### Video Transcript

In this video, we will learn about
the key principles of modern atomic theory and compare it to the Bohr model that
came before it. Every model of the atom was
developed to explain something. Dalton’s hard sphere model
accounted for the way atoms packed together. J. J. Thomson’s plum pudding model
accounted for the presence of negatively charged particles in the atom. These are electrons. Geiger, Marsden, and Rutherford
demonstrated the existence of the nucleus, a dense positively charged part of the
atom in the very center. It’s the nucleus that contains
protons. And Chadwick later demonstrated
that nuclei also contain uncharged particles. These were neutrons.

But even before Chadwick
demonstrated the existence of neutrons, Niels Bohr and Ernest Rutherford produced a
new model of the atom. In the Rutherford–Bohr model, often
simply called the Bohr model, electrons occupy orbits around the nucleus like the
planets around the sun. The nuclear sits in the middle, the
electrons go around the nucleus in a flat orbit, and the distance from the nucleus
of each orbit is determined by the number of electrons orbiting and the nuclear
charge. And it’s forbidden for an electron
to orbit the nucleus in between the fixed orbits.

The Bohr model accounted for the
fact that when we excite atoms or ions, they emit repeatable patterns of light,
individual lines, at specific wavelengths. The strict differences in energy
between orbits accounted for this behavior. An electron can be promoted to a
higher orbit and emit light with a specific energy when it drops down again. For each nucleus, there was a list
of specific allowed transitions, and these transitions for at least one element
matched up with the results. For atomic hydrogen, the Bohr model
was very accurate; however, for atoms with more than one electron, the Bohr model
was incapable of reproducing experimental results accurately.

Naturally, there’s a lot of
mathematics involved in the Bohr model, but we won’t be looking into the
specifics. Instead, we’d be looking at the
specific limitations of the Bohr model and then moving on to modern atomic
theory. As we’ve already mentioned, the
Bohr model in terms of the mathematics did not accurately describe multielectron
systems, which is most of chemistry. So the model was inappropriate even
for a simple system like a helium atom with two electrons.

It’s also important that the theory
of the atom allows us to move on to describing bonding in molecules and ionic
substances. However, the Bohr model didn’t
offer a clear way forward. One clear indication that Bohr
model wasn’t complete was that certain features of line spectra were not accounted
for, such as some lines being more intense than others, distinct lines that was so
very close together that no transition in the Bohr model could explain them, and in
a magnetic field, line spectra can split into two. This effect could not be explained
by the Bohr model.

A final nail in the coffin was that
the Bohr model violated Heisenberg’s uncertainty principle. Heisenberg’s uncertainty principle
is a part of quantum theory that came in later, and it states the more accurately
you determine a particle’s position in space, the less you can determine about the
particle’s momentum. This is a very deep, fundamental
feature of the universe, and we won’t be going into the details. But we can simplify it to mean that
we can either know where a particle is or how fast it’s going. The more precisely we measure one,
the more uncertain we are of the other. In the Bohr model, the position and
momentum of each electron is precisely defined and known.

This is a very high-level piece of
understanding, but we can boil it down to a very simple principle of matter. The Bohr model treated electrons
purely as particles, which orbited in a predictable way. However, de Broglie demonstrated
that electrons had wavelike properties as well as particle-like properties. Wave–particle duality is the name
for the concept that we can describe things in particle-like ways and also in
wavelike ways. The electron acts like a particle;
for instance, it has mass, and electrons can bounce off one another. But electrons also behave like
waves, creating diffraction patterns in the same way light does in a double-slit
experiment. An electron exhibits wave–particle
duality. It has particle-like properties and
wavelike properties.

The understanding that particles
also behave like waves is fundamental to modern atomic theory, which also relies on
quantum theory. In the early 1900s, there were many
theories and discoveries that revolutionized what we call classical physics. In classical physics, all types of
energy are seen to be continuous. You can adopt any value. But quantum theory introduced the
idea that certain types of energy came in discrete packets called quanta. The size of these quanta depends on
the system we’re dealing with. The details of this are
complicated. But the key thing to understand is
that this understanding allowed for a better model of the atom.

Quantum theory had a significant
effect in our understanding of light. Light comes in quanta called
photons. One of these green photons has
roughly the right amount of energy to break a chlorine-chlorine single bond. A photon of blue light has even
more energy, while a photon of red light has less. Armed with this understanding, we
can appreciate why some wavelengths of light have an effect, while others don’t. If the energy of the photon doesn’t
match the energy gap for the transition, the transition will not occur.

An understanding of wave–particle
duality and quantum theory led in part to a new model of the atom that we still use
today. Lots of people contributed to the
next model of the atom, and while it has undergone revisions since the 1900s, the
simple version of the model has stayed the same. The first tweak to the Bohr model
is that electrons can behave in wavelike ways. Electrons aren’t seen to have a
clear fixed position or momentum but can be spread out in a way that’s not easy to
understand. These electron waves act like
standing waves on a string. We can compare it to the way a
string on a guitar can vibrate, except electrons are doing this in three dimensions,
which makes it quite hard to visualize. Don’t worry if you can’t imagine
this; a lot of people struggle.

Just like with a guitar string,
only specific electron waves are allowed, and one of the most crucial features to
come out of the mathematics and the descriptions is that we don’t think so much
about the position of an electron, but where it might be. We then do averages to understand
the behavior of the electron. So while in the old description the
distance of an electron from the nucleus remained constant, the wave mechanical
model described electrons as having a range of possible positions. At any point in time, they may be
closer to the nucleus or they may be further away.

What’s more important from a
mathematical point of view is the distribution and its average. When we have positions with
different probabilities, we use a distribution. We can think of the electron being
a set distance from the nucleus for a certain proportion of the time. Sometimes the electron is close to
the nucleus. Sometimes it’s further away. But most of the time the electron
is in between. Just bear in mind that talking
about position of a wavelike electron gets very complicated, so this is just a
simplification.

When we consider these behaviors,
we start to talk about probabilities, and the probability distribution for the
position of an electron is known as its wave function. Some electron waves have
interesting shapes, so wave functions have to include the angle as well as the
distance from the nucleus. However, in this simple example,
we’ll stick with distance from the nucleus.

Erwin Schrodinger came up with a
formula that connected this probability distribution with the energy of the
electron, which matched the energies of the Bohr model of the hydrogen atom. The details of this equation are
far beyond the reach of this video, so don’t worry about remembering the
equation. What is important is that this
approach to probability and electron waves allowed for prediction of how systems
behave with multiple electrons. It also allowed us to understand
how electrons behave when they come together in chemical bonds.

We can think of the wave mechanical
model like a building. The floors of the building are at
fixed heights, just like the energy levels in an atom. Somebody working on the first floor
probably spends most of their time at their desks, but sometimes they’ll be getting
a drink from the water cooler, and sometimes they’re relaxed by the window. What’s important is that, on
average, they’re at their desks doing their job. If they put enough energy in, they
might get a promotion to a higher floor with a nicer desk. And if the reverse happens,
there’ll be a release of energy. Now that’s an overview of the
fundamentals. Let’s do a practice question.

The graph shows the probability of
finding the electron at a distance from the nucleus in the 1s orbital of an atom of
hydrogen. At what approximate distance is the
electron most likely to be found from the nucleus?

Here is the graph. The probability of finding the
electron is on the 𝑦-axis, and its distance from the nucleus is on the 𝑥-axis. Without units for the probability
axis, we can assume we’re dealing with relative probability. So points that are higher up the
𝑦-axis have a higher probability than points that are lower. The question also tells us we’re
dealing with an electron in the 1s orbital of an atom of hydrogen. An atom of hydrogen has the
electron configuration 1s1. s-type orbitals are spherical. This means the probability of
finding an electron doesn’t vary depending on which angle you’re pointing out. It’s only the distance from the
nucleus that matters.

We need to find the approximate
distance from the nucleus of this electron that’s most likely. The most likely event is the one
with the highest relative probability. So we need to find the highest
point of this curve and then draw down to the 𝑥-axis to find the distance. The highest point on this curve is
here. This corresponds with a distance
from the nucleus the 50 picometers. The question is only asking for the
approximate distance. But to my eye, that peak is bang on
the line of 50 picometers, so we can be comfortable that 50 picometers is the
correct answer. What this means is if you were to
check where the electron was in a 1s orbital of a hydrogen atom, more times than any
other it would be in about 50 picometers.

Let’s finish up with the key
points. The modern model of the atom is a
step forward from Bohr’s model, which says that electrons are in circular orbits
around the nucleus at fixed distances. The Bohr model was only able to
account for the energies in atoms like hydrogen with one electron. The Bohr model also violated
Heisenberg’s uncertainty principle, which is a fundamental feature of the
universe. Heisenberg’s uncertainty principle
tells us that the more accurately we know the position of a particle, the less
accurately we can know its momentum and vice versa.

The modern theory of the atom, the
wave mechanical model, tells us that electrons are like standing waves with
probability distributions for their positions. These probability distributions are
known as wave functions. The wave nature of an electron is
part of an understanding called wave–particle duality. The key thing we need to understand
about wave–particle duality is that particles like electrons have wavelike
properties as well.