From: Ellen Koivisto (igneous@earthlink.net)
Date: Tue Jun 28 2005 - 17:51:10 PDT
Message-Id: <CB6BD616-90E6-4320-AE81-648EEF8D1CE6@earthlink.net> From: Ellen Koivisto <igneous@earthlink.net> Subject: Re: pinhole transition metal ions electron configuration Date: Tue, 28 Jun 2005 17:51:10 -0700
Hi Geoff etc.
Just got over a summer bug -- aren't they lovely -- hence my delay in
following up on this topic. I love the explanation you got from the
other listserv. I have a way of showing it to my kids that seems to
work, though the focus is actually on understanding orbitals at all.
It's called the dance of the electrons and takes a whole class, but
it's worth it.
In prep, I spend a lot of time over the entire year going over what
models are, what they're good for, why we use them, and what they
don't do. I tell them at the beginning of the year that, while we're
learning about bonding, we'll use a model of the atom they all know
(the electrons as planets orbiting the sun/nucleus) but that we know
the model isn't accurate. We've done the 4 Forces by then so they
can see that it can't work, but it's a good enough explanation until
we get to quantum. They get comfortable with this provisional model
for why things work, which is a major thing I try to teach them about
science.
Anyhow, once we hit quantum -- usually around January -- I introduce
the whole weirdness in one fell swoop. As their little heads are
bursting, I show them pictures of all the orbitals, not just the s
and p that are in most textbooks. I particularly like Zumdahl's pix
in the AP/college text, as he also includes cut-aways of s orbitals
nested inside lower energy s orbitals, and he labels each orbital by
its axial orientation. We go over how electrons in these orbitals
fit inside each other as you get to higher and higher energy levels,
and I do a wicked mime of how the electrons fill all the space
available. As the energy levels get further away from the nucleus
there is more space available, so more electrons can co-exist on the
same energy level. They get it, pictures, explanations, teacher
moving around, but it's still not solid until we go into the gym.
Here we actually dance out a model of the electrons. We build
slowly. A kid in the middle is the H proton, a kid circling is the H
electron. Add another proton and another electron (we don't have
space for neutrons, and even SF class sizes aren't big enough to from
transition metals with correct proton/neutron/electron numbers.) The
electrons quickly discover they can only move in 2 dimensions in any
reasonable way (drilling through the floor or flying not being
options). The protons have to jiggle and jostle, the electrons have
to stay in motion. Anyhow, with electrical repulsion of like charges
keeping the electrons going, it's clear that there isn't room for any
more electrons at the 1s level. It's also clear that the s shape
gets the electrons as close as possible to the nucleus.
Next level out we get the 2s electrons (somewhere around carbon I
stop adding proton students to the nucleus because it just gets too
crowded, but we say we're adding another one every time), the s shape
still being closest but requiring more energy to cover, but suddenly
there's all this space at about the same level that doesn't have any
electrons around for significant amounts of time. So we start adding
in 2ps. Of course, we can't do the 2ps on the y axis (the flying
problem again) but we talk through it when we hit it. Also about
this time, the students see why each p orbital half fills before
electrons are added to completely fill the orbitals. And they
discover that even though they know the 2 electrons in the 2px, for
example, can exist in either of the 2 nodule of this orbital, the
students aren't capable of teleportation and so they tend to stay in
one nodule each.
We go on like this until we run out of students. I usually make it
to 4s and some 3ds. My 1s electrons are very tired by the time we're
done, so you can really have fun picking students for this one. Then
they take a few minutes to write down notes before the class is
over. A 1-page drawing with explanation of what we did and the short-
comings of this model is due the next class. And it seems to work.
They get how it works much better, and they don't have the problems
with transition from model to experimental evidence or to different
models that my students used to have before I thought this up.
I still need some help making this work better though. I can tell my
students that an electron acts both like a particle and a wave, and
that the wave nature explains the nodes where no electrons are, but
justifying that in terms of what they know about electrical
attraction between the electrons and protons is where I'm stuck.
Anyone have a good, math-free model that explains why the electrons
don't dive into the nucleus and just stay there? Especially the 1s
electrons, as these are unshielded.
Thanks,
Ellen Koivisto
SF, SOTA
On Jun 28, 2005, at 5:00 PM, Geoff Ruth wrote:
> I got an answer that I like a lot from another listserv to my prior
> question. I'm posting it below to share:
>
> First of all, the order we traditionally list is what I call
> the FILLING
> ORDER, which is the order in which electrons FIRST enter the orbitals.
> This is no guarantee that that continues to be the energy order of the
> orbitals after electrons are present. This order is affected by (as
> Mike
> mentioned) the number of electrons in the orbitals. Remember that the
> orbitals are different sizes, and the size is related most closely
> to the
> principal quantum number, n. By size, we are referring primarily to
> the
> distance away from the nucleus with the greatest probability of
> finding
> the electrons. Specifically, the 4s orbital is larger than the 3d
> orbitals. In general, the larger the orbital, the higher its energy.
>
> However, there is another factor that influences the INITIAL
> energy of an
> orbital, and that is the number of nodes the orbital has. A node is a
> "line/surface" where the likelihood of finding an electron is zero.
> The
> greater the number of nodes, the higher the energy of the orbital.
> This is
> similar to the number of nodes in a standing wave on a spring or a
> rope.
> The more nodes, the more energy is needed to produce the standing
> wave.
> There are two types of nodes in an orbital: Radial nodes (at a certain
> distance away from the nucleus) and angular nodes (at certain
> directions
> from the nucleus). The number of radial nodes is related to n, but the
> number of angular nodes is related to the azimuthal quantum number,
> l. The
> 4s has more radial nodes than the 3d's, but the 3d's have two angular
> nodes (as ALL d orbitals do) where the 4s has none (like all s
> orbitals).
> This gives the 3d orbitals more energy initially than the 4s orbitals.
>
> All bets are off, however, when we start placing electrons in the
> orbitals. As noted above, the 3d's are closer to the nucleus, so
> there is
> more attraction between 3d electrons and the nucleus than between 4s
> electrons and the nucleus (simple physics here: the force is inversely
> related to the distance between the two charges). This makes it
> harder to
> pull the 3d electrons away from the nucleus. In addition, chemists
> like to
> talk about "shielding" by inner electrons reducing the "effective
> nuclear
> charge" on the outer electrons. As soon as we start adding
> electrons to
> the 3d orbitals, the relative energies of the subshells change (as
> Mike
> noted), so that, before we have added very many electrons to the 3d
> subshell (2?) the 3d subshell has lower energy than the 4s subshell
> and
> the first electrons removed come from the 4s rather than the 3d.
>
> I hope this helps.
>
> Tom Harrison
> Sandy Spring Friends School
> Sandy Spring, MD
> tomh@ssfs.org
>
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