Chapter 4: Arrangement of Electrons in Atoms Section 1: The Development of a New Atomic Model Objectives: *Explain the mathematical relationship among the speed, wavelength, and frequency of electromagnetic radiation. *Discuss the dual wave-particle nature of light. *Discuss the significance of the photoelectric effect and the line-emission spectrum of hydrogen to the development of the atomic model. *Describe the Bohr model of the hydrogen atom. “ The Rutherford model of the atom was an improvement over previous models, but it was incomplete. It did not explain how the atom’s negatively charged particles are distributed in the space surrounding its positively charged nucleus. After all, it was well known that oppositely charged particles attract each other. So what prevented the negative electrons from being drawn into the positive nucleus? A new atomic model was developed in the twentieth century, which resulted from investigations into the way light is absorbed and emitted by matter. ” Scientists discovered that a close relationship exists between light and an atom’s electrons, which led to a revolutionary view of the nature of energy, matter, and atomic structure. Properties of Light *Prior to 1900, it was believed that light’s only behavior was as a wave. *It was later discovered that light could have particle-like characteristics, too. Despite having particle-like characteristics, light’s properties can still be described in terms of waves. Let’s review the wavelike properties of light to help you all understand the basic theory of light as it existed at the beginning of the twentieth century, which will eventually lead to understanding electron behavior. The Wave Description of Light First, we need to recall what electromagnetic radiation is, which you should have learned in Physical Science. Electromagnetic Radiation: a form of energy that exhibits wavelike behavior as it travels through space. Can anyone recall the 7 types of electromagnetic radiation? 1. 2. 3. 4. 5. 6. 7. Gamma rays X rays Ultraviolet light Visible light Infrared light Microwaves Radio waves Together, all the forms of electromagnetic radiation form the electromagnetic spectrum. Electromagnetic Spectrum Other important facts about the wavelike behavior of light: 1. All forms of electromagnetic radiation move at a constant speed of 3.00 x 10⁸ meters per second (m/s) through a vacuum and at slightly slower speeds through matter. THIS IS ALSO KNOWN AS THE SPEED OF LIGHT. 2. Significant feature of wave motion: its repetitive nature, which is characterized by wavelength and frequency. 3. Wavelength: the symbol we use is λ. It is the distance between corresponding points on adjacent waves. We use a distance unit to express wavelength, which can include meters, centimeters, and nanometers. 4. Frequency: the symbol we use is ν. It is the number of waves that pass a given point in a specific time, which is usually 1 second. Frequency is expressed in waves/second. One wave/second is called a hertz (Hz). Illustration of Wavelength and Frequency Frequency and wavelength are mathematically related to each other. We write this mathematical relationship in the following way: c = λν c is the speed of light in m/s λ is the wavelength in m ν is the frequency in s⁻¹ We’ve already learned what the speed of light is. Who can tell me what it is? Because the speed of light (c) is the same for all electromagnetic radiation, λν is a constant, and we know that λ is inversely proportional to ν. Who can tell me what that means? As the wavelength of light decreases, its frequency increases OR as the wavelength of light increases, its frequency decreases. The Photoelectric Effect Scientists conducted experiments in the 1900s involving the interactions of light and matter that the wave theory of light could not explain. Photoelectric Effect: refers to the emission of electrons from a metal when light shines on the metal. *Photoelectric effect involved the frequency (ν) of the light striking the metal. *For a given metal, no electrons were emitted if the light’s frequency (ν) was below a certain minimum, regardless of the light’s intensity. *Light was known to be a form of energy that was capable of knocking loose an electron from a metal. *The wave theory predicted that light of any frequency could supply enough energy to eject an electron. *Scientists needed to explain why the light had to be of a minimum frequency (ν) in order for the photoelectric effect to occur. Basically, the photoelectric effect causes electrons to be ejected from the surface of a metal when light of high enough frequency hits the metal’s surface. Take a look at the diagram to the right. The Particle Description of Light *Max Planck studied the emission of light by hot objects in the 1900s. *Proposal: a hot object does not emit electromagnetic energy continuously, as would be expected if the energy emitted were in the form of waves. *He suggested that the object emits energy in small, specific packets called quanta. *A quantum of energy is the minimum quantity of energy that can be lost or gained by an atom. *Planck proposed a mathematical relationship between a quantum of energy and the frequency of radiation: E = hν E is the energy in joules (J) of a quantum of radiation h is Planck’s constant: 6.626 x 10⁻³⁴ J•s ν is the frequency of the radiation emitted in s⁻¹ Albert Einstein expanded on Planck’s theory by introducing the radical idea that electromagnetic radiation has a dual wave-particle nature. What does this mean? Light exhibits many wavelike properties, but it can also be thought of as a stream of particles. Each particle of light carries a quantum of energy. Einstein called these photons. Photon: a particle of electromagnetic radiation having zero mass and carrying a quantum of energy. The energy of a particular photon depends on the frequency of the radiation. We can look at the equation Planck gave us in this way: Ephoton = hν Einstein’s explanation: He proposed that electromagnetic radiation is absorbed by matter only in whole numbers of photons. In order for an electron to be ejected from a metal surface, the electron must be struck by a single photon possessing at least the minimum energy required to knock the electron loose. According to the equation we just learned, this minimum energy corresponds to a minimum frequency. If a photon’s frequency is below the minimum, then the electron remains bound to the metal surface. Electrons in different metals are bound either more tightly or less tightly, so different metals require different minimum frequencies to exhibit the photoelectric effect. Think of it this way: If you were throwing balls at milk bottles to try to knock them over to win a prize at a carnival, would you choose to throw 3 baseballs or 12 table-tennis balls? You would choose the baseballs, because each table-tennis ball would not have enough energy to knock over a milk bottle. Similarly, because of the photoelectric effect, an electron remains bound to a metal unless a single photon with the required minimum energy hits the metal with enough energy to eject the electron.