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$\ce{C + O2}$ is awfully complicated, so let's just pretend you've asked this: In a single act of the reaction $\ce{H. + H .-> H2}$, how is momentum conserved? That's a legitimate concern all right. After all, we are taught that this reaction does happen instantly, once given a chance, and that's in fact true. Also, we know that it releases a lot of heat. ...


6

Firstly as @MaxW pointed out, using the given information, it is possible to find the shortest wavelength (or maximum frequency) X-ray only. In an X-ray tube, electrons are accelerated in a vacuum by an electric field and shot into a piece of heavy metal (e.g., $\ce{W, Rh, Mo, Cu, Ag}$) plate. X-rays are emitted as the electrons decelerate in the metal. The ...


5

An electron is not a wave nor a particle. An electron is usually described as a quantum object with some wave-like properties and some particle-like properties. Some of them, like particularly a spin, do not have direct counterpart in our familiar macro world. It is a kind of a mysterious, specifically quantum property of all elementary particles and atomic ...


4

Sure, it can be valid physically. You can use the full-electron basis set, like 6-31G*, and the ECP with associated basis set, like Lanl2dz, for instance, in calculations of transition metal compounds or compounds with heavier non-metals (Sb, Te, etc.) as an example. Important here would be to compare results obtained with available experimental data (such ...


3

When two isolated atoms collide the total energy and momentum must remain with the two atoms so both are conserved overall. In fact in a reaction such as $\ce{H\cdot + H\cdot <=> H2}$ the hydrogen molecule only lasts for a few femtoseconds. This is because even though the bond is formed the atoms will still approach one another (total energy being ...


3

If there is an infinite number of levels Yes, but the key point you are missing is that they are not equally spaced. The energy levels are not like stair cases (equally spaced). The electronic energy levels tend to converge. After that, you have basically provided enough energy to electron that it can overcome the attraction of the nucleus and leave the ...


3

I have been taught that electrons in atom are found in orbitals within shells This sentence is perhaps the source of all problems. Atomic structure has a history of 100 years. Best minds of the world spent their life in trying to understand atoms. The problem is that in the sub-atomic world, good teachers will teach you not to make a literal picture of ...


2

As the unperturbed Hamiltonian is Hermitian it follows that $$\int{ψ^{(0)*}_0}\hat {H}^{(0)}{ψ^{(2)}_0} dτ = \left[\int{ψ^{(2)*}_0}\hat {H}^{(0)}{ψ^{(0)}_0} dτ\right]^*=\left[\int{ψ^{(2)*}_0}E^{(0)}_0{ψ^{(0)}_0} dτ\right]^*=E^{(0)}_0\int{ψ^{(0)*}_0}{ψ^{(2)}_0} dτ$$ by the definition of Hermiticity and the fact that all eigenvalues of a Hermitian operator ...


2

Using a basis set that is not designed for the effective core potential is not a good idea. The problem is that an ECP is designed to produce the effective potential of core electrons, and an all-electron basis set will include basis functions meant to model the core electrons. At best, those core basis functions are poorly optimized for your problem. At ...


2

The formula only works when the orbital is directed along the bond line between two atoms. Since no orbitals can give you a $60^o$ bond angle, the orbitals are directed outside the triangle, forming a “banana” bond and the formula is being used inappropriately. So the negative sign in your Question #1 is not acceptable. We must do something different. Let’s ...


2

What we call "Hybridization" is really just a mathematical transformation of an approximated wavefunction. Your basic summation formula describes how to build some sort of customized wavefunction by forming a linear combination of some set of "basis" orbitals; you will find this equation over and over if you look up "basis set ...


2

First some basics.... Lithium has three electrons. $\ce{Li}$ electronic configuration: $1s^22s^1$ $\ce{Li -> Li+ + e-\quad\quad\mathrm{Ionization\ Energy= 0.520\ MJ/mol}}$ $\ce{Li+}$ electronic configuration: $1s^2$ $\ce{Li+ -> Li^2+ + e-\quad\quad\mathrm{Ionization\ Energy= 7.298\ MJ/mol}}$ $\ce{Li^2+}$ electronic configuration: $1s^1$ $\ce{Li^2+ -&...


1

The answer to the questions as well as those in the linked post lie in the following: the second peak is not equal to the second ionization energy, since the electrons are held more tightly by the nucleus once the outermost electron is removed It is worth reviewing the basic principle of the PES experiment: you irradiate the sample with high energy ...


1

In quantum mechanics, particles are waves, and as with any wave the longer the wavelength the less energy is in the wave. You don't need the box to see this; infrared light has less energy in the photon than ultraviolet (the former makes you warm but the latter can damage your skin) and a slow moving free electron (lower energy) has a shorter associated ...


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