# Tag Info

53

Wow, this one has been over-answered already, I know... but it is such a fun question! So, here's an answer that hasn't been, um, "touched" on yet... :) You sir, whatever your age may be (anyone with kids will know what I mean), have asked for an answer to one of the deepest questions of quantum mechanics. In the quantum physics dialect of High Nerdese, ...

8

As a useable heuristic I would go with something along the lines of the intermolecular forces between the surface molecules of the bodies are comparable to the scale of one-to-one intermolecular forces between nearby{*} molecules due to other components of the same body You could make it a little more strict by replacing "comparable to" with ...

7

The tangy taste of sodas comes from an acid in them. In most sodas, it's carbonic acid: ${\rm H}_2{\rm CO}_3$. Under pressure, like in a sealed can of soda at room temperature and usual pressure, the equilibrium reached keeps this molecule together. Once you open the can of soda, the lowered pressure inside the can "allows" this molecule to break apart ...

7

Your body is warmer than the surrounding air and as such when heat escapes from your body it warms up that air; if it didn't, you would have overheated years ago. However, if the air isn't moving, that air around you begins to warm up. Heat transfer is faster if the temperature difference is greater. What wind does is move that warm air away, and replace ...

5

I wish there was an easy answer, but this is actually somewhat complicated, and to some extent is more art than science. There are several simple models that are used to predict molecular geometry, one of the most common is the VESPR model. Based on this model, one can begin to perform calculations of energy associated with different vibrational modes of ...

5

Qualitatively, the Morse potential has two competing effects. The first is at small separations, where the potential becomes (infinitely) large; this effect is roughly due to the electrostatic repulsion between the two atoms, and it increases as the atoms get closer together. On the other hand, two atoms may covalently bond, and generally speaking, the ...

5

Yes, without gravity, the gas fill out the space evenly so you can get uniform distribution of gas. Certainly, it only occurs at thermodynamic equilibrium, that is, if you wait for a long time. With gravity, the density would be higher at location of lower gravitational potential. If we can treat the gas as ideal gas, then each gas molecule is independent ...

4

It does not work like that. The wave function of 6 electrons is the product, not the sum, of orbitals (wave functions of single electrons). However, since electrons are fermions the overall wave function must be antisymmetric. Thus, the simplest wave function that you can write for the 6 electron-benzene approximation (in the spirit of the H\"uckel method) ...

4

No, because the atoms in steel and plastic have different masses. Your example is a bit more complicated than it need be because steel (well iron) is an element while plastic is a compound. This complicates things because molecules can have internal motions that contribute to the energy. A better comparision might be between lead and lithium. These are both ...

4

Suppose your molecule is in a gas. This could be a gas made up just from the molecules you're thinking of, or your molecule could be dispersed in some carrier gas. Whichever the case, the temperature of the gas is related to the velocity of the gas molecules. So in a cool gas the molecules will be moving at some speed (that depends on their mass) and as you ...

4

The point is that when there is only a single phase there is no dividing surface that could hold any surface tension. One has surface tension precisely when a liquid and a gas phase (in general also two liquid phases would be possible) are present simultaneously. This holds only along the coexistence curve in the lower left corner of your phase diagram. ...

4

Actually, it's more complicated than that. If you want to generate one of these plots (an accurate one), you would need to solve the Schrodinger equation for the two atom system. There's various methods and approximations to do this, but once you have, you will find that the potential energy is a function of distance, and it just so happens there is a ...

4

Molecules vibrate with frequencies in the range 10$^{12}$ to 10$^{14}$Hz. Although I don't know of any strict definition, I would take the view that a molecule must hold together for a few vibrations otherwise what you have is a collision not a molecule. That means the lifetime must be greater than 10$^{-14}$ to 10$^{-12}$ seconds, depending on the molecule. ...

3

Suppose that for all $z$ in some open set $Z$ of complex numbers containing $z_0$, the Hamiltonian $H(z)$ is a compact perturbation of the self-adjoint $H(z_0)$ depending analytically on $z$. Then, for every simple eigenvalue $E_0$ of $H(z_0)$ and associated normalized eigenstate $\psi_0$, there exist a complex neighborhood $N$ of $z_0$ and unique functions ...

3

Semi-macroscopic view: The key word for understanding this problem is buoyancy. Buoyancy is the result of different pressures. Since the warm air is less dense than the cold one, there are less hits to the (imaginary) balloon of warmer particles from inside than from outside, so there is net pressure toward inside. However, since this pressure difference ...

3

The molecules are all moving, quite rapidly, all the time, and constantly colliding against each other. The warmer ones are moving even more rapidly, thus "winning out" in their collisions with the cooler ones, pushing them away. (That's what lower density is.) Then if there's some gravity field pulling all of them downwards against a surface (they're not ...

3

This is very legitimate question for something we usually take for granted. I think it would be possible to define macroscopically touching as the situation, in which the total force between two electrically neutral rigid bodies is larger than pure gravitational (for some measurable value). The difference is of course the normal component of the surface ...

3

There are lots of questions asked here, but I'll attempt to answer some of these... Oxygen is found in the triplet state because the triplet state is most stable. This is a complex function of the properties of the atoms (e.g. charge and separation between atoms) and the electrons (e.g. number of electrons present, possible combinations of orbitals). The ...

3

Your teacher is referring to the LCAO approximation as a way of calculating molecular orbitals. Suppose you bring two hydrogen atoms together i.e. create a hydrogen molecule. To calculate the electronic structure you need to solve the Schrodinger equation, but even for something as simple as the hydrogen molecule the Schrodinger equation is too complex to ...

3

All of the ice core methods of measuring temperature in past millenia from gas trapped in bubbles in ice, and measuring concentrations , depend on the fact that permeability is small even in imperfect containers, as the ice in the glaciers. So the answer to "how long" would depend on the exact materials and geometry and temperature, and it will be in any ...

3

Molecules don't know. Consider the following reaction as a template for some reaction that is favored to go in the direction indicated. \begin{align*} A-B +C \rightarrow A-C +B \end{align*} In a large collection of such molecules you can always find some $AB$ going to $AC$ and some going backwards. It is just that significantly more $AB$ are going to $AC$ so ...

3

Let's call the two types or particle $n$ and $e$. When summing over the interactions between particles of type $n$, say, you have a sum like this $\sum_i\sum_{j>i} H_{ij}$ where $i$ and $j$ are both sums over the $n$s. You need the $j>i$ because without it the pair $i=2, j=3$ (say) means the second particle of type $n$ and the third particle of ...

3

The approximation that we all started out learning is the linear combination of atomic orbitals (LCAO) approach. The molecular wavefunction, $\Psi$, can be expressed as a sum of some set of basis functions: $$\Psi(\vec{r}) = \sum_n f_n(\vec{r})$$ and a convenient set of basis functions is the atomic orbitals of hydrogen. As a starting point we could take ...

3

In the case of ice, the hydrogen and oxygen atoms are actually sharing electrons. They are bonded "covalently". Each oxygen is bonded to two particular hydrogens, and so you can divide the atoms into separate groups: this oxygen is bonded to these hydrogens, and that one to those, and so on. That is not the case in NaCl, where really the different atoms are ...

2

The molecules $O_2$ and $N_2$ are symmetric and have no dipole momentum. That's why they can not interact with EMW (at least within dipole approximation). One can say that transitions between the oscillator levels in these molecules are forbidden by symmetry in electrodipole approximation. The molecule $CO$ consists of two different atoms. The average ...

2

In answer to the title question, "yes, but...." (it's not practical and the effect is too small to be noticed in the sort of situation you describe) 1 - whatever energy you use to stir the water, ends up as heat pretty soon (which raises the temperature) 2 - it is a good idea to develop an intuitive feel for the magnitude of mechanical versus heat energy. ...

2

Well, photosynthesis has to do with the absorption of photons to break/make certain bonds. The most classical you can get with this is Bohr's model, nothing prior to that explains absorption of light. Bohr's model is kind of an extremely basic type of quantum mechanics, and anyways it does not work for multielectronic species. Bonds become impossible to ...

2

It looks like "electromagnetic interaction between molecules" is mostly due to Electrostatic force in the form of dipole-dipole forces and so on.

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