CHAPTER 4 Arrangement of Electrons in Atoms The Development of a New Atomic Model The Rutherford model was a great improvement over the Thomson model of the atom. But, there was one major question that needed to be answered. If the electrons are negatively charged and the nucleus is positively charged, what prevents the electrons from being drawn into the nucleus of an atom? Properties of Light Electromagnetic Radiation Prior to 1900, most scientists believed that light behaved as waves. Later, we found that light actually behaves as light and as particles. Most of light s behavior is due to its wave-like behavior. Electromagnetic radiation is any form of energy that exhibits wavelike behavior as it travels through space. Examples include X-rays, UV light, microwaves, visible light, and radio waves. All forms of EMR travel at the same speed, 3.0 x 10 8 m/s. This is called the speed of light.
Electromagnetic Spectrum Light as Waves Light is repetitive in nature like waves. Most of the measurable properties of waves are wavelength and frequency. Wavelength (!) is the distance between corresponding points on adjacent waves. Wavelength is measured mostly in nanometers (nm). (1nm = 1 x 10-9 m) Light as Waves (continued) Frequency (") is defined as the number of waves that pass a given point in a specific time, usually one second. Frequency is measured in hertz (Hz). 1 hertz = 1 wave/second Relating Wavelength and Frequency We can write a mathematical expression that relates frequency and wavelength. c =!" c is the speed of light,! is the wavelength, and " is the frequency. Since the speed of light is the same for all forms of EMR, the product of wavelength and frequency is constant. Wavelength and frequency are inversely proportional.
The Photoelectric Effect Wave theory could not explain everything involving the interactions between light and matter. One particular phenomenon that scientists were perplexed about was the photoelectric effect. The photoelectric effect refers to the emission of electrons from a metal when light shines on a metal. The Photoelectric Effect The central question surrounding the photoelectric effect focused on the frequency of the light that hits a metal. Particle theorists believed that there was a minimum frequency of light needed to remove electrons. Wave theorists believed that any frequency of light would knock loose electrons. Solution to the Photoelectric Effect Problem Planck s Constant Max Planck 1858-1947 1900: German physicist Max Planck proposes a partial solution to the photoelectric effect. Planck believes that hot objects give off EMR in small packets called quanta. A quantum is the minimum amount of energy that can be gained or lost by an atom. Planck finds a relationship that exists between quanta and the frequency of radiation. E = h" E (energy in joules), " (frequency), and h (Planck s constant) h = 6.626 x 10-34 J s
Einstein s Solution Photons, Photons, Photons 1905: Albert Einstein begins to expand on Planck s idea about quanta. Photons are particles of EMR that have zero rest mass and a quantum of energy. Einstein proposes that EMR has a wave-particle duality. Planck s equation can be rewritten in terms of a relationship between the energy of a photon and its frequency. He thought that since light and other forms of EMR can be thought of as waves, then EMR can also be thought of a a stream of particles. Ephoton = h" Einstein concluded that in order for an electron to be ejected from a metal, the electron must be struck by a photon with a minimum amount of energy. Albert Einstein 1879-1955 These particles were called photons. Light as Particles The minimum amount of energy needed is tied to the minimum frequency of the light needed. Different elements require different minimum frequencies to exhibit the photoelectric effect. Einstein wins a Nobel Prize in Physics in 1924 due to his work on the photoelectric effect. The Hydrogen-Atom LineEmission Spectrum Electrons can gain or lose energy. Electrons can be in the ground state or the excited state. The ground state of an electron is the lowest energy state for an atom and is the most stable. The excited state of an electron is any energy state higher in potential energy than the ground state.
The Hydrogen-Atom Line- Emission Spectrum (continued) Line Emission Spectrum When scientists passed an electric current through a vacuum containing hydrogen gas at low pressure, the excited hydrogen atoms had a pinkish glow. When this light was passed through a prism, the light split into specific color bands. This separation is called the line emission spectrum of hydrogen. Ground State vs. Excited State Ground State vs. Excited State In order for an atom (or electron) to reach an excited state from the ground state, energy must be added. Once an atom (or electron) reaches an excited state and begins to return to the ground state or lower energy state, the atom releases a photon of energy. This photon has an energy that is equal to the energy difference between the two energy states. Ephoton = E2 -E1 or Einitial - Efinal
Bohr Model of the Atom Bohr Model of the Atom Niels Bohr 1885-1962 1913: Danish physicist Niels Bohr proposes a model of the atom based on electrons and photon emission. Main idea: electrons revolve around the nucleus in circular paths called orbits. The atom and electrons are in the lowest energy state (ground state) when the electrons are in orbits closest to the nucleus. The energy of the electron increases as the distance between the orbit and nucleus increases. In order to move from orbit to orbit, a photon must be released or absorbed. Louis de Broglie 1892-1987 1924: French scientist Louis de Broglie suggests that electrons be considered as waves confined to the space around an atomic nucleus Werner Heisenberg 1901-1976 1927: German physicist Werner Heisenberg tries to detect electrons by using their interactions with photons. Since photons have about the same energy as electrons, finding a specific electron with a photon would cause the electron to veer off course.
Due to this fact, Heisenberg deduces that there is always an uncertainty in attempting to find an electron. Heisenberg Uncertainty Principle (HUP): It is impossible to know both the position and velocity of an electron. Erwin Schrödinger 1887-1961 1926: Austrian physicist Erwin Schrödinger uses the waveparticle duality to write an equation that treats electrons as waves. Pairing of the Schrödinger Wave Equation (SWE) with the HUP, leads to the foundation of modern quantum theory. When the SWE is solved, the results are called wave functions. Wave functions can only give the probability of finding an electron at a given point. Due to wave functions, we know that electrons do not travel in circular orbits. Instead, electrons reside in certain regions called orbitals (3-D regions about the nucleus that indicate the probable location of an electron).