Chapter 29: Quantum Physics PDF

Chapter 29: Quantum Physics Mrs. Pooja Brahmaiahchari Introduction Quantum mechanics is the branch of physics needed to deal with submicroscopic objects. Because these objects are smaller than we can observe directly with our senses and generally must be observed with the aid of ins...

Chapter 29: Quantum Physics Mrs. Pooja Brahmaiahchari Introduction Quantum mechanics is the branch of physics needed to deal with submicroscopic objects. Because these objects are smaller than we can observe directly with our senses and generally must be observed with the aid of instruments, parts of quantum mechanics seem as foreign and bizarre as parts of relativity.  In quantum mechanics we conceptualize discrete “electron clouds” around the nucleus. Atoms, molecules, and fundamental electron and proton charges are all examples of physical entities that are quantized. Quantized is the opposite of continuous. Quantum physics is the branch of physics that deals with small objects and the quantization of various entities, including energy and angular momentum. Quantization of Energy Energy is quantized in some systems, meaning that the system can have only certain energies and not a continuum of energies, unlike the classical case. This would be like having only certain speeds at which a car can travel because its kinetic energy can have only certain values. We also find that some forms of energy transfer take place with discrete lumps of energy.  An ideal radiator is one that has an emissivity of 1 at all wavelengths and, thus, is jet black. Ideal radiators are therefore called blackbodies, and their EM radiation is called blackbody radiation. It was discussed that the total intensity of the radiation varies as T4, fourth power of the absolute temperature of the body, and that the peak of the spectrum shifts to shorter wavelengths at higher temperatures. All of this seems quite continuous, but it was the curve of the spectrum of intensity versus wavelength that gave a clue that the energies of the atoms in the solid are quantized.  The German physicist Max Planck (1858–1947) used the idea that atoms and molecules in a body act like oscillators to absorb and emit radiation. The energies of the oscillating atoms and molecules had to be quantized to correctly describe the shape of the blackbody spectrum. Planck deduced that the energy of an oscillator having a frequency is given by 1 𝐸 = 𝑛+ ℎ𝑓 2 Here n is any nonnegative integer (0, 1, 2, 3, …). The symbol h stands for Planck’s constant, given by h = 6.626x10-34 J. s The equation means that an oscillator having a frequency can have its energy increase or decrease only in discrete steps of size ∆𝐸 = ℎ𝑓  Using the quantization of oscillators, Planck was able to correctly describe the experimentally known shape of the blackbody spectrum. This was the first indication that energy is sometimes quantized on a small scale and earned him the Nobel Prize in Physics in 1918. Although Planck’s theory comes from observations of a macroscopic object, its analysis is based on atoms and molecules. It was such a revolutionary departure from classical physics that Planck himself was reluctant to accept his own idea that energy states are not continuous.  The general acceptance of Planck’s energy quantization was greatly enhanced by Einstein’s explanation of the photoelectric effect, which took energy quantization a step further. Planck was fully involved in the development of both early quantum mechanics and relativity. He quickly embraced Einstein’s special relativity, published in 1905, and in 1906 Planck was the first to suggest the correct formula for relativistic momentum, 𝑝 = 𝛾𝑚𝑢. Atomic Spectra Now let us turn our attention to the emission and absorption of EM radiation by gases. The Sun is the most common example of a body containing gases emitting an EM spectrum that includes visible light. We also see examples in neon signs and candle flames. We now know that these EM emissions come from electrons transitioning between energy levels in individual atoms and molecules; thus, they are called atomic spectra. Atomic spectra remain an important analytical tool today.  One of the most important characteristics of these spectra is that they are discrete. By this we mean that only certain wavelengths, and hence frequencies, are emitted. This is called a line spectrum. The picture in previous slide is Emission spectrum of oxygen. When an electrical discharge is passed through a substance, its atoms and molecules absorb energy, which is reemitted as EM radiation. The discrete nature of these emissions implies that the energy states of the atoms and molecules are quantized. The Photoelectric Effect When light strikes materials, it can eject electrons from them. This is called the photoelectric effect, meaning that light (photo) produces electricity. One common use of the photoelectric effect is in light meters, such as those that adjust the automatic iris on various types of cameras. In a similar way, another use is in solar cells, as you probably have in your calculator or have seen on a roof top or a roadside sign. These make use of the photoelectric effect to convert light into electricity for running different devices.  The figure in previous shows an evacuated tube with a metal plate and a collector wire that are connected by a variable voltage source, with the collector more negative than the plate. When light (or other EM radiation) strikes the plate in the evacuated tube, it may eject electrons. If the electrons have energy in electron volts (eV) greater than the potential difference between the plate and the wire in volts, some electrons will be collected on the wire.  Since the electron energy in eV is qV, where q is the electron charge and V is the potential difference, the electron energy can be measured by adjusting the retarding voltage between the wire and the plate. The voltage that stops the electrons from reaching the wire equals the energy in eV. The number of electrons ejected can be determined by measuring the current between the wire and plate. The more light, the more electrons; a little circuitry allows this device to be used as a light meter.  Einstein realized that there were several characteristics of the photoelectric effect that could be explained only if EM radiation is itself quantized: The apparently continuous stream of energy in an EM wave is actually composed of energy quanta called photons. In his explanation of the photoelectric effect, Einstein defined a quantized unit or quantum of EM energy, which we now call a photon, with an energy proportional to the frequency of EM radiation. In equation form, the photon energy is 𝐸 = ℎ𝑓 Where E is energy of photon, h is planck’s constant and f is the frequency of light.  The energy of photons is absorbed and emitted in lumps, not continuously. This is exactly consistent with Planck’s quantization of energy levels in blackbody oscillators, since these oscillators increase and decrease their energy in steps of by absorbing and emitting photons having E = hf. We do not observe this with our eyes, because there are so many photons in common light sources that individual photons go unnoticed.  The photoelectric effect is a phenomenon in which the electrons are ejected from the metal surface when light of sufficient frequency is incident on it. Einstein suggested that light behaves like a particle and each particle of light had a energy called as PHOTONS. When photons falls on the metal surface its energy is transferred to the electrons. A part of energy is utilized in removing the electrons from metal surface and remaining goes into giving KE for the ejected electrons. Properties of EM radiation 1. If frequency of EM radiation is varied, For a given material, there is a threshold frequency for the EM radiation below which no electrons are ejected, regardless of intensity. Individual photons interact with individual electrons. Thus if the photon energy is too small to break an electron away, no electrons will be ejected. If EM radiation was a simple wave, sufficient energy could be obtained by increasing the intensity. 2. Once EM radiation falls on a material, electrons are ejected without delay. As soon as an individual photon of a sufficiently high frequency is absorbed by an individual electron, the electron is ejected. If the EM radiation were a simple wave, several minutes would be required for sufficient energy to be deposited to the metal surface to eject an electron. 3. The number of electrons ejected per unit time is proportional to the intensity of the EM radiation and to no other characteristic. High-intensity EM radiation consists of large numbers of photons per unit area, with all photons having the same characteristic energy hf. 4. If we vary the intensity of the EM radiation and measure the energy of ejected electrons, we find the following: The maximum kinetic energy of ejected electrons is independent of the intensity of the EM radiation. Since there are so many electrons in a material, it is extremely unlikely that two photons will interact with the same electron at the same time, thereby increasing the energy given it. Instead, increased intensity results in more electrons of the same energy being ejected. If EM radiation were a simple wave, a higher intensity could give more energy, and high energy electrons would be ejected. 5. The kinetic energy of an ejected electron equals the photon energy minus the binding energy of the electron in the specific material. An individual photon can give all of its energy to an electron. The photon’s energy is partly used to break the electron away from the material. The remainder goes into the ejected electron’s kinetic energy. In equation form, this is given by 𝐾𝐸𝑒 = ℎ𝑓 − 𝐵𝐸 where 𝐾𝐸𝑒 is the maximum kinetic energy of the ejected electron, hf is the photon’s energy, and BE is the binding energy of the electron to the particular material. (BE is sometimes called the work function of the material.)  This equation, due to Einstein in 1905, explains the properties of the photoelectric effect quantitatively. An individual photon of EM radiation (it does not come any other way) interacts with an individual electron, supplying enough energy, BE, to break it away, with the remainder going to kinetic energy. The binding energy is 𝐵𝐸 = ℎ𝑓0 , where 𝑓0 is the threshold frequency for the particular material. Figure shows a graph of maximum KEe versus the frequency of incident EM radiation falling on a particular material.  A graph of the kinetic energy of an ejected electron, 𝐾𝐸𝑒 , versus the frequency of EM radiation impinging on a certain material. There is a threshold frequency below which no electrons are ejected, because the individual photon interacting with an individual electron has insufficient energy to break it away. Above the threshold energy, 𝐾𝐸𝑒 increases linearly with f, consistent with 𝐾𝐸𝑒 = ℎ𝑓 − 𝐵𝐸. The slope of this line is h— the data can be used to determine Planck’s constant experimentally. Einstein gave the first successful explanation of such data by proposing the idea of photons—quanta of EM radiation. 1. What is the longest-wavelength EM radiation that can eject a photoelectron from silver, given that the binding energy is 4.73 eV? 2. What is the binding energy in eV of electrons in magnesium, if the longest- wavelength photon that can eject electrons is 337 nm? 3. UV radiation having a wavelength of 120 nm falls on gold metal, to which electrons are bound by 4.82 eV. What is the maximum kinetic energy of the ejected photoelectrons? Photon Energies and the Electromagnetic Spectrum Ionizing Radiation A photon is a quantum of EM radiation. Its energy is given by E = hf and is related to the frequency and wavelength of the radiation by ℎ𝑐 𝐸 = ℎ𝑓 = 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑝ℎ𝑜𝑡𝑜𝑛 𝜆 where E is the energy of a single photon and is the speed of light. When working with small systems, energy in eV is often useful. Note that Planck’s constant in these units is ℎ = 4.14 𝑥 10−15 𝑒𝑉. 𝑠  Since many wavelengths are stated in nanometers (nm), it is also useful to know that hc = 1240 eV. Nm. These will make many calculations a little easier. All EM radiation is composed of photons. Figure shows various divisions of the EM spectrum plotted against wavelength, frequency, and photon energy.  It was noted that these types of EM radiation have characteristics much different than visible light. We can now see that such properties arise because photon energy is larger at high frequencies. Photons act as individual quanta and interact with individual electrons, atoms, molecules, and so on. The energy a photon carries is, thus, crucial to the effects it has. When we compare photon energies from the EM spectrum in Figure with energies, we can see how effects vary with the type of EM radiation. Gamma rays, a form of nuclear and cosmic EM radiation, can have the highest frequencies and, hence, the highest photon energies in the EM spectrum.  In fact, gamma rays are one type of ionizing radiation, as are x rays and UV, because they produce ionization in materials that absorb them. Because so much ionization can be produced, a single -ray photon can cause significant damage to biological tissue, killing cells or damaging their ability to properly reproduce. When cell reproduction is disrupted, the result can be cancer, one of the known effects of exposure to ionizing radiation. Since cancer cells are rapidly reproducing, they are exceptionally sensitive to the disruption produced by ionizing radiation. This means that ionizing radiation has positive uses in cancer treatment as well as risks in producing cancer.  A curve like this is obtained by detecting many photons, and it is apparent that the maximum energy is unlikely. This decelerating process produces radiation that is called bremsstrahlung (German for braking radiation). The second feature is the existence of sharp peaks in the spectrum; these are called characteristic x rays, since they are characteristic of the anode material. Characteristic x rays come from atomic excitations unique to a given type of anode material.  Ultraviolet radiation (approximately 4 eV to 300 eV) overlaps with the low end of the energy range of x rays, but UV is typically lower in energy. UV comes from the de-excitation of atoms that may be part of a hot solid or gas. A UV photon has sufficient energy to ionize atoms and molecules, which makes its effects different from those of visible light. UV thus has some of the same biological effects as γ rays and x rays. For example, it can cause skin cancer and is used as a sterilizer.  The major difference is that several UV photons are required to disrupt cell reproduction or kill a bacterium, whereas single γ -ray and X-ray photons can do the same damage. One of the beneficial aspects of UV is that it triggers the production of vitamin D in the skin, whereas visible light has insufficient energy per photon to alter the molecules that trigger this production. Infantile jaundice is treated by exposing the baby to UV (with eye protection), called phototherapy, the beneficial effects of which are thought to be related to its ability to help prevent the buildup of potentially toxic bilirubin in the blood.  The range of photon energies for visible light from red to violet is 1.63 to 3.26 eV, respectively. These energies are on the order of those between outer electron shells in atoms and molecules. This means that these photons can be absorbed by atoms and molecules. A single photon can actually stimulate the retina, for example, by altering a receptor molecule that then triggers a nerve impulse. Photons can be absorbed or emitted only by atoms and molecules that have precisely the correct quantized energy step to do so. There are some noticeable differences in the characteristics of light between the two ends of the visible spectrum that are due to photon energies  Red light has insufficient photon energy to expose most black-and-white film, and it is thus used to illuminate darkrooms where such film is developed. Since violet light has a higher photon energy, dyes that absorb violet tend to fade more quickly than those that do not. Transparent materials, such as some glasses, do not absorb any visible light, because there is no energy step in the atoms or molecules that could absorb the light. Since individual photons interact with individual atoms, it is nearly impossible to have two photons absorbed simultaneously to reach a large energy step. Because of its lower photon energy, visible light can sometimes pass through many kilometers of a substance, while higher frequencies like UV, x ray, and γ rays are absorbed, because they have sufficient photon energy to ionize the material.  Infrared radiation (IR) has even lower photon energies than visible light and cannot significantly alter atoms and molecules. IR can be absorbed and emitted by atoms and molecules, particularly between closely spaced states. IR is extremely strongly absorbed by water, for example, because water molecules have many states separated by energies on the order of 10−5 𝑒𝑉 𝑡𝑜 10−2 𝑒𝑉. Microwaves are the highest frequencies that can be produced by electronic circuits, although they are also produced naturally. Thus, microwaves are similar to IR but do not extend to as high frequencies.  Photon energies for both IR and microwaves are so low that huge numbers of photons are involved in any significant energy transfer by IR or microwaves. Visible light, IR, microwaves, and all lower frequencies cannot produce ionization with single photons and do not ordinarily have the hazards of higher frequencies. But one difference is that at very high intensity, strong electric and magnetic fields can be produced by photons acting together. Such electromagnetic fields (EMF) can actually ionize materials. 4. State the following statement is true or false : “ Photoelectric emission is possible at all frequencies”? a. True b. False 5. What happens to the wavelength of a photon after it collides with an electron? A. Increases B. Decreases C. Constant D. Remains same THANK YOU