Homework 4, due April 6, Chapter 4, problem 13 5 points : The labeled transitions below represent an electron moving between energy levels in hydrogen. Answer each of the following questions and explain your answers.
Transition B — the electron absorbs a photon and is able to jump to a level with higher energy, the energy difference between the levels is Transition C — the electron jumps from the Transition E — the electron gains so much energy that it can leave the atom, left is a free electron and an ionized atom. Transition D — You cannot have an electron in between the discrete orbits.
The electron can jump more than one level at a time, as long as energy is conserved. In this case, it has to send off a photon with Then, at some point, these higher energy electrons give up their "extra" energy in the form of a photon of light, and fall back down to their original energy level.
The light that has suddenly been produced rushes away from the electron, atom and the LED to color our world. Typically, the light produced by a LED is only one color red or green being strong favorites. Although they are cheap, easy to make, don't cost a lot to run, LEDs are not usually used to light a room, because they cannot normally produce the wide range of different colors needed in "white" light. This is because of the quantum nature of the atoms being used in the LED and the quantum energies of the electrons within them.
When an excited electron within a LED gives up energy it must do so in those lumps called quanta. These are fixed packets of energy that cannot be changed or used in fractions; they must always be transferred in whole amounts. Thus, an excited electron has no option but to give off either 1 quanta or 2 quanta of energy, it cannot give up 1. Also, the electron can only move to very limited orbitals within the atom; it must end up in an orbital where the wavelength is now uses is "in phase" with itself.
These two restrictions limit the quality of the quanta of energy being released by the electron, and thus the nature of the photon of light that rushes away from the LED. Since the energy given off is strongly restricted to quanta, and quanta that allow the electron to move to a suitable place within the atom, the photons of light are similarly restricted to a tiny range of values of wavelength and frequency a property we see as "color".
Many LEDs have electrons that can only give up quanta of energy that, when converted into photons, produce light with a wavelength of about nm - which we then see as red light. These electrons are so restricted in the quanta they can emit that they never shine blue light, or green light, or yellow light, only red light.
Long, long before their were LEDs in our lives, scientists trying to understand electrons in atoms noted a similar phenomenon when light was either shone on certain materials or given off by certain materials. They used Bunsen's burner to strongly heat tiny pieces of various materials and minerals until they were so hot that they glowed and gave off light. Sodium, for example, when heated to incandescence, produced a strong yellow light, but no blue, green or red.
Potassium glowed with a dim sort of violet light, and mercury with a horrible green light but no red or yellow. When Kirchoff passed the emitted light through a prism it separated out into its various wavelengths the same way a rainbow effect is produced when white light is used , and he got a shock. He could only see a few thin lines of light in very specific places and often spread far apart. Clearly glowing sodium was not producing anywhere near all the different wavelengths of white light, in fact it was only producing a very characteristic band of light in the yellow region of the spectrum - just like a LED!
Kirchoff and Bunsen carefully measured the number and position of all the spectral lines they saw given off by a whole range of materials. These were called emission spectra , and when they had collected enough of them it was clear that each substance produced a very characteristic line spectrum that was unique.
No two substances produced exactly the same series of lines, and if two different materials were combined they collectively gave off all the lines produced by both substances. This, thought Kirchoff and Bunsen, would be a good way of identifying substances in mixtures or in materials that needed to be analyzed.
The reason is that the atoms in the gas reemit light in all directions , and only a small fraction of the reemitted light is in the direction of the original beam toward you. In a star, much of the reemitted light actually goes in directions leading back into the star, which does observers outside the star no good whatsoever.
Figure 3 summarizes the different kinds of spectra we have discussed. An incandescent lightbulb produces a continuous spectrum. When that continuous spectrum is viewed through a thinner cloud of gas, an absorption line spectrum can be seen superimposed on the continuous spectrum.
If we look only at a cloud of excited gas atoms with no continuous source seen behind it , we see that the excited atoms give off an emission line spectrum. Figure 3: Three Kinds of Spectra. When we see a lightbulb or other source of continuous radiation, all the colors are present. When the excited cloud is seen without the continuous source behind it, its atoms produce emission lines.
We can learn which types of atoms are in the gas cloud from the pattern of absorption or emission lines. Atoms in a hot gas are moving at high speeds and continually colliding with one another and with any loose electrons.
They can be excited electrons moving to a higher level and de-excited electrons moving to a lower level by these collisions as well as by absorbing and emitting light. The speed of atoms in a gas depends on the temperature. When the temperature is higher, so are the speed and energy of the collisions. The hotter the gas, therefore, the more likely that electrons will occupy the outermost orbits, which correspond to the highest energy levels.
This means that the level where electrons start their upward jumps in a gas can serve as an indicator of how hot that gas is. In this way, the absorption lines in a spectrum give astronomers information about the temperature of the regions where the lines originate. We have described how certain discrete amounts of energy can be absorbed by an atom, raising it to an excited state and moving one of its electrons farther from its nucleus. If enough energy is absorbed, the electron can be completely removed from the atom—this is called ionization.
The atom is then said to be ionized. The minimum amount of energy required to remove one electron from an atom in its ground state is called its ionization energy. Still-greater amounts of energy must be absorbed by the now-ionized atom called an ion to remove an additional electron deeper in the structure of the atom. Successively greater energies are needed to remove the third, fourth, fifth—and so on—electrons from the atom.
If enough energy is available, an atom can become completely ionized, losing all of its electrons. A hydrogen atom, having only one electron to lose, can be ionized only once; a helium atom can be ionized twice; and an oxygen atom up to eight times. When we examine regions of the cosmos where there is a great deal of energetic radiation, such as the neighborhoods where hot young stars have recently formed, we see a lot of ionization going on.
An atom that has become positively ionized has lost a negative charge—the missing electron—and thus is left with a net positive charge. It therefore exerts a strong attraction on any free electron. Eventually, one or more electrons will be captured and the atom will become neutral or ionized to one less degree again.
During the electron-capture process, the atom emits one or more photons. Which photons are emitted depends on whether the electron is captured at once to the lowest energy level of the atom or stops at one or more intermediate levels on its way to the lowest available level.
Just as the excitation of an atom can result from a collision with another atom, ion, or electron collisions with electrons are usually most important , so can ionization.
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