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Why is it that when two hydrogen atoms combine together, their combined energy is less than the energy of one hydrogen atom by itself? Why wouldn't the combined energy be twice as much?
To what combined energy is one referring?6021023 said:Why is it that when two hydrogen atoms combine together, their combined energy is less than the energy of one hydrogen atom by itself? Why wouldn't the combined energy be twice as much?
I'm guessing one means binding energy as alxm mentions.6021023 said:The combined energy of the two hydrogen atoms when they come together to form H2.
bcrowell said:There is a change in the classical electrostatic energy associated with the rearranged charge distribution, which others have described above. But there is also a purely quantum-mechanical effect, which is basically just a particle-in-a-box effect. The electrons' wavefunctions spread out to encompass both atoms, increasing their wavelengths and reducing their kinetic energies. Roughly, you're doubling the wavelength along one axis. Suppose the original kinetic energy corresponding to the wavelength of each electron along each of the three axes is K. Then the separated atoms have total kinetic energy 6K. If you treat the atom as a particle in a box, with a length of 0.1 nm, then you get K=38 eV. When the two atoms form a molecule, the wavelengths parallel to the bond axis are both roughly doubled. This reduces two of the K terms to K/4, giving a total kinetic energy of about 4.5K. This makes the binding energy 1.5K=57 eV. The actual binding energy is 15.43 eV. So the particle-in-a-box argument is crude, but it does give a result on the right order of magnitude to be an important contribution to the total binding energy.
That's all I was claiming -- that it was an argument to show it was significant.alxm said:bcrowell's approach doesn't quite work as a rationale (except in showing that it's significant)
alxm said:I'm not sure where that number came from, but the electronic energy of two hydrogen atoms is 1.0 Hartree = 27.2 eV. The binding energy of H2 is 4.52 eV.
RedX said:So if the total energy of two atoms apart is 6*38 eV=228 eV, and a particle-in-a-box says that close together, the total energy is 57 eV, but the real answer is 15.43 eV, would that mean the majority of the energy reduction is the particle-in-a-box effect?
bcrowell said:No, the whole thing is just an order-of-magnitude estimate that shows that the change in kinetic energy is of the right order of magnitude to be relevant to the binding energy. The effect is also in the right direction to help explain the binding. (It makes the bound system more bound.)
RedX said:So it's sort of like measuring the strength of nuclear forces by knowing the size of a nucleus and modeling it as a particle-in-a-box (or just using the uncertainty principle) and ignoring all the nuclear physics that goes on? Everything is just based on size?
The energy of a hydrogen atom is determined by the energy levels of its electrons. The lowest energy level, or ground state, has an energy of -13.6 electron volts (eV). As the electron moves to higher energy levels, the energy increases, with the highest energy level, or ionization energy, having an energy of 0 eV.
The energy of a hydrogen atom can be calculated using the Rydberg formula: E = -13.6/n2 eV, where n is the principal quantum number. This formula gives the energy of an electron in a specific energy level.
The energy of a hydrogen atom can be affected by external factors such as temperature, pressure, and electric or magnetic fields. It can also be affected by internal factors such as the presence of other atoms or molecules, which can cause energy level shifts through interactions with the hydrogen atom's electrons.
Energy can be released from a hydrogen atom through a process called emission. This occurs when an electron in a higher energy level moves to a lower energy level, releasing energy in the form of light or heat. The specific energy released depends on the difference in energy between the two levels.
Energy can be absorbed by a hydrogen atom through a process called absorption. This occurs when an electron in a lower energy level absorbs energy from an external source and moves to a higher energy level. The specific energy absorbed depends on the difference in energy between the two levels.