Chapter 3 Quantum Theory and the Electronic Structure of Atoms Energy and Energy Changes Forms of Energy Kinetic energy energy of motion energy a b a b I A 1 B 1 2 3 C Ek mu2 where m mass in kg u velocity in m s thermal energy is associated with the random motion of atoms and molecules Change in temperature causes change in thermal 2 Potential energy energy possessed by an object by virtue of its position chemical energy energy stored within the bonds of chemical substances electrostatic energy potential energy that results from the interaction of charged particles Q charges d distance between charges Eel Q1Q2 d Eattraction negative Erepulsion positive General Information About Energy Potential and kinetic energy are interconvertible The total amount of energy in the universe is constant Energy cannot be created or destroyed This is known as the law of conservation of energy Units of and Calculation of Energy The SI unit for energy is the joule J 1 J 1kg m 2 s2 Because the joule is a very small unit of energy the kJ is often used 1 Calculate the kinetic energy in joules of a 14 3 gram object moving at a speed of 500m s 1 2 Calculate the velocity in m s of a 53 5 gram object with Ek 73 5 J II The Nature of Light Electromagnetic radiation includes visible light microwaves x rays radio waves infrared ultraviolet and gamma rays All of these forms of radiation transmit energy in the form of waves A Properties of Waves Wavelength distance between identical points on successive waves Measured in m cm nm or pm Frequency number of waves that pass a given point in 1 second cycles per second s 1 1 cycle second 1 hertz 1 Hz Amplitude the vertical distance from the midline of a wave to the top of a peak or bottom of a trough The Electromagnetic Spectrum Electromagnetic waves have a magnetic and an electric component These waves have the same wavelength frequency and speed but travel in mutually perpendicular planes The constructive and destructive interference that is observed in the Double Slit Experiment demonstrates the wave nature of light Please read about constructive and destructive interference in the textbook 2 1 2 3 B 1 2 The Electromagnetic Spectrum v I b g y o r Note that visible light is a very small portion of the electromagnetic spectrum ranging from 400 nm to 700 nm Wavelength and frequency are related to the speed at which radiation is propagated This speed is equal to the speed of light in a vacuum c 3 00 x 108 m s frequency and wavelength are inversely related c c Sample calculations Calculate the frequency of light that has a wavelength 670 nm 3 4 a b What is the wavelength of radiation that has a frequency of 3 14 x 1014 s 1 What region of the electromagnetic spectrum is this wavelength found 3 III Quantum Theory A Quantization of Energy 1 2 3 4 5 B 1 When a solid is heated it emits energy in the form of radiation referred to as blackbody radiation The energy emitted by a heated body is related to its wavelength Max Planck a German physicist proposed that energy emitted from or absorbed by an object is of a discrete quantity that he named a quantum The quantum is the smallest quantity of energy that can be emitted or absorbed The energy of a single quantum is given by the equation E h where h is a proportionality constant known as Planck s constant with a value of 6 63 x 10 34 J s and is the frequency According to quantum theory energy is always emitted in whole number multiples of h Photons and the Photoelectric Effect The Photoelectric Effect the phenomenon that electrons are ejected from the surface of certain metals when exposed to light of a minimum frequency known as the threshold frequency 2 The photoelectric effect a b c d e Electrons are ejected when light strikes the surface of a metal Electrons are ejected only if the frequency of the light is high enough that is when the threshold frequency is met The number of electrons ejected is proportional to the intensity brightness of the light but energies of the ejected electrons are not related to intensity Below the threshold frequency no electrons are ejected regardless of the intensity of the light These observations could not be explained by the wave theory of light 4 3 a b c d 4 a Einstein s Proposal Einstein suggested that a beam of light is a stream of massless particles that he named photons The energy of a photon is Ephoton h A photon must have a minimum frequency to eject an electron If the frequency is higher than the threshold frequency electrons will not only be ejected but they will acquire some kinetic energy KE h W where KE is the kinetic energy of the electron and W is the energy with which the electron is bound in the metal The more intense the light the greater number of electrons are ejected from the target metal and the higher the frequency of light the greater the kinetic energy of the ejected electrons The photoelectric effect established the now accepted theory of the dual nature of light that light behaves both as a particle and as a wave Sample calculations Calculate the wavelength in nm of light with energy 8 76 x 10 19 J per photon b For light of wavelength 620 nm calculate the number of photons per joule Determine the binding energy in joules of a metal if the maximum kinetic energy of an ejected electron is 2 93 x 10 19 J and its wavelength is 420 c nm 5 IV Bohr s Theory of the Hydrogen Atom General Information About Emission Spectra When an object is energized by heat or by some other energy source the object releases that energy in the form of light and heat The red color of a red hot burner is due to the emission of energy in the visible region that we can see as red but it is also emitting in the infrared region that we cannot see but can feel as heat Emission spectra can be Continuous all wavelengths of visible radiation are present as in a rainbow Line only specific wavelengths are present Atoms in the gas phase produce line spectra A 1 2 3 a b 4 5 Each element has a unique emission spectrum that can be used to identify the element 6 B The Line Spectrum of Hydrogen Niels Bohr Background Information 1 2 3 4 5 6 1 2 3 4 It was believed that electrons move about the nucleus in circular orbits If this were true according to classical physics the electron would lose energy and spiral into the nucleus Since this did not happen Bohr imposed a restriction on the electron of the hydrogen atom by stating that the electron in the hydrogen atom is allowed to occupy only certain orbits of