

Erwin Schrödinger, in 1926, proposed an equation called Schrödinger equation to describe the electron distributions in space and the allowed energy levels in atoms. This equation incorporates de Broglie’s concept of wave-particle duality and is consistent with Heisenberg uncertainty principle. When Schrödinger equation is solved for the electron in a hydrogen atom, the solution gives the possible energy states the electron can occupy [and the corresponding wave function(s) (ψ) (which in fact are the mathematical functions) of the electron associated with each energy state]. These quantized energy states and corresponding wave functions which are characterized by a set of three quantum numbers (principal quantum number n, azimuthal quantum number l and magnetic quantum number ml) arise as a natural consequence in the solution of the Schrödinger equation. The restrictions on the values of these three quantum numbers also come naturally from this solution. The quantum mechanical model of the hydrogen atom successfully predicts all aspects of the hydrogen atom spectrum including some phenomena that could not be explained by the Bohr model.

According to the quantum mechanical model of the atom, the electron distribution of an atom containing a number of electrons is divided into shells. The shells, in turn, are thought to consist of one or more subshells and subshells are assumed to be composed of one or more orbitals, which the electrons occupy. While for hydrogen and hydrogen like systems (such as He+, Li2+ etc.) all the orbitals within a given shell have same energy, the energy of the orbitals in a multi-electron atom depends upon the values of n and l: The lower the value of (n + l ) for an orbital, the lower is its energy. If two orbitals have the same (n + l ) value, the orbital with lower value of n has the lower energy. In an atom many such orbitals are possible and electrons are filled in those orbitals in order of increasing energy in accordance with Pauli exclusion principle (no two electrons in an atom can have the same set of four quantum numbers) and Hund’s rule of maximum multiplicity (pairing of electrons in the orbitals belonging to the same subshell does not take place until each orbital belonging to that subshell has got one electron each, i.e., is singly occupied). This forms the basis of the electronic structure of atoms.

Measurement of Length

Measurement of Length

You are already familiar with some direct methods for the measurement of length. For example, a metre scale is used for lengths from 10–3 m to 102 m. A vernier callipers is used for lengths to an accuracy of 10–4 m. A screw gauge and a spherometer can be used to measure lengths as less as to 10–5 m. To measure lengths beyond these ranges, we make use of some special indirect methods.

 Measurement of Large Distances

Large distances such as the distance of a planet or a star from the earth cannot be measured directly with a metre scale. An important method in such cases is the parallax method.

When you hold a pencil in front of you against some specific point on the background (a wall) and look at the pencil first through your left eye A (closing the right eye) and then look at the pencil through your right eye B (closing the left eye), you would notice that the position of the pencil seems to change with respect to the point on the wall. This is called parallax. The distance between the two points of observation is called the basis. In this example, the basis is the distance between the eyes. 

To measure the distance D of a far away planet S by the parallax method, we observe it from two different positions (observatories) A and B on the Earth, separated by distance AB = b at the same time as shown in Fig. 2.2. We measure the angle between the two directions along which the planet is viewed at these two points. The ∠ASB in Fig. 2.2 represented by symbol θ is called the parallax angle or parallactic angle.

As the planet is very far away,

b/D <<1

and therefore, 

D = b/θ

is very small. Then we approximately take AB as an arc of length b of a circle with centre at S and the distance D as the radius AS = BS so that AB = b = D θ  where θ  is in radians.

(2.1)

Having determined D, we can employ a similar method to determine the size or angular diameter of the planet. If d is the diameter of the planet and α  the angular size of the planet (the angle subtended by d at the earth), we have 

α = d/D (2.2)

Fig. 2.2  Parallax method.

The angle α  can be measured from the same location on the earth. It is the angle between the two directions when two diametrically opposite points of the planet are viewed through the telescope. Since D is known, the diameter d of the planet can be determined using Eq. (2.2).

Estimation of Very Small Distances: Size of a Molecule

To measure a very small size, like that of a molecule (10–8 m to 10–10 m), we have to adopt special methods. We cannot use a screw gauge or similar instruments. Even a microscope has certain limitations. An optical microscope uses visible light to ‘look’ at the system under investigation. As light has wave like features, the resolution to which an optical microscope can be used is the wavelength of light (A detailed explanation can be found in the Class XII Physics textbook). For visible light the range of wavelengths is from about 4000 Å to 7000 Å 

(1 angstrom = 1 Å = 10-10 m). Hence an optical microscope cannot resolve particles with sizes smaller than this. Instead of visible light, we can use an electron beam. Electron beams can be focussed by properly designed electric and magnetic fields. The resolution of such an electron microscope is limited finally by the fact that electrons can also behave as waves . The wavelength of an electron can be as small as a fraction of an angstrom. Such electron microscopes with a resolution of 0.6 Å have been built. They can almost resolve atoms and molecules in a material. In recent times, tunnelling microscopy has been developed in which again the limit of resolution is better than an angstrom. It is possible to estimate the sizes of molecules. 

A simple method for estimating the molecular size of oleic acid is given below. Oleic acid is a soapy liquid with large molecular size of the order of 10–9 m.

The idea is to first form mono-molecular layer of oleic acid on water surface. 

We dissolve 1 cm3 of oleic acid in alcohol to make a solution of 20 cm3. Then we take 1 cm3 of this solution and dilute it to 20 cm3, using alcohol. So, the concentration of the solution is equal to  

(1/20×20) cm³

  of oleic acid/cm3 of solution. Next we lightly sprinkle some lycopodium powder on the surface of water in a large trough and we put one drop of this solution in the water. The oleic acid drop spreads into a thin, large and roughly circular film of molecular thickness on water surface. Then, we quickly measure the diameter of the thin film to get its area A. Suppose we have dropped n drops in the water. Initially, we determine the approximate volume of each drop (V cm3).

Volume of n drops of solution 

= nV cm3 

Amount of oleic acid in this solution

= 

nV(1/20×20) cm³

This solution of oleic acid spreads very fast on the surface of water and forms a very thin layer of thickness t. If this spreads to form a film of area A cm2, then the thickness of the film

t = Volume of the film /Area of the film

or, 

t = nV(1/20×20A) cm

(2.3)

If we assume that the film has mono-molecular thickness, then this becomes the size or diameter of a molecule of oleic acid. The value of this thickness comes out to be of the order of 10–9 m.

The International System of Units

The International System of Units

In earlier time scientists of different countries were using different systems of units for measurement. Three such systems, the CGS, the FPS (or British) system and the MKS system were in use extensively till recently.

The base units for length, mass and time in these systems were as follows :

• In CGS system they were centimetre, gram and second respectively.

• In FPS system they were foot, pound and second respectively.

• In MKS system they were metre, kilogram and second respectively. 

The system of units which is at present internationally accepted for measurement is the Système Internationale 

d’ Unites (French for International System of Units), abbreviated as SI. The SI, with standard scheme of symbols, units and abbreviations, developed by the Bureau International des Poids et measures (The International Bureau of weights and measures, BIPM) in 1971 were recently revised by the General Conference on weights and measures in November 2018. The scheme is now for international usage in scientific, technical, industrial and commercial work. Because SI units used decimal system, conversions within the system are quite simple and convenient. We shall follow the SI units in this book.

In SI, there are seven base units as given in  Table 2.1. Besides the seven base units, there are two more units that are defined for (a) plane angle dθ as the ratio of length of arc ds to the radius r and (b) solid angle dΩ as the ratio of the intercepted area dA of the spherical surface, described about the apex O as the centre, to the square of its radius r, as shown in Fig. 2.1(a) and (b) respectively. The unit for plane angle is radian with the symbol rad and the unit for the solid angle is steradian with the symbol sr. Both these are dimensionless quantities.

Fig.  2.1 Description  of  (a)  plane  angle  dθ  and  (b)  solid  angle

Table 2.1  SI Base Quantities and Units*

* The values mentioned here need not be remembered or asked in a test. They are given here only to indicate the extent of accuracy to which they are measured. With progress in technology, the measuring techniques get improved leading to measurements with greater precision. The definitions of base units are revised to keep up with this progress.

  

Table 2.2 Some units retained for general use (Though outside SI)

Note that when mole is used, the elementary entities must be specified. These entities may be atoms, molecules, ions, electrons, other particles or specified groups of such particles. 

We employ units for some physical quantities that can be derived from the seven base units (Appendix A 6). Some derived units in terms of the SI base units are given in (Appendix A 6.1). Some SI derived units are given special names (Appendix A 6.2 ) and some derived SI units make use of these units with special names and the seven base units (Appendix A 6.3). These are given in Appendix A 6.2 and A 6.3 for your ready reference. Other units retained for general use are given in Table 2.2.

Common SI prefixes and symbols for multiples and sub-multiples are given in Appendix A2. General guidelines for using symbols for physical quantities, chemical elements and nuclides are given in Appendix A7 and those for SI units and some other units are given in Appendix A8 for your guidance and ready reference.