Electromagnetic Radiation Inorganic chemistry Electromagnetic Radiation Dr.Sadeem Albarody

Electromagnetic Radiation Electromagnetic radiation: type of energy that travels through space in the form of waves composed of electric field and magnetic fields Waves: Wavelength, λ in meters Frequency,  in cycles per sec, 1/s, s-1 or Hertz (Hz) Speed, c = 2.9979 x 108 m/s

Waves wavelength (): is the distance between corresponding points on adjacent waves (λ meters). 1m=10dc,10 amplitude: is the height of the wave.

Waves  in cycles per sec, s-1 or Hertz (Hz) frequency (): is the number of waves passing a given point per unit of time.  in cycles per sec, s-1 or Hertz (Hz) For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.

Electromagnetic Radiation All electromagnetic radiation travels at the same velocity: the speed of light ( C ) c=3.00  108 m/s. =c /

Exercise: 1-What is the wavelength of an (EM) that has a frequency of 4.21 x 1013 Hz ? 7.13 mm You are given f = 4.21 x 1013 Hz and c = 3.00 x 108 m/s (speed of all electromagnetic (EM) waves) Given: l = ? f = 4.21 x 1013 Hz c = 3.00 x 108 m/s The formula used in this problem is: c = f l Re-arrange formula so that: l = c         f . l = 3.00 x 108 m/s         4.21 x 1013 Hz (s) l = 7.1259 x 10 -6 m l = 7.13 x 10 -6 m

HOME WORK: The distinctive green color is caused by the interaction of the radiation with oxygen and has a frequency of 5.38 x 1014 Hz.What is the wavelength of this light? (λ = 557.6 nm)

Photoelectric effect 1905 – Albert Einstein Explained photoelectric effect (Nobel prize in physics in 1921) Light consists of photons, each with a particular amount of energy, called a quantum of energy Upon collision, each photon can transfer its energy to a single electron The more photons strike the surface of the metal, the more electrons are liberated and the higher is the current E = h where h is Planck’s constant, 6.63  10−34 J-s.

Photoelectric effect work function The photon energy required to liberate the electron . The work function is a property of the metal; different metals have different values for their work function.

The Nature of Energy Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: c =  E = h

The Black Body Radiation Classical physics cant explain the observed wavelength distribution of EM radiation from such a hot object. This problem is historically the problem that leads to the rise of quantum physics during the turn of 20th century

Problems included: blackbody radiation: The electromagnetic radiation emitted by a heated object photoelectric effect: Emission of electrons by an illuminated metal Atomic Spectra.

Black Body Radiation Problem An object at any temperature is emit thermal radiation Characteristics depend on the temperature and surface properties The thermal radiation consists of a continuous distribution of wavelengths from all portions of the EM spectrum

Black Body Radiation Problem BBR emitted at a frequency can be illustrated with a graph of the radiation intensity versus wavelength. Such a graph is called a blackbody radiation curve.

Black Body Radiation Solution in 1900 A “solution” was devised by the German physicist Max Planck. He developed a mathematical equation for blackbody radiation curve. This gives the correct formula but no physical insight.

He proposed that an oscillating atom in a blackbody can only exchange certain fixed values of energy. It can have zero energy, or a particular energy E, or 2E, or 3E, …. This means that the energy of each atomic oscillator is quantized. The energy E is called the fundamental quantum of energy for the oscillator.

The idea of quantization can be illustrated with the following figure. On the right, the cat can rest at any height above the floor. On the left, the cat can only rest at certain heights above the floor.

This means that: The right cat’s potential energy can assume any value. The left cat’s potential energy can only assume certain values.

This says the energy is quantized Planck determined that the basic quantum of energy is proportional to the frequency: The constant h is called Planck’s constant. The allowed energies are then This says the energy is quantized Each discrete energy value corresponds to a different quantum state

Blackbody Approximation A black body is an ideal system that absorbs all radiation incident on it A good approximation of a black body is a small hole leading to the inside of a hollow object The hole acts as a perfect absorber The nature of the radiation leaving the cavity through the hole depends only on the temperature of the cavity

In 1918 he was awarded the Nobel Prize for the discovery of the quantized nature of energy Introduced the concept of “quantum of action”

QUIZ This figure shows two stars in the constellation Orion. Betelgeuse appears to glow red, while Rigel looks blue in color. Which star has a higher surface temperature? (a) Betelgeuse (b) Rigel (c) They both have the same surface temperature. (d) Impossible to determine.

Atomic Spectra The third problem that classical physics could not resolve is the emission spectra of the elements. Imagine shining the light from a heated filament through a prism. The light is separated into a range of colors. This spectrum is called a continuous spectrum since it is a continuous band of colors.

Atomic Spectra Now imagine heating a gas-filled tube. The gas will emit some EM radiation. After this light passes through a prism, only certain lines of color appear.

Atomic Spectra This type of spectrum is called an emission-line spectrum. Because it is due to the light emitted by the gas and it is not continuous

Bohr Model of the Atom Bohr constructed a model of the atom called the Bohr model: 1-The nucleus is at the center and the electrons move about the nucleus in well-defined orbits. 2-Electrons in an atom can only occupy certain orbits (corresponding to certain energies). 3-Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.

4-Energy is only absorbed or emitted as to move an electron from one “allowed” energy state to another; the energy is defined by E = h The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation: RH is the Rydberg constant, 2.18  10−18 J, ni and nf are the initial and final energy levels of the electron. RH = 1.0973732 x 107 m-1 RH = 10973732 cm

4-Transitions from one orbit to another involve discrete amounts of energy.

Energy Levels of Atoms An excited e- that returns to the ground state releases energy in the form of light. Review H2 Lab from regular chem!

Light Series Electron Jump: from any energy level down to… Name of Series Type of Spectrum …level 1 Lyman Ultraviolet Light …to level 2 Balmer Visible Light …to level 3 Paschen Infrared Light …to level 4 Brackett …to level 5 Pfund …to level 6 IR4

Rydberg Equation Calculating the energy released as an electron moves energy levels E = -2.178 x 10-18J (Z2) ( n2) Energy level: 1,2,3… Nuclear charge

The Wave Nature of Matter Louis de Broglie posited that if light can have wave and particle properties, matter should exhibit wave properties? 1-Louis de Broglie proposed that electrons have wavelike properties.  = h mv We know that light has wave-like properties. diffraction, refraction, etc. We also know light has particle-like properties. blackbody radiation, photoelectric effect, etc

The Wave Nature of Matter  

The Wave Nature of Matter photons exhibit mostly wave properties because mass is negligible. electrons exhibit particulate and wave properties you exhibit particulate behavior, waves are so small, not observed. Wave properties Particulate properties

Quiz  

Quantum mechanics 2-One unexplained result of the Bohr model was that the angular momentum of the electron in its orbit is quantized. Since the electron acts like a wave, the wave must fit along the circumference of the electron’s orbit. He suggested that the wavelength of a particle depends on its momentum. momentum is the product of mass and velocity

Example What is the de Broglie wavelength of an electron with speed 2.19×106 m/s? electron mass is 9.11×10-31 kg

Since the circumference must equal some multiple of the wavelength: This means This supports the Bohr model.

Example What is the de Broglie wavelength of an electron with speed 2.19×106 m/s? electron mass is 9.11×10-31 kg. find the radius of the smallest orbit in the hydrogen atom.

Quantum mechanics 3- Another limitation of the Bohr model was that it assumed we could simultaneously know both the position and momentum of an electron exactly. Werner Heisenberg’s development of quantum mechanics leads him to the observation that is impossible to determine simul tan eously both the position and momentum of a particle (Heisenberg Uncertainty Principle) Uncertainty in position Uncertainty in momentum

Modifications of the Bohr Theory – Elliptical Orbits Bohr’s concept of quantization of angular momentum led to the principal quantum number n, which determines the energy of the allowed states of hydrogen Sommerfeld theory retained n, but also introduced a new quantum number ℓ called the orbital quantum number, where the value of ℓ ranges from 0 to n - 1 in integer steps.

According to this model, an electron in any one of the allowed energy states of a hydrogen atom may move in any one of a number of orbits corresponding to different ℓ values

Modifications of the Bohr Theory – Zeeman Effect The Zeeman effect is the splitting of spectral lines in a strong magnetic field This indicates that the energy of an electron is slightly modified when the atom is immersed in a magnetic field A new quantum number, m ℓ, called the orbital magnetic quantum number, had to be introduced m ℓ can vary from - ℓ to + ℓ in integer steps

Modifications of the Bohr Theory – Fine Structure High resolution spectrometers show that spectral lines are, in fact, two very closely spaced lines, even in the absence of a magnetic field This splitting is called fine structure Another quantum number, ms, called the spin magnetic quantum number, was introduced to explain the fine structure

Modifications of the Bohr Theory – Fine Structure It is convenient to think of the electron as spinning on its axis The electron is not physically spinning There are two directions for the spin Spin up, ms = ½ Spin down, ms = -½ There is a slight energy difference between the two spins and this accounts for the Zeeman effect

The Pauli Exclusion Principle No two electrons in an atom can ever be in the same quantum state In other words, no two electrons in the same atom can have exactly the same values for n, ℓ, m ℓ, and ms This explains the electronic structure of complex atoms as a succession of filled energy levels with different quantum numbers

Example Question 1: What are values for l and m when n = 3? Solution: For 'l' = 0 m = 0 (s-orbital) For 'l' = 1 M = +1, 0, -1 (p-orbital) For 'l' = 2 m = +2, +1, 0, -1, -2 (d-orbital)  Question 2: Which orbital is specified by l = 2 and n = 3? Solution: 'l' = 2 means 'd' orbitals The given orbital is '3d'.

Home work (20 marks)