3

Setting aside the arguments over umlauts, yes you can add the nitrogen atom to the Hückel matrix; in fact, theoretically you should do so and allow the matrix eigenfunctions and eigenvalues to decide whether the nitrogen atom in this case is really conjugated. The carbonyl oxygen can also be coupled in. But there is a catch. Since the nitrogen or oxygen atom ...


3

Carbon nanotubes are 1-d materials which are confined in 2 dimensions. You cannot compare it with quantum dots which show confinement in 3 dimensions.The difference in optical properties maybe be primarily due to the very small size and 3-D confinement of quantum dots.


3

These plots are with respect to $r$, so it will only show radial nodes. An angular node would appear in a plot with respect to $\theta$. So for 3p, you will only have one node. To distinguish between options 3 and 4, you just need to realize that larger $n$ will have it's maximum further from the nucleus.


3

The wave function of the H atom have a number of nodal surfaces equal to the first quantum number. But these nodal surfaces are not always spheres, as you think. They can be planes or still different surfaces. In general the quantum number $n$ gives the total number of nodal surfaces. The second quantum number $l$ gives the number of nodal non-spherical ...


2

I will try to answer without using any mathematical formula, as your question is just made of words, without any mathematical symbols. You should know that the wave function of an electron in the $\ce{H}$ atom is normalized. It means that the integral of the wave function over the whole space is equal to $1$. And it must be equal to $1$. If you add two of ...


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