EPTI never studied chemistry again after grade 12. But I have taken a lot of university-level math and physics courses, so I'm accustomed to dealing with "negative energies".
physics/chemistry help :( - Page 2
| Blogs > letsbefree |
Bill307
Canada9103 Posts
I never studied chemistry again after grade 12. But I have taken a lot of university-level math and physics courses, so I'm accustomed to dealing with "negative energies". | ||
|
Bill307
Canada9103 Posts
On September 05 2008 07:06 letsbefree wrote: The energy of a given energy level is determined by the following equation: E = - R / n^2 ( where R is a constant of 2.18 x 10^-18 J, and "n" is the energy level/electron shell) Here comes my problem, let's say I have a hydrogen atom (cuz its easy), its valence electrons are in n = 1 energy level. So if you plug it into the equation, you get a negative value. But the thing is, how can energy be negative?? or did i misinterpret the equation in some way? ALso, it says that the energy of electron bound to the nucleus is lower than if the electron were at infinity, which imo makes sense. But next thing it says is that as n approaches infinity, Energy approaches ZERO. But how can that be? If n increases, doesn't energy also increase? so instead of the energy approaching zero, shouldn't it also approach infinity? Firstly, I'm 90% sure the energy here is potential energy. Potential energy can be negative because it's not really a physical quantity. In my experience, it's probably negative because the really complex math behind it all requires the potential energy to be negative. Aside from the fact that it's potential energy, your interpretation is correct. If n increases, the potential energy increases towards 0. (Remember: it's negative. Example: -1 is less than 0, so you can increase from -1 to 0.) | ||
|
Nitrogen
United States5345 Posts
i've never used this equation though, but i remember using bohr's equation for electrons moving to different energy levels in a hydrogen atom E = -2.178x10^-19 ( Z^2/n^2) where n is the energy level and z is the nuclear charge (always 1, this only works for hydrogen because bohr's model is fundamentally wrong) if n is infinity, then it would be incredibly far away from the nucleus and there would be no real attraction between them, making the energy 0. | ||
|
Bill307
Canada9103 Posts
I don't know what you guys are gonna do when you encounter gravitational potential energy, which is negative as well. ~_~ | ||
|
Nitrogen
United States5345 Posts
On September 05 2008 08:35 Bill307 wrote: Why am I the only person who doesn't try to explain away why the energy is negative? In this situation, it has nothing to do with changes in energy or energy being absorbed / released: the potential energy really is negative. I don't know what you guys are gonna do when you encounter gravitational potential energy, which is negative as well. ~_~ err actually i was thinking a few steps ahead of the problem where you would get the energy levels for them and find the change in them, and that would come out negative (because it's exothermic) the negative is because... you were right it actually is negative. smaller = farther away from nucleus... so yeah. my bad. | ||
|
zer0das
United States8519 Posts
On September 05 2008 08:35 Bill307 wrote: Why am I the only person who doesn't try to explain away why the energy is negative? In this situation, it has nothing to do with changes in energy or energy being absorbed / released: the potential energy really is negative. I don't know what you guys are gonna do when you encounter gravitational potential energy, which is negative as well. ~_~ Take more chemistry, we don't really give a rip about your conventions and that's what ours say. Anywho... yes you can calculate the energy of a level, but the one that is spit out when n=infinity makes zero (harhar) sense. And here's why: Because the electron has been ejected from the atom. It is the lowest "unbound state", so it quite simply isn't there. Hence it makes a lot more sense to think of it as a difference of energies in this case (and in the general case so you can interpret this situation). And here's what my PChem book says on the positive and negatives: "All the energies are negative. They refer to the bound states of the atom, in which the energy of the atom is lower than the infinitely separated, stationary electron and nucleus (note, this is an assumption, they aren't actually stationary) which correspond to the zero energy. There are also solutions of the Schroedinger equation with positive energies. These solution correspond to the unbound states of the electron, the states to which an electron is raised when it is ejected from the atom by a high-energy collision or photon)." I also have notes from that class stating that n=infinity is the first unbound state. BUt logically this must be so since zero is defined as occurring when the nucleus and electron are infinitely far apart. But I can guarantee almost every chemist thinks of it in terms of energy being emitted if the sign is negative, because if it's an emission spectra, it is. And quite frankly spectroscopy is the useful application of this stuff. | ||
micronesia
United States24785 Posts
On September 05 2008 08:07 zer0das wrote: Or it's because the chemists claim dominion over the quantum world... mwhaha. Find me a chemist who can calculate the Bohr radius in terms of fundamental constants (without cheating) and I'll find you a physics teacher who is really good at starcraft. | ||
|
zer0das
United States8519 Posts
On September 05 2008 07:06 letsbefree wrote:Here comes my problem, let's say I have a hydrogen atom (cuz its easy), its valence electrons are in n = 1 energy level. So if you plug it into the equation, you get a negative value. But the thing is, how can energy be negative?? or did i misinterpret the equation in some way? ALso, it says that the energy of electron bound to the nucleus is lower than if the electron were at infinity, which imo makes sense. But next thing it says is that as n approaches infinity, Energy approaches ZERO. But how can that be? If n increases, doesn't energy also increase? so instead of the energy approaching zero, shouldn't it also approach infinity? Hope you guys can help me out a little  Anyways, to concisely answer your question: you're confusing the energy of a particular level and the energy difference between levels. If you read the definition I posted above, if the electron and nucleus are infinitely far apart, the energy is defined as zero. At n=infinity the electron and the nucleus are infinitely far apart, so the energy of that level is 0. The energy to move an electron from n=1 to n=infinity is not zero. The energy to move an electron from n=1 to n=infinity is still finite, because it is a difference in energy levels. In this case the difference between whatever the energy of n=1 is and 0. This makes sense, since it's basically saying you need to put in as much energy to eject an electron as there is holding it there. Also at n=infinity, the electron has been ejected from the atom. That's why in the spectra the lines converge to a certain point and at the last line n=infinity (although it actually isn't, but that's the best you can do). After it has been ejected, the electron's emission spectrum can no longer be measured because it is simply gone (it needs to relax to a lower energy level to give off energy, which it can no longer do... at least until it smacks into an atom that is deficient in electrons). Hope that helps. :d | ||
|
zer0das
United States8519 Posts
On September 05 2008 09:10 micronesia wrote: Find me a chemist who can calculate the Bohr radius in terms of fundamental constants (without cheating) and I'll find you a physics teacher who is really good at starcraft. Funny.. my PChem teacher made us do that. -_- We did get to see the constants though, and we were given a spectra with some data. But yeah. ;p | ||
|
L
Canada4732 Posts
As for why these potential energies are negative... well, I'm not entirely sure. I am. Its pretty obvious. When an electron starts orbiting a nucleus, the relationship is at a lower energy level than previously. Since you're in a potential energy 'pit' so to speak, the current energy of the system is negative with respect to an electron and an atom at infinity distance apart. Basically you're measuring the amount of energy RELEASED by the system in forming the 'bond' if you will, and thus the system has less energy than when it started after the bonding is complete and the excess bond energy has been radiated away via light, heat, kinetics, or whatever other path it uses for relaxation. Nitrogen seems to be correct but i only read his first post. Find me a chemist who can calculate the Bohr radius in terms of fundamental constants (without cheating) and I'll find you a physics teacher who is really good at starcraft. I can do that? Once you know to use the gas law (which IS cheating) + electrostatic attraction + angular momentum, its pretty much done. | ||
|
micronesia
United States24785 Posts
| ||
|
Clutch3
United States1344 Posts
On September 05 2008 08:10 Bill307 wrote: I think you're wrong. If you look at the page I linked above, since gravity is a conservative force, point #3 basically says the gravitational force must be the negative derivative of the gravitational potential energy, with respect to r. Therefore, the equation for the gravitational potential energy must have that form: we cannot arbitrarily move the 0 point anywhere. Actually, he's right; what matters is not the overall number of any energy level, just the difference between levels. The page you mention is also valid. But, if you take a look at the equation you mention, you can see that adding a constant number to the potential energy (represented by phi) won't change the force at all, and so the physics will still be preserved. This is analogous to saying that the integral of a particular function can only be determined up to a constant (i.e. the integral of 2x is x^2 + c, where c can be anything). This is something that particularly snooty physicists might call gauge invariance. And the reason the energies are negative here, as some people have already mentioned, is that we choose to define the energy of a free electron as zero, just for convenience. Therefore, because it takes energy to remove an electron from any energy level, those energy levels have to be negative (think of the potential energy as elevation/altitude... since we're "below sea level" we need to add energy to the electron to get back up to sea level). | ||
|
Klockan3
Sweden2866 Posts
On September 05 2008 07:06 letsbefree wrote: The one big problem i have is that: we all know that the atom is made up of a nucleus and orbiting electrons. When an object is heated, it emits light. So according to my notes, it says that although electrons are orbiting around the nucleus and accelerating (change in direction because of its circular motion), and since its been scientifically proven that acceleration produce some type of light, the orbiting electrons would emit photons of electromagnetic radiation and lose energy, so theoretically they would crash into the nucleus. This is wrong on so many levels... Firstly objects producing electromagnetic waves due to temperature levels have nothing to do with electron orbits but instead the atoms movements. This is very important since heat radiation do not follow the same rules at all but instead just radiates electromagnetic waves of a distribution curve were the peak is determined by the temperature. The waves you are talking about are instead produced when you flow electrons through for example gases, this causes the electrons already bound by the gas to get knocked away by other electrons, and it is when these empty electron orbits gets filled the electrons are accelerated and an exact wavelength of light is emitted according to the difference in potential energy between the two points. (Potential energy is 0 furthest away while a low level orbit is -a, then a jump to the low level orbit gives 0-(-a)=a amount of energy which discharges the "photon" with an energy amount of exactly a) You can see the difference between these two light sources with everything which can create a spectrum. If you look at a neon light through a spectrum you will find that it only emits light in a single frequency, while light bulbs, which operate by heating the thread, emits of every visible frequency and thus creates the whole visible spectrum. This is the reason light bulbs are so inefficient while lamps that use electron jumps are much nicer on your electricity bills since the amount of heat needed creates a lot of waste while electron jumps can operate at low temperatures. Also you use the same technique to see which elements the stars are made of, since its only black body radiation which gives all of the light spectrum, every other source emits everything but the frequencies which corresponds to the electron cloud orbits which gives holes in the spectrum created. This gives us a very exact method of finding out what everything's surface is made of and together with the Doppler effect also the relative speed to every visible spot in the universe. | ||
|
eshlow
United States5210 Posts
On September 05 2008 09:19 zer0das wrote: Anyways, to concisely answer your question: you're confusing the energy of a particular level and the energy difference between levels. If you read the definition I posted above, if the electron and nucleus are infinitely far apart, the energy is defined as zero. At n=infinity the electron and the nucleus are infinitely far apart, so the energy of that level is 0. The energy to move an electron from n=1 to n=infinity is not zero. The energy to move an electron from n=1 to n=infinity is still finite, because it is a difference in energy levels. In this case the difference between whatever the energy of n=1 is and 0. This makes sense, since it's basically saying you need to put in as much energy to eject an electron as there is holding it there. Also at n=infinity, the electron has been ejected from the atom. That's why in the spectra the lines converge to a certain point and at the last line n=infinity (although it actually isn't, but that's the best you can do). After it has been ejected, the electron's emission spectrum can no longer be measured because it is simply gone (it needs to relax to a lower energy level to give off energy, which it can no longer do... at least until it smacks into an atom that is deficient in electrons). Hope that helps. :d This is correct. Here's a a picture to help you (OP) visualize.  Also, R is supposed to be negative.. but yeah. You get the point. Also, last point is if N=1 for the electron. If it's in a different shell, the (ionization) energy is less for the electron to escape. ![[image loading]](http://img513.imageshack.us/img513/5026/electronsandemtf8.png) P.S. Dotted lines mean nothing at all. I just put them there to show the exponential relationship of the energy of N shells since they're based on -R/N^2 | ||
| ||
