Radiation - Electromagnetic Waves (EMR): wave consisting of oscillating electric and magnetic fields that move at the speed of light through space. Photon: a quantum of light or electromagnetic wave. Quantum: a discrete amount of energy. Quantized: a property of a system that occurs only in multiples of a minimum amount. n: integer - refers to energy levels in an atom. Photoelectron: electrons emitted in the photoelectric effect. Photoelectric Effect: the emission of electrons when electromagnetic radiation falls on an object. Incandescent body: object that emits light because of its high temperature.
TEXT pg 838 For 200 + years, physicists accumulated evidence for the wave nature of light and all forms of electromagnetic radiation. Maxwell (1831-1879) summarized in 4 equations everything that was known about electromagnetism and electromagnetic waves. Maxwell's main ideas: 1. Electric field lines start on a positive charge and end on a negative charge. 2. Magnetic field lines form closed loops and do not begin or end. 3. An electric field must exist around a changing magnetic field. 4. A changing electric field generates a magnetic field. Maxwell correctly predicted the existence of magnetic waves and their properties but he never saw experimental evidence of their existence. many years of experiments supported Maxwell's ideas as well as other classical physics theories. but, the world of physics was about to change.
Electric and Magnetic Fields Oscillating in Space Maxwell (1860s) predicted that electric charges moving in space during a time interval produced magnetic fields and magnetic fields moving in space during a time interval produced electric fields. when these two are produced simultaneously by vibrating atomic particles, the energy is transmitted as electromagnetic waves (radiation) across space. No medium is required. electric and magnetic fields oscillating at right angles (90 o ) to each other.
all electromagnetic radiation (light, radiowaves, x- rays, etc.) have a velocity in a vacuum, c = 3.00x10 8 m/s, and have frequencies and wavelengths related by c = f λ
In the early part of the twentieth century, Einstein's Theory of Relativity and the Quantum Theory shook the world of physics. Einstein's Theory of Relativity was theorized in a year but the Quantum Theory required almost 3 decades to unfold. Einstein (1879-1955)
Quantum Theory (Modern Physics) by the 1890s, scientists could not explain two troubling phenomena by using traditional Newtonian physics and the wave theory of electromagnetic waves (classical physics). 1. Blackbody Radiation Kirchhoff defined properties of a blackbody. A blackbody is a "perfect radiator" - it will emit a complete spectrum of electromagnetic radiation. objects that normally give off no radiation (appear black) can be made to do so by heating them. As the energy added to them increased, the type of radiation emitted changed. However, at a certain temperature and frequency (ultraviolet range) the graph and experimental data did not continue to produce the expected results.
pg 842 the power radiated by a blackbody depends on its temperature. P α T 4 the intensity is related to the frequency. pg 841 Kirchhoff needed a mathematical relationship. He could not determine the relationship so he challenged other scientists to come up with one. It was very complex. When physicists applied
classical physics theories, the graph obtained was not what was happening experimentally. this discrepancy between theory and observation was so shocking they called it the ultraviolet catastrophe. in 1900, Max Planck, did mathematically calculate the observed spectrum of radiation ONLY if he assumed that the vibrations of atoms could only have specific frequencies. According to Planck, the energy given off by atoms was E = nhf where n: an integer; 0, 1, 2.. f: frequency of vibration of atom h: mathematical constant h: Planck's constant = 6.63x10-34 J/Hz or J s
energy could only be specific values like hf, 2hf, 3hf, etc. pg 843 what Planck was essentially saying was that energy emitted or absorbed by atoms is QUANTIZED or exists in packages (bundles) of energy in specific sizes.
2. Photoelectric Effect the photoelectric effect confirms the theory of the quantization of energy. Hertz was attempting to verify Maxwell's theories. ( 1887) He assembled a circuit that generated an oscillating current that caused sparks to jump back and forth across a gap. He showed that the sparks were generating electromagnetic waves by seeing sparks forming in the gap of the receiver. with this, he verified Maxwell's theories that when the metal electrodes were exposed to ultraviolet light, the sparks were enhanced. 10 years later, the electron was discovered. Physicists suggested that the UV light had ejected electrons from the electrodes.
the ejection of electrons by UV light is the photoelectric effect. Lenard was the first to perform detailed experiments on the photelectric effect. (1902) He designed an apparatus where electrodes were sealed in a vacuum tube with a quartz window. (UV light does not penetrate glass.) pg 845 He wanted to determine the kinetic energy of the photoelectrons. When the emitter was - and the collector was +, he found that when the intensity increased, the current increased. when he switched the polarity of the emitter and the collector, he found that when he increased the
potential difference (voltage), the current would eventually stop. the potential difference that stopped all photoelectrons is the stopping potential. his findings: i) as the intensity of the light increases, energy absorbed by the surface increases and the number of photoelectrons increases. (classical physics) more intense light more energy absorbed by metal more electrons ejected from metal ii) classical physics also indicates that as the kinetic energy increases, the intensity increases. Lenard found that the kinetic energy is not affected by the intensity. Kinetic energy is determined ONLY by the frequency of the light.
KE dependent on frequency not intensity at roughly the same time as Planck, Einstein was working with vacuum tubes that had positive + (Anode) and negative - (Cathode) terminals separated by a gap. When a source of potential difference was applied, no current flowed. But when one terminal had electromagnetic radiation shone on it, a current began to flow. Current is the result of photoelectrons being ejected from the cathode by the radiation. The electrons travel to the anode. This did not happen with all EMR. Einstein proposed that 'photoelectrons' are only ejected from the surface of the metal terminal if the frequency of the EMR was above a certain minimum level called the threshold frequency, f o.
brightness or intensity of EMR had nothing to do with it, as EMR wave theory had predicted. in 1905, Einstein explained the photoelectric effect by saying EMR consisted of discrete bundles of energy which he called photons and that atoms would only absorb energy in these bundles. Photons have an energy, KE. They either give up all their energy or none of it. the energy possessed by these photons depended on the frequency of the EMR. E = hf Einstein was the first one to indicate that light and other EMR acted like particles. kinetic energy (E k ) of electron freed by photoelectric effect is given by: E k = hf - hf o W. hf o is sometimes replaced by Where hf is the total energy absorbed by an electron and hf o or W is called the work function of
the metal electrode and is the minimum energy needed to free the most loosely held electrons from the metal's surface. very few scientists accepted Einstein's arguments on the quantum (particle) theory of light. pg 849
Example. What is the E k of a photoelectron that absorbs energy from yellow light (f = 5.17x10 14 Hz) if the work function of the metal from which the electron is ejected is 2.78x10-19 J.
Expressing extremely small amounts of energy at the atomic level is usually done in units called electron volts (ev). 1 ev = 1.6x10-19 J So, answer from example: 6.4x10-20 J / 1.6x10-19 J/eV = 0.40 ev Stopping Potential (Cut-off Potential) to stop the photoelectric effect, you simply have to apply a potential difference in the opposite direction (cut-off potential) to balance the E k of released electrons. E = QV so E k = QV o where V o is the cut-off potential
Photons travel at the speed of light, therefore, they have zero rest mass. If a photon exists it moves at c. If it does not move with a speed, c, it ceases to exist.
Example 1. A helium neon laser produced light with a frequency of 4.7 x 10 14 Hz. What is the energy of the photons produced by this laser? Example 2. How many photons are emitted from a 1.50 x 10-3 W laser each second if the frequency of the laser light is 4.75 x 10 14 Hz? P 852 # 1-4
Compton Effect - momentum of a photon (1923) can something that has no mass have a momentum? Compton directed high energy x-rays at thin metal foil. as well as ejected electrons, Compton detected photons of lower frequency than x-rays. Compton explained that x-ray photons had collided (like particles). momentum was conserved so photons must have a mass-equivalence from Einstein's equation E = mc 2 m = c E 2 mass equivalence
a new way had to be used to calculate the momentum, p, of a photon. E E p = v = c = 2 2 c c E c But E = hf hc p = λ = c h λ so
hf = hf ' + 1 2 m e v 2 photon ' photon E = E + E electron
Example 1. Calculate the momentum of a 4.00 MeV photon. Example 2. Calculate the momentum of an electron which was accelerated from rest through a potential difference of 2.10 x 10 3 V.
DeBroglie - wave nature of matter (mid late 1920s) it was suggested that since EMR has particle properties (Compton) that the reverse was true and particles had wave characteristics. he determined that all particles (large or small) had wavelengths given by λ = h mv for small particles such as electrons, λs are large enough to be significant. why can't we observe the λs of large objects? Example. A 1.0 kg bowling ball is rolled at 5.0 m/s down the alley. What is its debroglie wavelength? λ = h.34 6.63x10 J / Hz = = 1.3x10 34 m mv 1.0kg(5.0m / s) This is such an extremely small λ that at the physical state in which we exist, we cannot detect wave motion.
Example 1. What is the kinetic energy of an alpha particle that has a wavelength of 1.46 x 10-15 m? Example 2. Through what potential difference must an electron be accelerated so that its wavelength is 2.75 x 10-11 m?
Wave - Particle Duality of Light modern age physics accepts that light sometimes acts as a wave and at other times acts like a particle. both matter and electromagnetic energy exhibit some properties of waves and some properties of particles.
Bohr model, emission spectra, energy levels problem: only 4 visible lines appeared when hydrogen atoms were energized. How do we explain this as a model for an atom. problem: electrons moving around a nucleus in roughly circular or elliptical paths would feel a centripetal force and would therefore have centripetal acceleration. But accelerating charges produce EMR, therefore these electrons should continuously emit energy, slow down, and eventually collapse into the nucleus. Obviously, this does not happen. Bohr's Explanation laws of electromagnetism do not apply at atomic level. within an atom energy is only absorbed or emitted when electrons change energy levels and this energy is QUANTIZED. electrons are either in lowest energy state (ground state) or certain allowed levels (excited state).
to move from one level to another, electrons must emit or absorb a photon with a certain amount of energy (E = hf). this absorbed or emitted photon had an energy value equal to the difference between energy levels. hf = E excited E ground Bohr found that for the hydrogen atom, the energy associated with a particular level was given by: E n 13.6 ev = 2 n Where n is principle quantum number (energy level) and energy is negative because energy is being added to pull the electron away from the nucleus.
Example 1. A hydrogen atom emits a line spectra showing its electron has dropped from the 4 th to 1 st energy level. What is the frequency and wavelength of the photon that has been emitted? Example 2. What values of n are involved in the transition that gives rise to the emission of a 388 nm photon from hydrogen gas? Example 3. Determine the wavelength and frequency of the fourth Balmer line (n=6 to n=2) for hydrogen.
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