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- 1. Atomic Emission Spectra - Origin of Spectral Lines When a sample of gaseous atoms of an element at low pressure is subjected to an input of energy, such as from an electric discharge, the atoms are themselves found to emit electromagnetic radiation. On passing through a very thin slit and then through a prism the light (electromagnetic radiation) emitted by the excited atoms is separated into its component frequencies. Solids, liquids and dense gases glow at high temperatures. The emitted light, examined using a spectroscope, consists of a continuous band of colours as in a rainbow. A continuous spectrum is observed. This is typical of matter in which the atoms are packed closely together. Gases at low pressure behave quite differently. The excited atoms emit only certain frequencies, and when these are placed as discreet lines along a frequency scale an atomic emission spectrum is formed. The spectral lines in the visible region of the atomic emission spectrum of barium are shown below. Spectral lines exist in series in the different regions (infra-red, visible and ultra-violet) of the spectrum of electromagnetic radiation. The spectral lines in a series get closer together with increasing frequency. Each element has its own unique atomic emission spectrum.
- 2. The problem was now to explain the observations outlined above... It was necessary to explain how electrons are situated in atoms and why atoms are stable. Much of the following discussion refers to hydrogen atoms as these contain only one proton and one electron making them convenient to study. Principal Quantum Levels, denoted by the Principal Quantum Number, n. Principal Quantum Level n = 1 is closest to the nucleus of the atom and of lowest energy. When the electron occupies the energy level of lowest energy the atom is said to be in its ground state. An atom can have only one ground state. If the electron occupies one of the higher energy levels then the atom is in an excited state. An atom has many excited states. Here's what happens... When a gaseous hydrogen atom in its ground state is excited by an input of energy, its electron is 'promoted' from the lowest energy level to one of higher energy. The atom does not remain excited but re-emits energy as electromagnetic radiation. This is as a result of an electron 'falling' from a higher energy level to one of lower energy. This electron transition results in the release of a photon from the atom of an amount of energy (E = h) equal to the difference in energy of the electronic energy levels involved in the transition. In a sample of gaseous hydrogen where there are many trillions of atoms all of the possible electron transitions from higher to lower energy levels will take place many times. A prism can now be used to separate the emitted electromagnetic radiation into its component frequencies (wavelengths or energies). These are then represented as spectral lines along an increasing frequency scale to form an atomic emission spectrum. The Bohr theory was a marvellous success... The Bohr theory was a marvellous success in explaining the spectrum of the hydrogen atom. His calculated wavelengths agreed perfectly with the experimentally measured wavelengths of the spectral lines. Bohr knew that he was on to something; matching theory with experimental data is successful science. More recent theories about the electronic structure of atoms have refined these ideas, but Bohr's 'model' is still very helpful to us. For clarity, it is normal to consider electron transitions from higher energy levels to the same Principal Quantum Level. The diagram below illustrates the formation of aseries of spectral lines in the visible region of the spectrum of electromagnetic radiation for hydrogen, called the Balmer Series.
- 3. Atomic SpectrumA mi Light emitted or absorbed by single atoms contributes only very little to the colours of our surroundings. Neon signs (or other gas discharge tubes) as used for advertising, sodium or mercury vapour lamps show atomic emission; the colours of due to it. The aurora borealis (northern light) is very rare at ourfireworks are latitudes, and to appreciate the colours of cosmic objects, powerful telescopes are necessary. Neon, which gives red colour in a gas discharge, is a colourless gas. If the is spread out into different colours by a simple glass prism, thelight of the sun narrow absorption lines cannot be seen. Atomic structure Only with quantum theory atomic structure can be understood. Quantum theory is, so to say, the mathematical formulation of particle–wave duality. While we cannot dive into mathematical details here, the basic principles shall be sketched. Waves always have some spatial extension, while one may imagine the elementary, indivisible particles as being "pointlike". The fact that these apparently contradictory attributes are compatible in matter waves and also in light (photons) is hard to understand, but all experimental data point out that this is the case. Thus the electrons bound by electric force to an atomic nucleus (which contains almost all of the atom's mass) must be considered to be waves. Wavefunctions are used to calculate observable quantities; in particular, the probability to find the (pointlike) particle in some volume is given by the squared value of the wavefunction integrated over the volume. The hydrogen atom is the simplest of all atoms. Its nucleus carries one unit of positive elementary charge and thus binds only one electron to it. Its possible wavefunctions can be obtained as solutions of the Schrödinger equation. This is described in detail in all textbooks on quantum mechanics. For us it is important to realize that the electron forms some kind of standing wave. Some simple examples will be used to demonstrate general properties of oscillating systems, standing waves in particular.
- 4. Normal modes The exact way how a guitar's string vibrates depends on the spot where it has been plucked. It is always possible to describe the motion of the string as a superposition of simple modes which have the peculiar property that all parts of the string move sinusoidally with the same frequency and phase. These are called normal modes or eigenmodes. The superposition of different normal modes is heard as superposition of ground- and overtones. The picture below shows how a string vibrates in the lowest three normal modes. The motion is so fast that it cannot be resolved by the eye, one sees a sequence of nodes and antinodes. Important properties of three-dimensional waves cannot be seen on strings; vibrating membranes show somewhat more. Instead of nodes the normal modes exhibit nodal lines. In the case of vibrating metal plates, the nodal lines are known from classroom demonstrations as Chladni figures.
- 5. The Bohr Model of the Atom Niels Bohr proposed a model for the hydrogen atom that explained the spectrum of the hydrogen atom. The Bohr model was based on the following assumptions. The electron in a hydrogen atom travels around the nucleus in a circular orbit. The energy of the electron in an orbit is proportional to its distance from the nucleus. The further the electron is from the nucleus, the more energy it has. Only a limited number of orbits with certain energies are allowed. In other words, the orbits are quantized. The only orbits that are allowed are those for which the angular momentum of the electron is an integral multiple of Planck's constant divided by 2p. Light is absorbed when an electron jumps to a higher energy orbit and emitted when an electron falls into a lower energy orbit. The energy of the light emitted or absorbed is exactly equal to the Finally, Bohr restricted the number of orbits on the hydrogen atom by limiting the allowed values of the angular momentum of the electron. Any object moving along a straight line has a momentum equal to the product of its mass (m) times the velocity (v) with which it moves. An object moving in a circular orbit has an angular momentum equal to its mass (m) times the velocity (v) times the radius of the orbit (r). Bohr assumed that the angular momentum of the electron can take on only certain values, equal to an integer times Planck's constant divided by 2p. Bohr then used classical physics to show that the energy of an electron in any one of these orbits is inversely proportional to the square of the integer n. The difference between the energies of any two orbits is therefore given by
- 6. The Bohr Model vs. Reality At first glance, the Bohr model looks like a two-dimensional model of the atom because it restricts the motion of the electron to a circular orbit in a two-dimensional plane. In reality the Bohr model is a one-dimensional model, because a circle can be defined by specifying only one dimension: its radius, r. As a result, only one coordinate (n) is needed to describe the orbits in the Bohr model. Unfortunately, electrons aren't particles that can be restricted to a one-dimensional circular orbit. They act to some extent as waves and therefore exist in three- dimensional space. The Bohr model works for one-electron atoms or ions only because certain factors present in more complex atoms are not present in these atoms or ions. To construct a model that describes the distribution of electrons in atoms that contain more than one electron we have to allow the electrons to occupy three- dimensional space. We therefore need a model that uses three coordinates to describe the distribution of electrons in these atoms. Wave Functions and Orbitals We still talk about the Bohr model of the atom even if the only thing this model can do is explain the spectrum of the hydrogen atom because it was the last model of the atom for which a simple physical picture can be constructed. It is easy to imagine an atom that consists of solid electrons revolving around the nucleus in circular orbits. Erwin Schrdinger combined the equations for the behavior of waves with the de Broglie equation to generate a mathematical model for the distribution of electrons in an atom. The advantage of this model is that it consists of mathematical equations known as wave functions that satisfy the requirements placed on the behavior of electrons. The disadvantage is that it is difficult to imagine a physical model of electrons as waves. The Schrdinger model assumes that the electron is a wave and tries to describe the regions in space, or orbitals, where electrons are most likely to be found. Instead of trying to tell us where the electron is at any time, the Schrdinger model describes the probability that an electron can be found in a given region of space at a given time. This model no longer tells us where the electron is; it only tells us where it might be.
- 7. Emission Spectrum of Hydrogen When an electric current is passed through a glass tube that contains hydrogen gas at low pressure the tube gives off blue light. When this light is passed through a prism (as shown in the figure below), four narrow bands of bright light are observed against a black background. The Schrödinger equation supplies both the energies and the wavefunctions of the possible states of an electron in a Coulomb potential well (hydrogen atom and hydrogenlike ions). The zero of the energy scale is chosen to correspond to infinite separation of an electron at rest from the nucleus. Then the energies of the bound states are negative and the absolute values are equal to the minimum energy necessary to ionize the atom i.e. to separate the electron from the nucleus. E1 = –13.6 eV For an electron in a Coulomb potential, the energies depend only on the principal quantum number (which we have introduced by simply numbering the energies): En = E1/n2 , and thus the following level scheme results: Transitions from lower to higher states can occur if the necessary energy is supplied by an electromagnetic wave or by a collision with an other particle (if the temperature is high enough), and vice versa transitions from higher to lower states can occur through emission of radiation or in collisions with other atoms or molecules. The emitted photons carry the energy difference between initial and final state of the atom. For photons, the basic quantum mechanical relation between energy and frequency νholds (h is the Planck constant): Ephoton = h ν 1/λ = (1/nf 2 – 1/ni 2 ) |E1| / hc
- 8. Hydrogen Spectrum This spectrum was produced by exciting a glass tube of hydrogen gas with about 5000 volts from a transformer. It was viewed through a diffraction grating with 600 lines/mm. The colors cannot be expected to be accurate because of differences in display devices. At left is a hydrogen spectral tube excited by a 5000 volt transformer. The three prominent hydrogen lines are shown at the right of the image through a 600 lines/mm diffraction grating. An approximate classification of spectral colors: Violet (380-435nm) Blue(435-500 nm) Cyan (500-520 nm) Green (520-565 nm) Yellow (565- 590 nm) Orange (590-625 nm) Red (625-740 nm)
- 9. Measured Hydrogen Spectrum The measured lines of the Balmer series of hydrogen in the nominal visible regionare: Wavelength (nm) Relative Intensity Transition Color 383.5384 5 9 -> 2 Violet 388.9049 6 8 -> 2 Violet 397.0072 8 7 -> 2 Violet 410.174 15 6 -> 2 Violet 434.047 30 5 -> 2 Violet 486.133 80 4 -> 2 Bluegreen (cyan) 656.272 120 3 -> 2 Red 656.2852 180 3 -> 2 Red The red line of deuterium is measurably different at 656.1065 ( .1787 nm difference).
- 10. Flame test, spectroscopy Hydrogen is a colourless gas; under "normal" circumstances the atoms are bound in pairs to H2-molecules and nothing can be seen of the possibility that light may be absorbed or emitted. Air (mainly nitrogen and oxygen) and the noble gases are colourless, and the same holds for many other substances. To observe emission of light or even spectral lines, one has to supply energy to excite the atoms. In a gas discharge tube, the molecules are broken by collisions with electrons and ions, atoms are excited or even ionized by collisions, and then emission of light as well as absorption can be observed. High temperatures have the same effect: in the sun there is atomic hydrogen in excited states, and in the solar spectrum the absorption lines of hydrogen can be seen. The temperature of the flame of a Bunsen burner is sufficiently high to split molecules and to ionize atoms which after recombination give off their energy by emission of photons. With traces of alkali metal or alkaline earth metal ions (and other substances as well) flames can be coloured; this is used in pyrotechnics and also for quick tests on these substances in minerals etc., see e.g the Wikipedia "Flame test". Lithium: Crimso n Sodium: intense orange- yellow Potassium : Lilac Calcium: Red- orange Strontium : Crimso n Barium: Light green Copper: Blue- green Boron: Bright green Lithium Boron Copper Calcium The spectra which, after the one of hydrogen, are the simplest to explain, are those of the alkali metals. These atoms have a single, relatively weakly bound electron in the outermost shell in addition to the spherical, noble-gas like core. The transitions of the outer electron from the low lying excited states to the ground state produce the visible part of the spectrum. The sodium spectrum is dominated by a line of 589 nm wavelength, coming from the transition from the 3p state to the 3s state. (In fact, due to fine structure splitting of the p state, which has not been dealt with here, this line is actually a doublet, i.e. two very closely neighbouring lines.)
- 11. Amr Mohamed Farok Sec6 Faculty of Science ,Helwan University Second year.-Physical&chemistry deparment SupervisionUnder Dr/ ElZine Nasr

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