Quantum mechanics is the discipline of physics that focuses on physical phenomenon that occur at an atomic or sub-atomic scale. In particular quantum mechanics attempts to describe the interaction of energy and matter, which can be described using both particle-like and wave-like interactions.

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Heisenberg uncertainty principle

What is the significance of the quantity 4π in the Heisenberg uncertainty principle? $Δp \times Δx = \frac{h}{4π}$
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How do electrons travel through nodes

I understand this is a basic question, but I'm having such a hard time wrapping my head around it. I'm trying to avoid thinking about it as an actual "particle" but as a wave, but that confuses me ...
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58 views

Which is the bigger ion, F- or O-?

Well, according to the proton-electron ratio $\ce{O-}$ should be bigger than $\ce{F-}$ What about the charge/electron density in $\ce{F}$? Will it not affect the size of the atom of $\ce{F-}$?
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How much energy does it cost to have electron configurations that are not in accordance with Hund's rules?

What is a ballpark figure for the difference in energy for an atom that follows Hund's rule vs one that has two electrons with opposite spins? I'd be interested to know carbon and nitrogen. Is there ...
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55 views

What are the Waves Modeling when Referring to the Atomic Orbitals

It is taught that the orbital shapes derive from wave functions with different numbers of nodes. For example, the "s" orbital comes from a wave that has one node. But what are the waves modeling? A ...
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Can electrons switch orbitals within a shell?

I know that electrons can move from say 2s orbital to an unoccupied 2p orbital, as in Carbon atom which can form 4 bonds this way. But I want to know is it possible for an electron say in orbital 2p ...
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How can two electrons lie together in an orbital?

Two electron of opposite spin can lie in a single orbital.. But what about the electron-electron repulsion. Okay! I got that the nuclear charge rather the large Z-effective overcome this repulsion by ...
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160 views

Difference between actual position of electron and Radial Distribution Probability

Its known that the radius of maximum probability of 2s orbitals is more than that of 2p orbitals. It means that the maximum probability of finding an electron in an 2s is further away from electron ...
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Energetic Placement of Atomic Orbitals in the HCl Molecular Orbital Diagram

How are the 3p orbitals of chlorine lower in energy than the 1s orbital of hydrogen?
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Find n and the wavelength too

To start with its a homework problem, quite lengthy. A particle of mass equal to 208 times the mass of electron moves in a circular orbit around a nucleus of charge +3e. Assuming the BOHRs model of ...
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51 views

Subtle implications of quantum numbers

Question: Given the subshells 1s, 2s, 2p, 3s, 3p , and 3d , identify those that meet the following descriptions: a) has l=2 b)Can contain two electrons with spin $m_{s}=\pm\dfrac{1}{2}$. For a) From ...
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Heisenbergs uncertainty principle

Why can't we find the exact position and velocity of a particle. And why is it that is the uncertainty is very very large the velocity can be determined and vice versa also is true. Please explain to ...
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45 views

What happens when we heat an atom?

Question is simple.. If we take an atom of any element and then supply heat energy to it then what will happen? Acc to me in beginning energy[quanta(due to excitement of electron and then moving ...
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What Quantum Chemistry Model Should I Use?

Sorry for such a elementary question, My Main purpose is using Quantum Chemistry for simulation of some reactions. Actually we are working on making some new polymers and I need to simulate some ...
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Bombarding atoms with electron gun?

Just to explain this question in a better way just think about the Rutherford's experiment(the alpha particle bombarded on Gold foil) be conducted using a electron gun in place of the Alpha one.. So ...
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51 views

Wavelength of X-rays

What will be the wavelength of X-ray if we apply a potential difference of , say 20 KV across the ends of the x-ray tube ? Alright, i started with the modified de-broglie equation ...
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52 views

How to identify ions by their quantum number?

If the quantum numbers of an ion are given, how can we identify this ion by its quantum numbers? For example : n = 3; $l$ = 2; $m_l$ = 0; m$_s$ = + ½ What I have so far: $n$ is 3 and $l$ is 2 ...
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How to make approximation of rotational partition function of diatomic linear molecules?

Using the rigid rotor approximation to the level energies, and such other appropriate assumptions, we can approximate rotational partition function, $Q_{\mathrm{rot}}$, of linear molecules as follows: ...
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Number of orbitals in full configuration interaction

I am using one quantum chemistry package where I am supposed to assign a number of active orbitals I want to be included in the FCI (full configuration interaction) calculation. For example if I have ...
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Reduce sizing of molecule - Oxygen

Can the size of molecule oxygen reduce smaller? If yes, how is that possible? Is it related to proton and electron surrounding the nucleus?
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Meaning of depiction of atomic orbitals

There was a section about atomic orbitals in my organic chemistry textbook that I did not quite understand. First the author explained a bit about the Schrödinger equation, which I understood to be ...
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Semi-Infinite Potential Square Well: Negative Potential

I am having trouble with a problem involving a Semi-infinite potential square well: I have written down some notes that I added to the post. I have problems understanding the physical situation. See ...
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178 views

Why does the Schroedinger equation for hydrogen atom look like this?

Here is how I saw the Hamiltonian being written in one Quantum Mechanics book: Well, That's all very nice and complicated, but looking at the last term, and seeing the use of $r$ in there, ...
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Probability of measuring a particle in the ground state: having trouble with the integration

I am working on a problem in the context of an infinite symmetric potential barrier around the origin, with barriers at $x=- \frac{a}{2}$ and $x=\frac{a}{2}$. The wave function is a symmetric ...
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Normalizing the wave function $\psi (x) = A$

I was trying to normalize the wave function $$ \psi (x) = \begin{cases} 0 & x<-b \\ A & -b \leq x \leq 3b \\ 0 & x>3b \end{cases} $$ This is done simply by evaluating $$ ...
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Calculating Commutator of Differential Angular Momentum

First, I realise this may not strictly quality as chemistry, but it is part of a quantum chemistry/quantum physics course, so I hope it goes through! I have tried for hours to calculate the ...
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Why is a singlet state called singlet and a triplet state called triplet?

I kind of get the idea of singlet and triplet states. But why are they called singlet and triplet (what is the single and what is the triple in these cases)? I feel that I am missing something ...
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How strict is the “to excite electrons the energy must equal the energy state difference” fact?

We are always told that to excite an electron from one state to a higher energy states, for example from the valance band to the conduction band, the energy must equal the energy difference between ...
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Reaction Pathways: What to do when IRC geometries are relaxed (optimized) and the energy changes significantly

The Story: Reaction pathways can be difficult things to deal with using electronic structure methods. Intrinsic reaction coordinates (IRCs) can be determined a number of ways (a discussion of these ...
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Is there an energy cost associated with flipping the spin of an electron?

THE STORY: A common example used to illustrate the limitations of restricted Hartree-Fock (RHF) theory is the H$_2$ dissociation energy ($D_e$) curves. RHF enforces electrons to be paired into spin ...
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What exactly happens to mass during deuterium fusion?

I know that the mass of Helium-4 is slightly less than the mass of 2x Deuterium it may be made of and that it is the reason fusion gives a lot of energy. But where exactly is this missing mass taken ...
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Conservation of angular momentum in electronic transition

My book says the "angular momentum is always conserved in a transition". But if suppose we have a s electron then it's angular momentum is $\hbar\sqrt{l(l+1)}+\hbar\sqrt{s(s+1)}$ $\implies ...
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What does the subscript of atomic orbital mean?

As everyone knows, the atomic orbital can be classified as $s, p_z, p_x, p_y, d_{z^2},d_{xz},d_{yz},d_{xy},d_{x^2-y^2}$ and so on. I want to know the meaning of $z^2,x^2-y^2$ and so on. Maybe this is ...
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Calculate the wavelength of the radiation released when an electron moves from n= 5 to n=2

Calculate the wavelength of the radiation released when an electron moves from n= 5 to n=2. I thought this question was easy. But I did it 5 times and I get the wrong answer every time. I don't know. ...
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Why is the orbital angular momentum of a pi electron along the axis of two atoms' molecule one?

I'm reading quantum chemistry. The book says that the orbital angular momentum of a $\pi$ electron along the symmetry axis of a molecule made up of two atoms is $\pm 1$. I think this is a primary ...
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Why is the alpha particle called a particle when it is made of four particles?

We know the alpha particle is the nucleus of helium. It contains four subatomic particles - two protons and two neutrons. The protons and neutrons are further made of particles called up and down ...
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The energy gap between a pi-conjugated system with (2 bonding and 1 anti-bonding orbital) and (1 bonding and 2 anti-bonding) orbitals

I asked a question previously about "why" it is the case the expanding the size of pi-conjugated systems decreases the required energy to excite an electron from a HOMO to a LUMO band: Why does the ...
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230 views

Why are excited Slater determinants used to describe electron correlation?

Usually the first step in describing the electronic wave function of a molecule or atom is to describe it with a single Slater determinant. I get that this is an independent particle approximation, ...
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What is Inert Pair effect?

I was reading the p-block elements and found this fancy thing used everywhere in this topic. But the book does not explain it very well. So, What is Inert Pair effect? Give full explanation and also ...
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How to properly relate quantum mechanical energy to the classical world

The Equation of Interest The energy equation derived from the "Particle in a 1-D box" problem is as follows: $E=\dfrac{n^2h^2}{8mL^2}$ where $n$ is the principle quantum number, $h$ is Planck's ...
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Predicting bond-strength of metal carbonyls

The metal carbonyls (and similar organometallic compounds) involve a combination of sigma bond, a pi bond and backbonding. The bond strengths under consideration are the metal-carbon bond and the ...
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Suggest methods and basis sets for a variety of systems

Please help me with any/all of the cases below. In the following cases, the named method and basis set are not suitable for the chemical systems. Why aren't they? Could you suggest a suitable ...
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Why are noble gases stable

I was recently asked the question "Why are noble gases stable? with the expectation of providing an answer beyond the general explanation of "they have full valence layers" and I couldn't think of ...
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123 views

Wasn't Rutherford's assumption of gold foil to be made of single layer wrong?

My teacher taught about Rutherford's gold foil experiment today. Sir said that, Rutherford used gold foil of thickness $10^{-7}$ m and concluded atom to be of size $10^{-10}$ m. Sir also said that ...
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573 views

Why are wave functions orthogonal?

It seems that all wave functions studied in physical chemistry are orthogonal (e.g. particle in a box, hydrogen atomic orbitals). Does this come about because we purposefully make them orthogonal, or ...
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Magnetic moment of coordination complexes?

To understand the commonly quoted magnetic values of coordination complexes (central ion) we use $$m_l=\sqrt{n(n+2)} \text{BM where BM}=\frac{e\hbar}{2m_e}\text{JT}^{-1}$$ $n$=number of unpaired ...
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Understanding moseley's law from the rydberg-type equation?

To explain the characteristic X-ray emission peaks for various elemental targets, a formula was developed which was similar in construct to the rydberg equation for H-atom as derived by the ...
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How can we write the wave function in quantum mechanics?

In quantum mechanics, while writing the wave functions we can take a product of the spatial and the spin parts.But what does it means? What is the meaning of the spatial wave function and the spin ...
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How do 1s and 2p orbitals overlap?

In the following figure we can see that the p-orbitals overlap 1s orbital (though relatively very little). How can an electron in p-orbital, be simultaneously in the 1s orbital at any given point ...
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Why are the total energies of transition states so commonly corrected for zero-point vibrational energy?

So often I see total energies of transition states corrected for zero-point vibrational energy which always confuses me. Zero point energy is the lowest energy that a ground state molecule can have ...