What is Quantum number: Definition and 83 Discussions
In chemistry and quantum physics, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can be known with precision at the same time as the system's energy—and their corresponding eigenspaces. Together, a specification of all of the quantum numbers of a quantum system fully characterize a basis state of the system, and can in principle be measured together.
An important aspect of quantum mechanics is the quantization of many observable quantities of interest. In particular, this leads to quantum numbers that take values in discrete sets of integers or half-integers; although they could approach infinity in some cases. This distinguishes quantum mechanics from classical mechanics where the values that characterize the system such as mass, charge, or momentum, all range continuously. Quantum numbers often describe specifically the energy levels of electrons in atoms, but other possibilities include angular momentum, spin, etc. An important family is flavour quantum numbers – internal quantum numbers which determine the type of a particle and its interactions with other particles through the fundamental forces. Any quantum system can have one or more quantum numbers; it is thus difficult to list all possible quantum numbers.
TL;DR Summary: Quantum number of a state
What is the largest quantum number of a state of the Li3+ ion with an orbital radius equal to 60 A?
I tried solving the question as below
Assume spin 1/2 particle
So the spin operator gives +/- hbar/2
eg. S |n+> = +/- hbar/2 |n+>
But S= s(s+1) hbar = sqrt(3)/2 hbar
So I'm off by a factor of sqrt(3).
I suspect I am missing something fundamental about my understanding of spin.
My apologies and thanks in advance.
Hello,
I was wondering if it was possible to define good quantum numbers in solid state physics or chemistry when systems posses a discrete cylindrical symmetry Cnv. I know that in terms of angular momentum, L and L_z will be good quantum numbers for spherical symmetry, then only L_z is a good...
This problem had me take the taylor series of the Morse Potential,
until I got the first non zero term.
My result was U(x)=Aα2(x-x0)2.
I know to find the quantum number I can use En=(n+1/2)ℏω and I know I can relate that to the potential energy of a harmonic oscillator, 1/2kx2. So if this...
Summary:: Calculate the quantum number of a pendulum
I want to calculate the quantum number of pendulum. L = 1m, m = 1 kg., A= 3cm. I get a period of 2.01 sec. and f = 1/T = .498 sec. E =nhf gives me 2.67x10^31. The correct answer is 1.33x10^31, Where am I going wrong?
[Thread moved from...
Here is a question I have been given
I have started by setting up the formula and rearranging for n_2
Only problem is that I do not know the quantum number for ground state? What value do I sub in for n_1?
Any help would be appreciated! Thanks
Hi all,
Group theory show us that irreducible representation of SO(3) have dimension 2j+1. So we expect to see state with 2j+1 degeneracy.
But does group theory help to understand the principle quantum number n ? And in the case of problems with SO(3) symmetry does it explain its strange link...
n is the principal quantum number.
l is the angular momentum quantum number.
ml is the magnetic quantum number.
The possible values of l are 2, 3, and 4. I'm not sure if l can be equal to 4.
On the answer key, it shows l = 2, 3.
A spin quantum number can have a value of 1/2 or -1/2. I assume that the negative means that these two spins are in opposite directions. However, what does the 1/2 mean? Why 1/2, rather than a whole integer? Are there some sort of units associated with this value?
Hi everyone,
As the title says, I was wondering if the third quantum number affects spin since they are both linked by magnetism. If not, will an excited particle have a different spin than a non-excited one ?
Thanks for your answer and sorry for the possible mistakes, I'm just a young french...
Homework Statement
http://i.imgur.com/GQ9Xk6d.png
Homework Equations
Quantum mechanical model of atomic structure
The Attempt at a Solution
Why all sets are allowed?
H atom only got one e- which only one orbital should be there, isn't it?
If there aren't second or more e- , no second...
What are the weak isospins (T3 values) of various hadrons, including the proton, neutron, mesons, hyperons and other hadrons? How is the weak isospin calculated for any hadron?
Published sources provide T3 only for fundamental fermions, that is, quarks and leptons. In the fundamental bosonic...
how does the quantum number n in the wavefunction equation for a particle in a 1D box lead to increasingly well-separated energy levels?
I know that the separation of energy between the levels is given by ΔE = (2n+1)h^2 / 8mL^2 which means that the higher the n, the greater the energy...
What is the correct set of quantum numbers for the eighth electron that fills the orbitals in an atom of oxygen?
A. n = 2, l = 1, ml = –1, ms = –1/2
B. n = 2, l = 1, ml = +1, ms = –1/2
C. n = 2, l = 1, ml = +1, ms = +1/2
D. n = 2, l = 0, ml = –1, ms = +1/2
E. n = 1, l = 1, ml = +1, ms = –1/2
I...
Hello everyone,
In case of hydrogen atom, when we say spin up or spin down we refer to the z component of the spin. Why are we interested only in the z component of spin and not in the x and y components?
Thanks in advance
Hello everyone,
Why don't neutral particle oscillations have to obey conservation of (quark) flavor quantum numbers, with the example of neutral Kaon oscillations?
According to "Nat. Nanotechnol., vol. 7, no. 8, pp. 488–489, 2012 (http://www.nature.com/nnano/journal/v7/n8/full/nnano.2012.117.html?WT.ec_id=NNANO-201208)":
Valley quantum number is associated with different crystal axes that differ only in their orientations. Such axes can support electron...
So in class we went through the process of solving the S.W.E for the hydrogen atom.
During the process a constant ##\lambda_n=\frac{ze^2}{4\pi\epsilon_0\hbar}(\frac{\mu}{2|E_n|})^{\frac{1}{2}}## is introduced, where mu represents the reduced mass of the electron.
Later this constant is put on...
Hi,
Just wanted to ask, the principal quantum number represent the number of peaks of the probability wave and I think more the value of n, more the energy of the electron as the wave has more peaks so higher frequency,am I right? Then in azimuthal quantum number, the orbitals with same energy...
The question: Consider two masses of 0.1 gm each, connected by a rigid rod of length 0.5 cm, rotating about their center of mass with an angular frequency of 800 rad/s. a.) What is the value of l corresponding to this situation? b.) What is the energy difference between adjacent l-values for the...
I am wondering and have been thinking, exactly how does the energies of hydrogen atom orbital depend on quantum numbers? I am just curious because all of what I have learned/read discusses only one-dimensional situaiton, like a particle in a box, and I want to know how it can be applied to the...
For an atom, the single photon electric dipole selection rules for the magnetic quantum number require that delta_m = -1, 0 or +1.
As I understand, the physical explanation for this set of selection rules is usually related to the conservation of the projection of the angular momentum on the...
Hi--could someone explain how can one calculate for the root mean square fluctation in position when an electron (confined in a box) is quantum-mechanical and happens to be in a state (an infinitely large quantum number n) and why?
I do know how to calculate root mean square fluctation in...
My book on Physics by Beiser specifies that the rotational energy levels of a diatomic molecule are given by J(J+1)/ℏ2, where J = 0, 1, 2, 3, ... .
However, in the next page, it goes on to mention that the lowest rotational energy level corresponds to J = 1.
I don't see why that shouldn't...
Why isn't the Orbital angular momentum quantum number in the nuclear shell model restricted by the principal quantum number like it is in the atomic shell model? Also, does the principal quantum number even correspond to energy in the shell model?
The principal quantum number refers to the energy of the electron in an atom, and the average distance of the electron from the nucleus. It seems to me to be analogous to the concept of amplitude for a classical wave. Is there a relation?
Hi, please could someone provide me with an explanation of the differences between the magnetic quantum number and the spin. I thought that the magnetism of an electron/fermion comes from its intrinsic quantum angular momentum (i.e. its quantum spin) which was evidenced by the Stern–Gerlach...
Homework Statement
A nitrogen molecule (N2) has a mass of 4.68 x 10-26 kg. It is confined to a onedimensional
box of length L = 100 nm. What is the approximate quantum number n of
the molecule if it has a kinetic energy equal to the thermal energy kBT at room
temperature? What is n if it has a...
I have a pair of non interacting, identical 1/2 spin fermions in a one dimensional infinite square well with walls at x=0 and x=L.
One particle is in ground state, the other in first excited state.
This two-particle system has total spin quantum number S=0
I have normalized energy...
I was reading the following article regarding solution of wavefunction of hydrogen :
http://skisickness.com/2009/11/22/
To solve the angular part they gave the substitution of y = \sin \theta and then assumed that Y is a polynomial i.e. Y(y) = \sum b_n x^n and then arrived at the...
Hi,
I am going through the hydrogen atom at the moment, and I saw that the magnetic quantum number must run between ±L. I cannot find the reason in a simple enough form for me to understand, so I was hoping someone here could quickly (or slowly!) explain why ml can't be greater than L.
Thanks
Normally, Oxygen has 8 electrons in its neutral form that is 1s2 2s2 2p4. In this case, its principal quantum number (n) is two.
But what happens if it got excited and its electronic configuration becomes 1s2 2s2 2p3 3s1? In this case, Is the principal quantum number (n) of oxygen two or...
Homework Statement
An electron moves with speed v=10-4c inside a one dimensional box (V=0) of length 48.5 nm. The potential is infinite elsewhere. The particle may not escape the box. What approximate quantum number does the electron have?Homework Equations
En =...
So we are doing problems involving potential energy of electrons, wave functions, and all that jazz, but I am utterly lost on how to do this problem... The professor threw it at us, and I am completely lost on how to even begin. Please help me
In a different universe from ours the spin...
Hi,
For single-electron atomic systems, the electron can be specified by four quantum numbers n, l, m_l, m_s (principal, orbital, z-orbital, z-spin). The orbital quantum numbers are well defined since the problem is spherically symmetric.
However, for many-electron systems, the spherical...
I am aware that n is the principal quantum number and determines the energy of a specific energy level of an atom. In my notes, I see that n goes from 1,2,3... which implies to me all the way to infinity. If this is the case, why doesn't this imply that there can be infinitely many shells in an...
I have measured some fluorescence emission from excited iodine and am now trying to do a Birge-Sponer extrapolation. I'm just wondering if the vibrational quantum number increases or decreases with increasing wavelength?
In my instructions there's a plot showing how it might look, the linear...
Homework Statement
The level n=3 for atoms with 1 electron have the states 3s_{1/2}, 3p_{1/2}, 3p_{3/2}, 3d_{3/2}, 3d_{5/2}. If we ignore the spin-orbit coupling these states are degenerated. Calculate the degeneration due to the the spin-orbit coupling for the levels 3p and 3d for the...
Not really a homework problem, just a question on the Pauli exclusion principle.
I understand that each electron has two different spins, characterized by the possible values of the spin magnetic quantum number.
However, I do not understand why it is necessary that in each orbital the two...
Hi,
I am a second year physicist and I have completed 2 courses on quantum mechanics. The first was a decent overview of wave mechanics and the second was only 12 lectures long and applied this knowledge to the hydrogen and helium atoms and introduced aspects of atomic and molecular physics...
Hello,
What prevents the S_z quantum number from having a value of zero? With a standard angular momentum system the quantum number can have values between -l and +l.
Homework Statement
A helium atom had two electrons in the first shell (1s). Explain, withour detailed derivation, what the value of the total spin quantum number is.
Homework Equations
?
The Attempt at a Solution
Since the 2 electrons are in the first (1s) shell they must have...
Hi folks. I was always under the impression that the 'good quantum numbers' that we use to classify a particle species were always the eigenvalues of operators that commute with Hamiltonian governing that species. But it just struck me that weakly interacting particles have definite parity...