Questions tagged [orbitals]

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$\langle r \rangle$ and orbital energy [duplicate]

Even though $\langle r_{2s} \rangle > \langle r_{2p} \rangle$ based on the following formula $$ \langle r_{n\ell} \rangle = \frac{{a}_{0}}{2}(3{n}^{2}-\ell(\ell+1)) $$ $2s$ has a lower orbital ...
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1answer
74 views

What happens to the $3d$ and $4s$ levels during the ionisation of a transition metal?

I'm just wondering about the transition state of a transitional metal before (ex: $[\mathrm{Ar}]\, 3d^3 \,4s^2$) and after ionisation (which means $[\mathrm{Ar}]\, 3d^3 \,4s^1$) because before ...
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1answer
156 views

Must the total orbital angular momentum quantum number $L$ be less than the principal quantum number $n$? If so, why?

I am studying LS coupling and term symbols. In my textbook, there is an exercise: Why is it impossible for a $2\ ^{2}\text{D}_{3/2}$ state to exist? The answer says, the total orbital angular ...
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4answers
249 views

Could an electron enter the nucleus, and if so would it be captured by a proton?

I've been trying to find an answer to this question, but have come across contradictory answers, and have limited knowledge of quantum mechanics myself. Almost all the threads (here and on Quora) ...
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3answers
405 views

What are the experiments performed to determine the position of an electron inside an atom to verify the probability wave function data?

What are the experiments performed to determine the position of an electron inside the atom to verify the probability wave function data? Is it possible to do those experiments in real life?
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20 views

Understanding the radial distribution function [duplicate]

I am confused why the maximum of the radial distribution function for 2p orbital is closer to the nucleus than that for 2s orbital. Doesnt this mean that there is a higher chance of finding 2p orbital ...
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1answer
202 views

How to get the radius of Bohr from the uncertainty principle?

I would like to know how to get the following result: \begin{eqnarray} a_0=\frac{4\pi\varepsilon_0 \hbar^2}{\mu e^2} \end{eqnarray} from the beginning of the uncertainty of heisenberg. If possible, I ...
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3answers
350 views

Would an $H_2O$ Molecule actually look like this 3D representation if we could see it?

I'm trying to get a much better grasp on atoms and molecules and I am a visual learner. I found the above image here. This intuitively makes sense to me because I can see how the electron orbitals ...
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2answers
69 views

What is the energy of an atomic orbital?

When we refer to energy of an atomic orbital what is this energy ? is potential energy ? but if is potential energy then shouldn't be considered the whole potential energy of the atom ( potential ...
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1answer
69 views

Can electron jump from $n=2$ to $n=3$?

Assume Bohr's Model. Lets not consider latest modern theory. Consider a Hydrogen atom in ground state (n=1). It excites to next level n=2. It will stay here for 10^-8 seconds. Now we supply more ...
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48 views

Term Symbols of Carbon Atom [duplicate]

For a neutral Carbon Atom, the electron (ground) configuration is $1s^2$$2s^2$$2p^2$. I am told that the term symbols $^{3}S_{1}$ and $^{3}D_{1,2,3}$ are forbidden by Pauli Exclusion Principle. May ...
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2answers
42 views

Force to step down atomic level of an electron?

How much force is needed to step down atomic level of an electron? Where does it gets it energy to overcome the orbits to step up?
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1answer
40 views

Why does $2p$ have highest RDF at $4a_{0}$?

I was reading notes from my first class in Quantum Physics that I received and left confused at the following statement: For each principal quantum number $n$, the orbital set with the highest $\...
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0answers
78 views

Quantum numbers $n$ and $\ell$ relation in many electrons atom [duplicate]

Solving the Schrodinger equation for hydrogen atom we arrive to the conclusion that quantum numbers $n$ and $\ell$ have the relation $$\ell=0,1,...,n-1.$$ Now,since we can not solve the Schrodinger ...
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1answer
39 views

Electronic configuration

In chemistry the lithium electronic configuration is $$1s^22s^1 \, .$$ Can we prove this using approximation method like perturbation theory that this the ground state and not for example $1s^22p^...
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1answer
58 views

Bad value for sphere of influence with Venus [closed]

I would like to get value of sphere of influence than Wikipedia for Venus: on https://en.wikipedia.org/wiki/Sphere_of_influence_%28astrodynamics%29 It is indicated for Venus: $S_{\text{OI}}=0.616\,\...
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1answer
36 views

Given the wavefunction of an electron in hydrogen, what possible energies can it obtain and what are the probabilities of those energies? [closed]

we are given, $$\psi(\textbf{r})=A\left[R_{2,1}(r)Y_{1,-1}(\theta,\phi)+iR_{2,1}(r)Y_{1,0}(\theta,\phi)+2R_{2,1}(r)Y_{1,1}(\theta,\phi)\right]$$ we can rewrite this as: $$\left|\psi(\textbf{r})\right&...
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1answer
48 views

A dreidel on a spinning table

In the spirit of the holidays. Let's assume that a dreidel is spinning counter-clockwise at frequency $f$ on a table. From external point of view, what will I see if I rotate the table clockwise at ...
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1answer
272 views

String behavior in electron orbitals?

It feels like this should be a incredibly easy question to find an answer to, but I’m coming up zeroes in my search - if I’ve overlooked a parallel question please feel free to close this. ...
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1answer
82 views

Ground state of Beryllium (${\rm Be}$)

Why is the ground state of Beryllium (${\rm Be}$) with electronic configuration $[{\rm He}]2s^2$ is $^1S_0$ and not $^3S_1$? The state $^3S_1$ has higher spin multiplicity.
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56 views

What is the point of talking about three axes for hydrogen orbitals?

The hydrogen orbitals are usually described using polar coordinates ($\Psi(r, \theta, \varphi)$). I understand that $r$ is the distance from the center of the atom, but how are the angles defined? ...
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2answers
86 views

Do empty orbitals have energy?

Suppose we have the Na (Sodium) atom. It has half-filled the 3s orbital and unfilled 3p orbital. Does the empty 3p orbital have energy? also does the energy of 3p change if an electron occupy it?
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52 views

Completely Non-classical Spin-orbit Interaction [closed]

Question: What is the reason for spin-orbit interaction without just assuming that the electron moves on a circular path around a nucleus? Every explanation for spin-orbit coupling that I have read ...
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2answers
61 views

How are line spectra explained after rejecting/improving Bohr's theory?

I learned that Bohr explained line spectra by postulating that electrons can only be at certain discrete distances from the nucleus. Later, this theory was refuted/improved by de Broglie and ...
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1answer
39 views

Quantum mechanics: orbitals with opposite signs in the magnetic quantum number

In quantum mechanics, the orbitals, psi (n, l, m) and psi (n, l, -m) have opposite signs in the magnetic quantum number but they have the same absolute value. (i) Are the probability density ...
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1answer
57 views

Relation of Hydrogen orbitals to its spectral series?

I'm looking for the link between the Rydberg formula for hydrogen spetcral series $$\frac{1}{\lambda_{\mathrm{vac}}} = R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$$ and this image. Is it right to ...
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0answers
45 views

A question about almost stationary orbits

For an orbit around the earth with period equal to a sidereal day with eccentricity $e=0$ and inclination $i=0$, the path on earth would be a single point on the equator. I have done some simulations ...
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3answers
287 views

What does the principal quantum number really mean? [closed]

What do principal quantum numbers actually represent? The modern structure represent that electrons do not revolve around the nucleus. It says there are no shells or orbits for electron rather there ...
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1answer
47 views

Orbitals, shapes and wave function relation

Are the shapes of orbitals like $s$ which is sphere due to wave function or due to square of the wave function?
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1answer
213 views

Electron transitions and spin [closed]

Take a single proton and electron. Write $n,\ell,m$ for the quantum numbers of the electron, and $1/2$ or $-1/2$ for its spin. The space of states of this system is the separable Hilbert space $V$ ...
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1answer
49 views

State with highest energy of Carbon atom

A possible excited state of the $C$-Atom is one with a $3s$ electron: $(1s)^2(2s)^2(2p)^1(3s)^1$. One can find out that there are the 4 possibilities $^1P_1, ^3P_2,^3P_1,^3P_0$. Why is the $^1P_1$ ...
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4answers
336 views

How do orbitals exist in an atom?

I have come across a picture online which talks about 1s,2s,2p orbitals of a sodium atom. Observation:In the picture we see some volume of space in common to two orbitals. For example:The circled(...
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1answer
76 views

Can an electron absorb a photon even if it exceeds the energy required for the electron to jump up an energy level?

To clarify my question, consider the hydrogen atom. An electron on the ground state needs 10.2 eV to be excited to the second state (first excited state). If a photon with less than 10.2 eV strikes ...
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1answer
71 views

How can an ion ever capture an electron if an electron requires a precise momentum to match a subsequent orbital?

Suppose an electron approaches a proton with greater energy than the hydrogen ground state. Will the electron scatter? If so, how could an electron ever be captured given it would require exactly the ...
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1answer
51 views

What effect causes energy difference between $2 \:^1 S$ and $2\: ^1 P$ electron state in a helium atom

I'm wondering where the energy difference between the two electron states $2 \:^1 S$ and $2\: ^1 P$ comes from in a helium atom. I thought it is the fine structure, but the fact that $S = 0$ is ...
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2answers
99 views

Does an electron's drop from $2s$ to $1s$ produce the exact same type of photon in different atoms and molecules? [closed]

Does an electron's drop from $2s$ to $1s$ produce the exact same type of photon in different atoms and molecules? Also, does a change from a higher principal quantum number to a lower one always ...
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1answer
77 views

Why does the nuclear charge remain the same in Moseley's law?

So Today I was taught about the Moseley's law and its relation with Bohr's formula : $$\frac{hc}{\lambda} = R \left(\frac{(Z-\sigma)^2}{n^2}-\frac{(Z-\sigma)^2}{m^2}\right)$$ My understanding is ...
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5answers
220 views

Why does an electron not emit energy when it is in a stationary state?

The Bohr's postulate states that an electron does not emit energy when it is in a stationary state. My question is, is it only a postulate or does it have proof? Also on what basis did Bohr come to ...
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1answer
57 views

Formula for number of atomic orbitals for a given $n$

In my studies, it is stated that an atomic orbital is usually described in terms of three quantum numbers: $n$, the principal quantum number, $l$, the orbital quantum number and $m$, the magnetic ...
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2answers
55 views

Is a boron atom isotropic in the absence of a field? If so, how can one write its electronic state?

Is a boron atom isotropic in the absence of a field? If so, how can one write its electronic state? An atom in the absence of any field should obey a spherical symmetry (unless there's spontaneous ...
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2answers
100 views

Physical meaning of quantized energy of electron (or n=1,2,3…) in Bohr's model

To solve objections on Rutherford's model, one of which is energy deficit, Bohr postulated that the energy of the electron is quantized and $n=1,2,3...$ . But what does this postulate mean physically? ...
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2answers
370 views

How is the wavefunction of an electron related to the atomic orbital?

Why is it that wavefunction $\psi$ is maximum at the nucleus for $1 \text{s}$ orbital, even if the probability of finding electron is zero there. What is the significance of wavefunction. Can anyone ...
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0answers
129 views

Why do electrons abide by Hund's rule?

Is the reason why Hund's rule exists, that when electrons are in different orbitals (such as 2px, 2py, or 2pz), they are most stable (lowest energy)? If the purpose is stability/lowest energy, ...
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0answers
86 views

How to use Hund's third rule for excited electronic configurations?

Hund third rule states: For a given term, in an atom with outermost subshell half-filled or less, the level with the lowest value of the total angular momentum quantum number ${\displaystyle J\...
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3answers
132 views

Why are there three $p$-orbitals?

This question is specifically about Schrödinger quantum mechanics, but if an answer in some other mode would illuminate it could be acceptable, as demonstrating a physical or mathematical reason for ...
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1answer
101 views

How electrons really revolve around nucleus through nodal plane in $p$ orbital? [duplicate]

I have read somewhere that electrons revolve around the nucleus and electrons are most probably found in orbitals. Can someone explain how electrons really revolve around nucleus through nodal plane ...
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2answers
97 views

Bohr quantization hypothesis [closed]

To explain Rydberg formula, Bohr have assumed somewhat general hypothesis which is applicable to various classical system. As far as I know he assumed that for any classical system with periodic ...
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2answers
77 views

If $2p$ is circular, why is $2p_x$ not circular and what does $x$ mean?

I was reading about atomic orbitals. From Bohr's model, electron orbitals are considered circular. But as I saw the sub-orbitals like $2p_x$, $3d_{x^2-y^2}$ I noticed something strange. These sub-...
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1answer
80 views

Term symbols and Pauli principle

Given a Silicium atom with $1s^22s^22p^63s^23p^2$ I have to write down all possible term symbols. The solution says a possibility - apart from $^1S$, $^1D$ and $^3P$ - would be $^1P$, which - due to ...
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0answers
47 views

atomic orbitals calculation in Heisenberg picture

It sounds like this question was answered at the beginning of the last century. Nevertheless, going through some notes on basic quantum mechanics I noticed that Schordinger picture enables one to ...