structure of atom

CHEMISTRY PROJECT UNIT 2: 

CHEMISTRY PROJECT UNIT 2 STRUCTURE OF ATOM SUBMITTED BY: Firoz rathor XI_A SUBMITTED TO: P. GUPTA MA’AM CLASS 11

Contents:: 

Contents: 1). Sub-atomic Particles 2). Atomic Models 3). Developments Leading to the Bohr’s Model of Atom 4). Bohr’s Model for Hydrogen Atom 5). Towards Quantum Mechanical Model of the Atom 6). Quantum Mechanical Model of Atom

Discovery of nucleus: 

Discovery of nucleus 1911 - Ernest Rutherford (1871-1937)

1). SUB-ATOMIC PARTICLES: 

1). SUB-ATOMIC PARTICLES 1.1). Discovery of Electron In 1830, Michael Faraday showed that if electricity is passed through a solution of an electrolyte, chemical reactions occurred at the electrodes, which resulted in the liberation and deposition of matter at the electrodes. An insight into the structure of atom was obtained from the experiments on electrical discharge through gases. Before we discuss these results we need to keep in mind a basic rule regarding the behaviour of charged particles : “Like charges repel each other and unlike charges attract each other”. In mid 1850s many scientists mainly Faraday began to study electrical discharge in partially evacuated tubes, known as cathode ray discharge tubes. It is depicted in Fig.

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A cathode ray tube is made of glass containing two thin pieces of metal, called electrodes, sealed in it. The electrical discharge through the gases could be observed only at very low pressures and at very high voltages. The pressure of different gases could be adjusted by evacuation. When sufficiently high voltage is applied across the electrodes, current starts flowing through a stream of particles moving in the tube from the negative electrode (cathode) to the positive electrode (anode). These were called cathode rays or cathode ray particles. The flow of current from cathode to anode was further checked by making a hole in the anode and coating the tube behind anode with phosphorescent material zinc sulphide . When these rays, after passing through anode, strike the zinc sulphide coating, a bright spot on the coating is developed (same thing happens in a television set)

1.2). Discovery of Protons and Neutrons: 

1.2). Discovery of Protons and Neutrons Electrical discharge carried out in the modified cathode ray tube led to the discovery of particles carrying positive charge, also known as canal rays. The characteristics of these positively charged particles are listed below. Unlike cathode rays, the positively charged particles depend upon the nature of gas present in the cathode ray tube. These are simply the positively charged gaseous ions. (ii) The charge to mass ratio of the particles is found to depend on the gas from which these originate. (iii) Some of the positively charged particles carry a multiple of the fundamental unit of electrical charge. (iv) The behaviour of these particles in the magnetic or electrical field is opposite to that observed for electron or cathode rays.

2). ATOMIC MODELS: 

2). ATOMIC MODELS Thompson develops the idea that an atom was made up of electrons scattered unevenly within an elastic sphere surrounded by a soup of positive charge to balance the electron's charge like plums surrounded by pudding. 2.1) Thomson Model of Atom

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atoms positive charge is concentrated in the nucleus proton (p) has opposite (+) charge of electron mass of p is 1840 x mass of e - (1.67 x 10 -24 g) 2.2 2.1) Rutherford’s Nuclear Model of Atom

2.2) Atomic Number and Mass Number : 

2.2) Atomic Number and Mass Number The presence of positive charge on the nucleus is due to the protons in the nucleus. As established earlier, the charge on the proton is equal but opposite to that of electron. The number of protons present in the nucleus is equal to atomic number ( Z ). For example, the number of protons in the hydrogen nucleus is 1, in sodium atom it is 11, therefore their atomic numbers are 1 and 11 respectively. In order to keep the electrical neutrality, the number of electrons in an atom is equal to the number of protons (atomic number, Z ). For example, number of electrons in hydrogen atom and sodium atom are 1 and 11 respectively. Atomic number ( Z) = number of protons in the nucleus of an atom = number of electrons in a nuetral atom

2.3) Isobars and Isotopes : 

2.3) Isobars and Isotopes The composition of any atom can be represented by using the normal element symbol (X) with super-script on the left hand side as the atomic mass number (A) and subscript ( Z) on the left hand side as the atomic number (i.e., A Z X). Isobars are the atoms with same mass number but different atomic number for example, 6 14C and 7 14N. On the other hand, atoms with identical atomic number but different atomic mass number are known as Isotopes. In other words (according to equation 2.4), it is evident that difference between the isotopes is due to the presenceof different number of neutrons present in the nucleus. For example, considering of hydrogen atom again, 99.985% of hydrogen atoms contain only one proton. This isotope is called protium (11H).

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Rest of the percentage of hydrogen atom contains two other isotopes, the one containing 1 proton and 1 neutron is called deuterium (12D, 0.015%) and the other one possessing 1 proton and 2 neutrons is called tritium (13T ). The latter isotope is found in trace amounts on the earth. Other examples of commonly occuring isotopes are: carbon atoms containing 6, 7 and 8 neutrons besides 6 protons (12 13 14 6 6 6 C, C, C); chlorine atoms containing 18 and 20 neutrons besides 17 protons ( 35 37 17 17 Cl , Cl ).

3) DEVELOPMENT LEADING TO THE BOHR’S MODEL OF ATOM: 

3) DEVELOPMENT LEADING TO THE BOHR’S MODEL OF ATOM Historically, results observed from the studies of interactions of radiations with matter have provided immense information regarding the structure of atoms and molecules. Neils Bohr utilised these results to improve upon the model proposed by Rutherford. Two developments played a major role in the formulation of Bohr’s model of atom. These were: ( i ) Dual character of the electromagnetic radiation which means that radiations possess both wave like and particle like properties, and (ii) Experimental results regarding atomic spectra which can be explained only by assuming quantized (Section 2.4) electronic energy levels in atoms.

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3.1) Wave Nature of Electromagnetic Radiation James Maxwell (1870) suggested that when electrically charged particle moves under acceleration, alternating electrical and magnetic fields are produced and transmitted. These fields are transmitted in the forms of waves called electromagnetic waves or electromagnetic radiation.

3.2) Particle Nature of Electromagnetic Radiation: Plank’s Quantum Theory: 

3.2) Particle Nature of Electromagnetic Radiation: Plank’s Quantum Theory Some of the experimental phenomenon such as diffraction* and interference** can be explained by the wave nature of the electromagnetic radiation. However, following are some of the observations which could not be explained with the help of even the electromagentic theory of 19th century physics (known as classical physics): ( i ) the nature of emission of radiation from hot bodies (black -body radiation) (ii) ejection of electrons from metal surface when radiation strikes it (photoelectric effect) (iii) variation of heat capacity of solids as a function of temperature (iv) line spectra of atoms with s pecial reference to hydrogen. Figure: Wavelength-intensity relationship

3.3) Photoelectric Effect: 

3.3) Photoelectric Effect In 1887, H. Hertz performed a very interesting experiment in which electrons (or electric current) were ejected when certain metals (for example potassium, rubidium, caesium etc.) were exposed to a beam of light as Shown in Fig The phenomenon is called Photoelectric effect. The results observed in this experiment were: ( i ) The electrons are ejected from the metal surface as soon as the beam of light strikes the surface, i.e., there is no time lag between the striking of light beam and the ejection of electrons from the metal surface. (ii) The number of electrons ejected is proportional to the intensity or brightness of light. (iii) For each metal, there is a characteristic minimum frequency,ν0 (also known as threshold frequency) below which photoelectric effect is not observed. At a frequency ν >ν 0, the ejected electrons come out with certain kinetic energy. The kinetic energies of these electrons increase with the increase of frequency of the light used.

3.4) Evidence for the quantized* Electronic Energy Levels: Atomic Spectra: 

3.4) Evidence for the quantized* Electronic Energy Levels: Atomic Spectra It is observed that when a ray of white light is passed through a prism, the wave with shorter wavelength bends more than the one with a longer wavelength. Since ordinary white light consists of waves with all the wavelengths in the visible range, a ray of white light is spread out into a series of coloured bands called spectrum. The spectrum of white light, that we can see, ranges from violet at 7.50 × 1014 Hz to red at 4×1014 Hz. Such a spectrum is called continuous spectrum. Continuous because violet merges into blue, blue into green and so on. Emission and Absorption Spectra: The spectrum of radiation emitted by a substance that has absorbed energy is called an emission spectrum. Atoms, molecules or ions that have absorbed radiation are said to be “excited”. To produce an emission spectrum, energy is supplied to a sample by heating it or irradiating it and the wavelength (or frequency) of the radiation emitted, as the sample gives up the absorbed energy, is recorded.

4) BOHR’S MODEL FOR HYDROGEN ATOM: 

4) BOHR’S MODEL FOR HYDROGEN ATOM Neils Bohr (1913) was the first to explain quantitatively the general features of hydrogen atom structure and its spectrum. Though the theory is not the modern quantum mechanics, it can still be used to rationalize many points in the atomic structure and spectra. Bohr’s model for hydrogen atom is based on the following postulates: i ) The electron in the hydrogen atom can move around the nucleus in a circular path of fixed radius and energy. These paths are called orbits, stationary states or allowed energy states. These orbits are arranged concentrically around the nucleus. ii) The energy of an electron in the orbit does not change with time. However, the electron will move from a lower stationary state to a higher stationary state when required amount of energy is absorbed by the electron or energy is emitted when electron moves from higher stationary state to lower stationary state. The energy change does not take place in a continuous manner.

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iii) The frequency of radiation absorbed or emitted when transition occurs between two stationary states that differ in energy by Δ E, is given by : ν = Δ E/h = E2 − /h Where E1 and E2 are the energies of the lower and higher allowed energy states respectively. This expression is commonly known as Bohr’s frequency rule.

4.1) Explanation of Line Spectrum of Hydrogen: 

4.1) Explanation of Line Spectrum of Hydrogen Line spectrum observed in case of hydrogen atom, as mentioned in section 2.3.3, can be explained quantitatively using Bohr’s model. According to assumption 2, radiation (energy) is absorbed if the electron moves from the orbit of smaller Principal quantum number to the orbit of higher Principal quantum number, whereas the radiation (energy) is emitted if the electron moves from higher orbit to lower orbit. The energy gap between the two orbits is given by equation (2.16)

Limitations of Bohr’s Model: 

Limitations of Bohr’s Model Bohr’s model of the hydrogen atom was no doubt an improvement over Rutherford’s nuclear model, as it could account for the stability and line spectra of hydrogen atom and hydrogen like ions (for example, He+, Li2+, Be3+, and so on). However, Bohr’s model was too simple to account for the following points. i ) It fails to account for the finer details (doublet, that is two closely spaced lines) of the hydrogen atom spectrum observed by using sophisticated spectroscopic techniques. This model is also unable to explain the spectrum of atoms other than hydrogen, for example, helium atom which possesses only two electrons. Further, Bohr’s theory was also unable to explain the splitting of spectral lines in the presence of magnetic field (Zeeman effect) or an electric field (Stark effect). ii) It could not explain the ability of atoms to form molecules by chemical bonds.In other words, taking into account the points mentioned above, one needs a bettertheory which can explain the salient features of the structure of complex atoms.

5) TOWARDS QUANTUM MECHANICAL MODEL OF THE ATOM: 

5) TOWARDS QUANTUM MECHANICAL MODEL OF THE ATOM In view of the shortcoming of the Bohr’s model, attempts were made to develop a more suitable and general model for atoms. Two important developments which contributed significantly in the formulation of such a model were : 1. Dual behaviour of matter, 2. Heisenberg uncertainty principle.

5.1) Dual behavior of Matter : 

5.1) Dual behavior of Matter The French physicist, de Broglie in 1924 proposed that matter, like radiation, should also exhibit dual behaviour i.e., both particle and wavelike properties. This means that just as the photon has momentum as well as wavelength, electrons should also have momentum as well as wavelength, de Broglie, from this analogy, gave the following relation between wavelength (λ) and momentum (p) of a material particle. where m is the mass of the particle, v its velocity and p its momentum. de Broglie’s prediction was confirmed experimentally when it was found that an electron beam undergoes diffraction, a phenomenon characteristic of waves. This fact has been put to use in making an electron microscope, which is based on the wavelike behaviour of electrons just as an ordinary microscope utilises the wave nature of light. An electron microscope is a powerful tool in modern scientific research because it achieves a magnification of about 15 million times.

5.2) Heisenberg’s Uncertainty Principal and its Significance : 

5.2) Heisenberg’s Uncertainty Principal and its Significance Werner Heisenberg a German physicist in 1927, stated uncertainty principle which is the consequence of dual behaviour of matter and radiation. It states that it is impossible to determine simultaneously, the exact position and exact momentum (or velocity) of an electron. Mathematically, it can be given as in equation (2.23). where Δx is the uncertainty in position and Δ px ( or Δvx ) is the uncertainty in momentum (or velocity) of the particle. If the position of the electron is known with high degree of accuracy ( Δx is small), then the velocity of the electron will be uncertain [Δ( vx ) is large]. The “light” used must have a wavelength smaller than the dimensions of an electron. The high momentum photons of such light would change the energy of electrons by collisions

6) QUANTUM MECHANICAL MODEL OF ATOM: 

6) QUANTUM MECHANICAL MODEL OF ATOM Classical mechanics, based on Newton’s laws of motion, successfully describes the motion of all macroscopic objects such as a falling stone, orbiting planets etc., which have essentially a particle-like behaviour as shown in the previous section. However it fails when applied to microscopic objects like electrons, atoms, molecules etc. This is mainly because of the fact that classical mechanics ignores the concept of dual behaviour of matter especially for sub-atomic particles and the uncertainty principle. The branch of science that takes into account this dual behavior of matter is called quantum mechanics.

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Hydrogen Atom and the Schrödinger Equation: When Schrödinger equation is solved for hydrogen atom, the solution gives the possible energy levels the electron can occupy and the corresponding wave function(s) (ψ) of the electron associated with each energy level. 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. When an electron is in any energy state, the wave function corresponding to that energy state contains all information about the electron.

6.1) Orbitals and Quantum Numbers: 

6.1) Orbitals and Quantum Numbers A large number of orbitals are possible in an atom. Qualitatively these orbitals can be distinguished by their size, shape and orientation. An orbital of smaller size means there is more chance of finding the electron near the nucleus. Similarly shape and orientation mean that there is more probability of finding the electron along certain directions than along others. Atomic orbitals are precisely distinguished by what are known as quantum numbers. Each orbital is designated by three quantum numbers labelled as n, l and ml. The principal quantum number ‘ n’ is a positive integer with value of n = 1,2,3....... . The principal quantum number also identifies the shell. With the increase in the value of ‘ n’, the number of allowed orbital increases and are given by ‘ n2’ All the orbitals of a given value of ‘n’ constitute a single shell of atom and are represented by the following letters n = 1 2 3 4 ............ Shell = K L M N ............

6.2) Shapes of Atomic Orbitals : 

6.2) Shapes of Atomic Orbitals The orbital wave function or ψ for an electron in an atom has no physical meaning. It is simply a mathematical function of the coordinates of the electron. However, for different orbitals the plots of corresponding wave functions as a function of r (the distance from the nucleus) are different. Fig. 2.12(a), (page 54) gives such plots for 1 s (n = 1, l = 0) and 2 s (n = 2, l = 0) orbitals . According to the German physicist, Max Born, the square of the wave function ( i.e.,ψ 2) at a point gives the probability density of the electron at that point. The variation of ψ 2as a function of r for 1s and 2 s orbitals is given in Fig. 2.12(b), Here again, you may note that the curves for 1 s and 2s orbitals are different.

6.3) Filling of Orbitals in Atom : 

6.3) Filling of Orbitals in Atom The filling of electrons into the orbitals of different atoms takes place according to the aufbau principle which is based on the Pauli’s exclusion principle, the Hund’s rule of maximum multiplicity and the relative energies of the orbitals . Aufbau Principle The word ‘ aufbau ’ in German means ‘building up’. The building up of orbitals means thefilling up of orbitals with electrons. The principle states : In the ground state of the atoms, the orbitals are filled in order of their increasing energies. In other words, electrons first occupy the lowest energy orbital available to them and enter into higher energy orbitals only after the lower energy orbitals are filled.

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The order in which the energies of the orbitals increase and hence the order in which the orbitals are filled is as follows : 1 s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 4f, 5 d, 6p, 7s... The order may be remembered by using the method given in Fig. 2.17. Starting from the top, the direction of the arrows gives the order of filling of orbitals , that is starting from right top to bottom left.

6.4) Electronic Configuration of Atom : 

6.4) Electronic Configuration of Atom The distribution of electrons into orbitals of an atom is called its electronic configuration. If one keeps in mind the basic rules which govern the filling of different atomic orbitals , the electronic configurations of different atoms can be written very easily. The electronic configuration of different atoms can be represented in two ways. For example : In the first notation, the subshell is represented by the respective letter symbol and the number of electrons present in the subshell is depicted, as the super script, like a, b, c, ... etc. The similar subshell represented for different shells is differentiated by writing the principal quantum number before the respective subshell . In the second notation each orbital of the subshell is represented by a box and the electron is represented by an arrow (↑) a positive spin or an arrow (↓) a negative spin. The advantage of second notation over the first is that it represents all the four quantum numbers.

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The hydrogen atom has only one electron which goes in the orbital with the lowest energy, namely 1 s. The electronic configuration of the hydrogen atom is 1 s1 meaning that it has one electron in the 1 s orbital. The second electron in helium (He) can also occupy the 1 s orbital. Its configuration is, therefore, 1 s2. As mentioned above, the two electrons differ from each other with opposite spin, as can be seen from the orbital diagram. The third electron of lithium (Li) is not allowed in the 1 s orbital because of Pauli exclusion principle. It, therefore, takes the next available choice, namely the 2 s orbital. The electronic configuration of Li is 1 s22s1. The 2 s orbital can accommodate one more electron. The configuration of beryllium (Be) atom is, therefore, 1 s2 2s2 (see Table 2.6, page 62 for the electronic configurations of elements).

6.5) Stability of Completely Filled and Half Filled Subshells : 

6.5) Stability of Completely Filled and Half Filled Subshells The ground state electronic configuration of the atom of an element always corresponds to the state of the lowest total electronic energy. The electronic configurations of most of the atoms follow the basic rules given in Section 2.6.5. However, in certain elements such as Cu, or Cr, where the two subshells (4 s and 3d) differ slightly in their energies, an electron shifts from a subshell of lower energy (4 s) to a subshell of higher energy (3d), provided such a shift results in all orbitals of the subshell of higher energy getting either completely filled or half filled. The valence electronic configurations of Cr and Cu, therefore, are 3 d5 4s1 and 3d10 4s1 respectively and not 3 d4 4s2 and 3d9 4s2. It has been found that there is extra stability associated with these electronic configurations.

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Causes of Stability of Completely Filled and Half Filled Sub-shells The completely filled and completely half filled sub-shells are stable due to the following reasons: 1.Symmetrical distribution of electrons: It is well known that symmetry leads to stability. The completely filled or half filled subshells have symmetrical distribution of electrons in them and are therefore more stable. Electrons in the same subshell (here 3d) have equal energy but different spatial distribution. Consequently, their shielding of oneanother is relatively small and the electrons are more strongly attracted by the nucleus.

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2. Exchange Energy : The stabilizing effect arises whenever two or more electrons with the same spin are present in the degenerate orbitals of a subshell . These electrons tend to exchange their positions and the energy released due to this exchange is called exchange energy. The number of exchanges that can take place is maximum when the subshell is either half filled or completely filled. As a result the exchange energy is maximum and so is the stability. You may note that the exchange energy is at the basis of Hund’s rule that electrons which enter orbitals of equal energy have parallel spins as far as possible. In other words, the extra stability of half-filled and completely filled subshell is due to: Relatively small shielding, smaller coulombic repulsion energy, and larger exchange energy.

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