I need a 75 on my final exam for an A, but I'd obviously get as close to a 100 as possible. I understand n and l (memorized l) but I'm confused about ml and spin. Can someone explain that to me?
In general, the quantum numbers precisely specify the state. The electron in a hydrogen atom can be described by n, l, m, and s. These are the principal number (which shell), l is orbital angular momentum, with projection m. So far that specifies a spatial orbital which can be occupied by up to two electrons (required to have differing spin).
n,l, and m_l cannot vary independently - it has to do with the solution of Schroedinger’s equation. I presume you’re talking about Hydrogen orbitals.
n and l come from the solutions of the radial equation and the solution is only defined for integer values of n and integer values of l between 0 and n - 1. Solutions without integers are non-convergent and/or non-physical.
n: associated with total energy: E_n = -13.6 eV/n^2
l: associated with total angular momentum, L^2 = hbar^2*l(l+1)
m_l is the z-component of the angular momentum and it can take on values of -l to l. Essentially two important things are at work, The z-component cannot be as large as the total vector and we must obey the uncertainty principle. The total angular momentum cannot be aligned along the z-axis, otherwise we’d precisely know x*p_y - y*p_x and that can never happen.
The Aufbau principle helps you to fill the orbits of multiple electron atoms correctly and it balances the attraction between the electron and the nucleus while minimizing repulsion between the e-. Think of it as the traffic cop that puts electrons on opposite sides of the nucleus to keep the peace.
How would this apply to higher orbitals though? By this, I mean atoms with more than one electron level
The hydrogenic orbitals are solutions of a one-electron equation. Once you have even one additional electron, they interact via what is called electron correlation. Nevertheless, chemists, especially at your level use the hydrogenic orbitals as a model even when there are many electrons. Wikipedia has handy pages on term symbols and electron configurations that give the restrictions on l and m for a given n.
looks like the previous two posters are actual physical chemists (or maybe physicists). kudos to them. here's a basic and less rigorous answer that should be suitable for the knowledge level expected of a general chemistry course.
every electron in an atom is uniquely described by a set of four quantum numbers. the quantum numbers are like coordinates that tell you what orbital the electron resides in, and also the spin of that electron.
n: principle quantum number - this specifies the shell. for a 1s orbital, n = 1. for a 4f orbital, n = 4. etc.
l: angular momentum - this specifies the type of orbital. l = 0 -> s orbital, l = 1 -> p orbital, l = 2 -> d orbital, l = 3 -> f orbital, etc.
m_l: magnetic quantum number - you can think of this as specifying which specific orbital. for example, let's consider the 2p orbitals: there are three of them. m_l can vary from -l to +l, so for 2p orbitals, you will have m_l values of -1, 0, and +1. each of these m_l values corresponds to a unique 2p orbital. you might have learned elsewhere about p_x, p_y, and p_z orbitals. these are convenient for thinking about the orbitals in real space, but don't correspond to hydrogenic solutions to the schrodinger equation. to be more precise, m_l = 0 corresponds to p_z. p_x and p_y are linear combinations of m_l = +1 and m_l = -1.
m_s: spin quantum number - denotes whether your electron is spin up or spin down. pauli exclusion principle says two electrons in the same orbital cannot have the same spin. n, l, and m_l tell you which orbital you're in. m_s tells you which electron you're talking about in that orbital.
with that, you have completely described the unique "coordinates" of an electron in an atom.
looks like the previous two posters are actual physical chemists (or maybe physicists). kudos to them. here's a basic and less rigorous answer that should be suitable for the knowledge level expected of a general chemistry course.
every electron in an atom is uniquely described by a set of four quantum numbers. the quantum numbers are like coordinates that tell you what orbital the electron resides in, and also the spin of that electron.
n: principle quantum number - this specifies the shell. for a 1s orbital, n = 1. for a 4f orbital, n = 4. etc.
l: angular momentum - this specifies the type of orbital. l = 0 -> s orbital, l = 1 -> p orbital, l = 2 -> d orbital, l = 3 -> f orbital, etc.
m_l: magnetic quantum number - you can think of this as specifying which specific orbital. for example, let's consider the 2p orbitals: there are three of them. m_l can vary from -l to +l, so for 2p orbitals, you will have m_l values of -1, 0, and +1. each of these m_l values corresponds to a unique 2p orbital. you might have learned elsewhere about p_x, p_y, and p_z orbitals. these are convenient for thinking about the orbitals in real space, but don't correspond to hydrogenic solutions to the schrodinger equation. to be more precise, m_l = 0 corresponds to p_z. p_x and p_y are linear combinations of m_l = +1 and m_l = -1.
m_s: spin quantum number - denotes whether your electron is spin up or spin down. pauli exclusion principle says two electrons in the same orbital cannot have the same spin. n, l, and m_l tell you which orbital you're in. m_s tells you which electron you're talking about in that orbital.
with that, you have completely described the unique "coordinates" of an electron in an atom.
This is all good info probably at the right level. I was trying to keep it basic. It really depends what is expected for the test. I figured the atomic term symbol stuff and working out the electron configuration for ground and excited states of a few low Z elements might be more or less what is needed. Not worth typing out too much when there are some on line resources.
The Aufbau principle helps you to fill the orbits of multiple electron atoms correctly and it balances the attraction between the electron and the nucleus while minimizing repulsion between the e-. Think of it as the traffic cop that puts electrons on opposite sides of the nucleus to keep the peace.
This principled traffic cop was named Wolfgang Pauli (supposedly also the guy who coined the phrase "not even wrong").
Yeah, you have to give a nod to Hund and even Bohr too for this.
It’s hard to imagine a more acerbic personality in science than Pauli.
He is an absolute hero of mine for proposing the existence of neutrinos. IMO, the discovery of them is right up there with Neptune and the work of Hertz on EM waves.
looks like the previous two posters are actual physical chemists (or maybe physicists). kudos to them. here's a basic and less rigorous answer that should be suitable for the knowledge level expected of a general chemistry course.
every electron in an atom is uniquely described by a set of four quantum numbers. the quantum numbers are like coordinates that tell you what orbital the electron resides in, and also the spin of that electron.
n: principle quantum number - this specifies the shell. for a 1s orbital, n = 1. for a 4f orbital, n = 4. etc.
l: angular momentum - this specifies the type of orbital. l = 0 -> s orbital, l = 1 -> p orbital, l = 2 -> d orbital, l = 3 -> f orbital, etc.
m_l: magnetic quantum number - you can think of this as specifying which specific orbital. for example, let's consider the 2p orbitals: there are three of them. m_l can vary from -l to +l, so for 2p orbitals, you will have m_l values of -1, 0, and +1. each of these m_l values corresponds to a unique 2p orbital. you might have learned elsewhere about p_x, p_y, and p_z orbitals. these are convenient for thinking about the orbitals in real space, but don't correspond to hydrogenic solutions to the schrodinger equation. to be more precise, m_l = 0 corresponds to p_z. p_x and p_y are linear combinations of m_l = +1 and m_l = -1.
m_s: spin quantum number - denotes whether your electron is spin up or spin down. pauli exclusion principle says two electrons in the same orbital cannot have the same spin. n, l, and m_l tell you which orbital you're in. m_s tells you which electron you're talking about in that orbital.
with that, you have completely described the unique "coordinates" of an electron in an atom.
I wonder how humans were able to figure out that stuff in the first place.
On a related note, what happens to those electrons when matter is compressed (i.e., white dwarfs?)
looks like the previous two posters are actual physical chemists (or maybe physicists). kudos to them. here's a basic and less rigorous answer that should be suitable for the knowledge level expected of a general chemistry course.
every electron in an atom is uniquely described by a set of four quantum numbers. the quantum numbers are like coordinates that tell you what orbital the electron resides in, and also the spin of that electron.
n: principle quantum number - this specifies the shell. for a 1s orbital, n = 1. for a 4f orbital, n = 4. etc.
l: angular momentum - this specifies the type of orbital. l = 0 -> s orbital, l = 1 -> p orbital, l = 2 -> d orbital, l = 3 -> f orbital, etc.
m_l: magnetic quantum number - you can think of this as specifying which specific orbital. for example, let's consider the 2p orbitals: there are three of them. m_l can vary from -l to +l, so for 2p orbitals, you will have m_l values of -1, 0, and +1. each of these m_l values corresponds to a unique 2p orbital. you might have learned elsewhere about p_x, p_y, and p_z orbitals. these are convenient for thinking about the orbitals in real space, but don't correspond to hydrogenic solutions to the schrodinger equation. to be more precise, m_l = 0 corresponds to p_z. p_x and p_y are linear combinations of m_l = +1 and m_l = -1.
m_s: spin quantum number - denotes whether your electron is spin up or spin down. pauli exclusion principle says two electrons in the same orbital cannot have the same spin. n, l, and m_l tell you which orbital you're in. m_s tells you which electron you're talking about in that orbital.
with that, you have completely described the unique "coordinates" of an electron in an atom.
I wonder how humans were able to figure out that stuff in the first place.
On a related note, what happens to those electrons when matter is compressed (i.e., white dwarfs?)
Many persistent misunderstandings regarding matter are born from a desire to understand what it is in our own terms. As an example, consider wave-particle duality - a supposed mystery in quantum mechanics. It really just reflects the fact that we lack the vocabulary to describe quantum objects. Intrinsic angular momentum is another example - we are often asked to imagine electrons as spinning tops, but such a description fails spectacularly when put to the test.
Not trying to be pedantic, but just alerting you to the fact that white dwarf stars are typically a million times the density of water. They’re around 10,000K and can have magnetic fields of up to 100 T - about 70 times bigger than in an MRI. All of these things are pretty well documented and you can find them online.
What they don’t really tell you is this:
A white dwarf is what happens when you shrink an object the size of the sun down so that it behaves more or less like an an isolated macro-atom. That’s what degenerate matter is.