Period table Periodic table Periodic table Periodic table, Lecture notes of Chemistry

Download Period table Periodic table Periodic table Periodic table and more Lecture notes Chemistry in PDF only on Docsity! 1. Matter is composed of extremely small indivisible particles called atoms. 2. An element consists of only one type of atoms. All the atoms of a particular element have identical properties such as mass, shape, colour, density, chemical properties, etc. 3. All atoms of an element are identical, and different from those of other elements. 4. Atom is the smallest particle that takes part in chemical reactions. 5. Atoms can neither be created nor destroyed during chemical reactions. 6. Atoms of different elements may combine in a simple whole number ratio to form compound atoms or molecules. • Limitation of Dalton’s Atomic theory 1. The indivisibility of an atom was proved wrong: an atom can be further subdivided into protons, neutrons and electrons. 2. According to Dalton, the atoms of same element are similar in all respects. However, atoms of same element vary in their masses and densities. These atoms of different masses are called isotopes. For example, chlorine has two isotopes with mass numbers 35 and 37. 3. Dalton also claimed that atoms of different elements are different in all respects. This has been proven wrong in certain cases: argon and calcium atoms each have an atomic mass of 40 amu. These atoms are known as isobars. 4. According to Dalton, atoms of different elements combine in simple whole number ratios to form compounds. This is not observed in complex organic compounds like sugar (C12H22O11). 5. The theory fails to explain the existence of allotropes. it does not account for differences in properties of charcoal, graphite, diamond. Postulates of Dalton’s Atomic Theory In the alpha particle experiment, the effect of bombarding thin gold foil with alpha radiation from radioactive substances (uranium) was observed. Alpha rays consist of positively charged particles. He found that most of the alpha particles passed through a metal foil as though nothing were there, but a few (about 1 in 8000) were scattered at large angles and sometimes almost backward. According to Rutherford’s model, most of the mass of the atom (99.95% or more) is concentrated in a positively charged center, or nucleus, around which the negatively charged electrons move. Although most of the mass of an atom is in its nucleus, the nucleus occupies only a very small portion of the space of the atom. Nuclei have diameters of about 10-15 m, whereas atomic diameters are about 10-10 m, a hundred thousand times larger. The nuclear model easily explains the results of bombarding gold with alpha particles. Alpha particles are much lighter than gold atoms (196). (Alpha particles are helium nuclei(He2+)). Since most of the alpha particles pass through the metal foil, so they are undeflected by the lightweight electrons. When an alpha particle hit the positively charged nucleus, it is either scattered at a wide angle or deflected back by the massive, positively charged nucleus Ernest Rutherford Alpha particle experiment • Bohr model assumed that electrons have both a known radius and orbit. But according to Heisenberg “The position and momentum of a particle cannot be simultaneously measured with arbitrarily high precision”. • Bohr model useful for predicting the behavior of electrons in hydrogen atoms but it fails to explain the spectra of larger atoms and atoms have multiple electrons. The model also didn’t work with neutral helium atoms. • The Bohr model also could not account for the Zeeman effect, where spectral lines are split into two or more in the presence of an external, static magnetic field. Limitation of Bohr model According to Bohr model, the attractive force between electron and nucleus is balanced by centrifugal force of electron which is due to motion of electron and tend to take electron away from nucleus. Let’s assume, Atomic number of atom = Z Charge on electron = e Charge on nucleus = Ze Radius of nth orbit = r The electrostatic force of attraction = 𝑍𝑒2 4π𝜖0𝑟 2 …(1) The centripetal force = 𝑚𝑉2 𝑟 …… . (2) Since both forces balanced each other. Hence 𝑚𝑉2 𝑟 = 𝑍𝑒2 4π𝜖0𝑟 2 or m𝑉2 = 𝑍𝑒2 4π𝜖0𝑟 ………..(3) Form Bohr postulate m𝑉𝑟 = 𝑛ℎ 2𝜋 Or, m2𝑉2𝑟2 = 𝑛2ℎ2 4𝜋2 Radius of nth orbit Or, m𝑉2 = 𝑛2ℎ2 4𝑚𝑟2𝜋2 ………. (4) From (3) and (4), we have 𝑍𝑒2 4π𝜖0𝑟 = 𝑛2ℎ2 4𝑚𝑟2𝜋2 Or, 𝑟 = 𝑛2ℎ2 𝑍𝑚𝜋𝑒2 for H , Z = 1, so 𝑟 = 𝜖0𝑛 2ℎ2 𝑚𝜋𝑒2 ………..(5) 𝑟 = 𝑛2 × 0.529 Å imputing the values of h, m, e, 𝜖0 and π Radius of an orbit is directly proportional to the principal quantum number. Energy of electron in each orbit For hydrogen atom, the energy of the revolving electron, E, is the sum of its kinetic energy ( 𝑚𝑉2 2 ) and potential energy (− 𝑒2 4π𝜖0𝑟 ). 𝐸 = 𝑚𝑉2 2 − 𝑒2 4π𝜖0𝑟 -------(7) From equation (3), we have 𝑚𝑉2= 𝑒2 4π𝜖0𝑟 where Z = 1 for hydrogen atom. Thus, 𝐸 = 1 2 x 𝑒2 4π𝜖0𝑟 − 𝑒2 4π𝜖0𝑟 = − 1 8 𝑒2 π𝜖0𝑟 -------(8) Substituting the values of r form equation 5, we get 𝐸 = − 𝑒2 8𝜋𝜖0 × 𝑚𝜋𝑒2 𝜖0𝑛 2 ℎ2 = − 𝑚𝑒4 8𝜖0 2𝑛2 ℎ2 -------(9) Now putting the value of m, π, e and h, we get, 𝐸= − 1311.8 𝑛2 Kjmole-1-------(10) Energy of an electron is inversely proportional to the principal quantum number. Isotopes: The atoms having same atomic number but different atomic mass number are called Isotope. E.g. 1H 1, 1H 2, 1H 3 are all isotopes of hydrogen Isobars: Nuclides having the same mass number but having the different Proton/Atomic number are called Isobar. Isotones: Atoms of different elements having different mass number and different atomic number but same neutron number are called Isotones. isobars Isotopes, isobar and isotones Heisenberg’s uncertainty principle states that it is impossible to know precisely and accurately both the position and momentum of a particles simultaneously. It is also stated that the product of the uncertainty in position and the uncertainty in momentum of a particle can be no smaller than Planck’s constant divided by 4π . Thus, letting ∆ x be the uncertainty in the x coordinate of the particle and letting ∆px be the uncertainty in the momentum in the x direction, we have Applicability of uncertainty principle The uncertainty product is negligible in case of large objects. For a moving ball of iron weighing 500 g, the uncertainty expression assumes the form Δx × mΔν ≥ ℎ 2π or,Δx × Δν ≥ ℎ 4mπ ≈ 6.625 × 10−27 4 × 500 × 3.14 ≈ 5 × 10-31 erg sec g–1 which is very small and thus negligible. Therefore for large objects, the uncertainty of measurements is practically nil. But for an electron of mass m = 9.109 × 10– 28 g, the product of the uncertainty of measurements is quite large as Δx × mΔν ≥ ℎ 2π or,Δx × Δν ≥ ℎ 4mπ ≈ 6.625 × 10−27 4 ×9.109 × 10– 28× 3.14 ≈ 0.3 erg sec g–1 This value is large enough in comparison with the size of the electron and is thus in no way negligible. It is therefore very clear that the uncertainty principle is only important in considering measurements of small particles comprising an atomic system. Louis de Broglie Louis de Broglie reasoned that if light (considered as a wave) exhibits particle aspects, then perhaps particles of matter show characteristics of waves under the proper circumstances. He therefore postulated that a particle of matter of mass m and speed v has an associated wavelength, by analogy with light: 𝜆 = ℎ mv Derivation of de Broglie equation According to Planck, The photon energy E is given by 𝐸 = ℎ𝜈------(1) Where ℎ is the Planck’s constant, 𝜈 is the frequency of radiation. By applying Einstein’s mass- energy relationship, the energy associated with photon of mass ‘m’ is given as 𝐸 = 𝑚𝑐2------(2) Where c is the velocity of the radiation, From equation (1) and (2), we get 𝑚𝑐2 = ℎ𝜈 = ℎ 𝑐 𝜆 ∵ 𝜈 = 𝑐 𝜆 Or, 𝑚𝑐 = ℎ 𝜆 Or, 𝑝 = ℎ 𝜆 Or, Momentum = ℎ Wavelength Or, Momentum ∝ 1 Wavelength ………..(3), this equation (3) is called De Broglie equation. 2. Angular Momentum Quantum Number (l) (Also Called Azimuthal Quantum Number) This quantum number distinguishes orbitals of given n having different shapes; it can have any integer value from 0 to n-1. Within each shell of quantum number n, there are n different kinds of orbitals, each with a distinctive shape denoted by an l quantum number. For example, if an electron has a principal quantum number of 3, the possible values for l are 0, 1, and 2. Thus, within the M shell (n =3), there are three kinds of orbitals, each having a different shape for the region where the electron is most likely to be found. Although the energy of an orbital is principally determined by the n quantum number, the energy also depends somewhat on the l quantum number (except for the H atom). For a given n, the energy of an orbital increases with l. Orbitals of the same n but different l are said to belong to different subshells of a given shell. The different subshells are usually denoted by letters as follows: Quantum Number 3. Magnetic Quantum Number (l) This quantum number distinguishes orbitals of given n and l—that is, of given energy and shape but having a different orientation in space; the allowed values are the integers from -l to l. For l = 0 (s subshell), the allowed l quantum number is 0 only; there is only one orbital in the s subshell. For l =1 ( p subshell), l = -1, 0, and 1; there are three different orbitals in the p subshell. The orbitals have the same shape but different orientations in space. there are 2l +1 orbitals in each subshell of quantum number l. Quantum Number 4. Spin Quantum Number (s) This quantum number refers to the two possible orientations of the spin axis of an electron; possible values are -1/2 and +1/2. An electron acts as though it were spinning. Such an electron spin would give rise to a circulating electric charge that would generate a magnetic field. In this way, an electron behaves like a small bar magnet Quantum Number For n = 4, there are four possible values of azimuthal quantum number. l = 0, 1, 2, and 3 Thus fourth energy level consists of four subshells or orbitals which are designated as 4s, 4p, 4d and 4f. What is the total number of orbitals associated with the principal quantum number n = 4? Write the four quantum numbers for an electron in a 4p orbital. For 4p, Principal quantum number is n = 4 Since p subshell is represented by l = 1, thus for 4p the azimuthal quantum number is 1. When l = 1, then, magnetic quantum number m = +1, 0, -1. 4p n l m s 4 1 +1 + 1 2 , − 1 2 0 + 1 2 , − 1 2 -1 + 1 2 , − 1 2 K.E = - ℎ2 8𝜋 2mΨ . 𝑑2Ψ 𝑑𝑥2 ………(6) Total energy is the sum of kinetic energy and potential energy E = K.E + P.E Or K.E = E- P.E = - ℎ2 8𝜋 2mΨ . 𝑑2Ψ 𝑑𝑥2 Or, 𝑑2Ψ 𝑑𝑥2 = - 8𝜋 2m ℎ2 (E- P.E)Ψ Or, 𝑑2Ψ 𝑑𝑥2 + 8𝜋 2m ℎ2 (E- P.E)Ψ = 0……… (7) This is Schrödinger’s equation in one dimension. It need be generalised for a particle whose motion is described by three space coordinates x, y and z. Thus, 𝑑2Ψ 𝑑𝑥2 + 𝑑2Ψ 𝑑𝑦2 + 𝑑2Ψ 𝑑𝑧2 + 8𝜋 2m ℎ2 (E- P.E)Ψ = 0 ………(8) This equation is called the Schrödinger’s Wave Equation. The first three terms on the left-hand side are represented by Δ2ψ. ∆2Ψ+ 8𝜋 2m ℎ2 (E- P.E)Ψ = 0 ………(9) Where, ∆2 = 𝑑2 𝑑𝑥2 + 𝑑2 𝑑𝑦2 + 𝑑2 𝑑𝑧2 is called Laplacian Operator. Schrödinger’s Wave Equation Information about a particle in a given energy level is contained in a mathematical expression called a wave function, ψ. Its square, ψ2, gives the probability of finding the particle within a region of space. The wave function and its square, ψ2, have values for all locations about a nucleus. Figure 1 shows values of ψ2 for the electron in the lowest energy level of the hydrogen atom along a line starting from the nucleus. Note that ψ2 is large near the nucleus (r = 0), indicating that the electron is most likely to be found in this region. The value of ψ2 decreases rapidly as the distance from the nucleus increases, but ψ2 never goes to exactly zero, although the probability does become extremely small at large distances from the nucleus. This means that an atom does not have a definite boundary, unlike in the Bohr model of the atom. Significance of ψ and ψ2 Plot of ψ2 for the lowest energy level of the hydrogen atom. The square of the wave function is plotted versus the distance, r, from the nucleus.