1. 5.1 Revising the Electron Model
Read the lesson title aloud to students.

2. Development of modern atomic theory
1803- Dalton model: tiny, indestructable particles
1897- Thomson model: sphere of positive charge with negative charges attached to the outside
1911- Rutherford model: small, dense, positively charged nucleus
1913- Bohr model: electrons in circular, fixed orbits
1926- Quantum mechanical model: electron cloud

3. Spectrum: Discreet or Continuous
Spectrum: Discreet or Continuous? Energy added to atoms allows electrons to change energy levels. Electrons emit light energy when they lose energy.
Continuous spectrum
Discreet spectrum
Explain that the difference between a continuous and a discreet spectrum must be understood before discussing the different models of atoms that were proposed in the early twentieth century.
Ask: Which spectrum is continuous?
Answer: The top spectrum is continuous. It contains essentially all the visible colors in equal amounts, and there are no “gaps” in the spectrum.
Click to label the spectra.
Explain that “spectrum” in this context refers to the spatial separation of different colors of light, as happens in a rainbow. A rainbow is an example of a continuous spectrum because it displays essentially all visible wavelengths and all wavelengths are essentially equally represented, so there are no “gaps” in the spectrum. A “discreet spectrum” refers to a spectrum with a few very-well-defined wavelengths. Thus, the spectrum is black (that is, no light) for most wavelengths, but certain well-defined wavelengths are visible, as in the bottom spectrum.
410 nm
656 nm

4. Limitations of Rutherford’s Atomic Model
Main characteristics of model: heavy nucleus about which
light electrons orbit
Could not explain:
discreet spectrum of
hot gases
sequence of colors
emitted when you heat
materials
Ask: What were the main characteristics of Rutherford’s model of the atom?
Answer: The model proposed that atoms consisted of a heavy nucleus about which orbited very light electrons.
Click to reveal the response.
Tell students: After discovering the atomic nucleus, Rutherford used existing ideas about the atom to conceive an atomic model in which the electrons move around the nucleus like the planets move around the sun.
Explain that the experimental designs and conclusions that Rutherford used in developing his nuclear atomic model explained only a few simple properties of atoms, such as why a He nucleus would backscatter (that is, rebound back in the direction from which it came) when collided with atoms, which is explained by invoking a collision with the heavy atomic nucleus.
Click to reveal text of what model could not explain.
Explain that the model could not explain many other properties of atoms, including the two shown on the screen.
Explain that hot gasses emit discreet spectra such as the one shown on the previous slide (which is the visible part of the spectrum of hydrogen).
Ask: What colors are emitted by a piece of say, iron, as you heat it up?
Answer: As the iron gets progressively hotter, the colors emitted are first red, then yellow, then finally white.
Explain that Rutherford’s planetary model of the atom could not explain this phenomenon. According to Rutherford’s model, the atoms would emit a continuous spectrum of light. The observed behavior could be explained only if the atoms in the iron gave off light in certain specific (or discreet) amounts of energy.
For advanced students, explain that another limitation of the Rutherford model was the stability of the atom. According to the classical physics known at the time, electrons that accelerate around an orbit should continuously radiate electromagnetic radiation, which would reduce the energy of their orbit until they crashed into the nucleus. Thus, classical theory applied to Rutherford’s model predicts that an atom would have a lifetime on the order of seconds, which is not true.

5. Bohr Nuclear Atomic Model
Bohr proposed that an electron is found only in specific circular paths, or orbits, around the nucleus.
656 nm
Explain that Niels Bohr (1885–1962), a young Danish physicist and a student of Rutherford, used experimental designs and drew conclusions that resulted in a new atomic model. New discoveries had shown that hydrogen gas emitted light only at certain frequencies. Bohr wanted to explain why a hydrogen atom would emit only specific frequencies of light, not a range of frequencies as expected in Rutherford’s model.
Click to reveal the statement of Bohr’s proposed atomic model.
Invite a student to read Bohr’s statement aloud.
Explain that each possible electron orbit in Bohr’s nuclear atom has a fixed energy. The electron energy increases if the electron is in orbit farther from the center. The lowest-energy orbit is the smallest orbit.
Explain that the gold sphere is a proton, which is the nucleus of a hydrogen atom, and the circles around it are possible orbits for the electron. The electron is currently orbiting at two energy levels above the lowest-energy orbital. If the electron drops to the next-lower-energy orbital, one photon of light is emitted at the wavelength that corresponds to the energy difference between the orbitals. So the discreet orbitals lead to the discreet emission spectrum of hot gases.
Click to show the electron transferring to lowest-energy state and the corresponding photon creating the red spectral line.
Explain that Bohr labeled each energy level with an integer “n.”
Click to show the orbit labels.
Explain that the energy of the electrons in their orbits increases with increasing n.
Ask: If the electron were to drop from the outermost orbit to the innermost orbit, would the energy of the photon released be greater than, less than, or equal to the energy of the photon released in the animation?
Answer: The energy would be greater because the electron drops from the n = 3 orbit to the n = 1 orbit, so the difference in energy of the orbits is greater than the difference between the n = 3 and n = 2 orbits.
Ask: If the electron were to drop from the n = 2 orbit to the innermost orbit, would the energy of the photon released be greater than, less than, or equal to the energy of the photon released in the animation?
Answer: Without knowing how the energy of the electron in a given orbit depends on n, we cannot know the relative magnitudes of the differences in energies between orbits.
n = 1
n = 2
n = 3

6. Electron Energy Levels
Electron Energy Levels Electrons have fixed energies called energy levels. They can’t exist between levels. A quantum is the amount of energy required to move up to the next level. Electrons are said to be “quantized”.
Ordinary Ladder
Quantum Ladder
n = 1
n = 2
n = 3
Explain that the fixed energies an electron can have are called energy levels. The fixed energy levels of electrons are somewhat like the rungs of the ladder. The lowest rung of the ladder corresponds to the lowest energy level.
Explain that a person can climb up or down the ladder by stepping from rung to rung. Similarly, an electron can move from one energy level to another. A person on the ladder cannot stand between the rungs. Similarly, the electrons in an atom cannot exist between energy levels. To move from one rung to another, a person climbing the ladder must move just the right distance. To move from one energy level to another, an electron must gain or lose just the right amount of energy.
Explain that for an ordinary ladder, the rungs are equally spaced. For the ladder rungs to represent the energy levels of electrons in atoms, the ladder should look like this.
Click to reveal the quantum ladder.
Ask: How does the quantum ladder differ from the ordinary ladder?
Answer: The rungs in the quantum ladder are unequally spaced. The higher energy levels are closer together.
Explain that the energy levels of atoms are not equally spaced, similar to the rungs of the quantum ladder. The higher energy levels are closer together. It takes less energy to climb from one rung to another near the top of the ladder, where the rungs are closer. Similarly, the higher the energy level occupied by an electron, the less energy it takes the electron to move from that energy level to the next-higher energy level. A quantum of energy is the amount of energy required to move an electron from one energy level to another energy level.
Ask: On the quantum ladder, which rung would correspond to the smallest orbit in the Bohr model of the atom?
Answer: The lowest rung corresponds to the smallest orbit because they are both the lowest-energy state (electronic energy for the atom, gravitational potential energy for the ladder).
Ask: What orbital number would correspond to the lowest rung?
Answer: The smallest orbit has n = 1.
Click to label the rungs.
Explain that the rungs, or the energy levels of atoms, are numbered with integers, starting with 1 for the lowest energy level.
Explain that Bohr’s nuclear atom provided results in agreement with experiments using the hydrogen atom. However, the Bohr model failed to explain the energies absorbed and emitted by atoms with more than one electron.

7. Quantum Mechanical Model
Quantum Mechanical Model Schrodinger devised a mathematical equation describing the behavior of electrons. It determines where the electron is likely to be.
Similar to Bohr model
Different from Bohr model
Restricts the energy of electrons to certain values
No exact path for electron around the nucleus
Electron cloud
Explain that the Rutherford model and the Bohr model of the atom described the path of a moving electron as you would describe the path of a large moving object. Later theoretical calculations and experimental results were inconsistent with describing electron motion this way. In the early twentieth century, scientists discovered that very small objects (subatomic particles) behave very, very differently from “normal” size objects that we deal with in our daily lives. New physics was needed to describe the very small.
In 1926, the Austrian physicist Erwin Schrödinger devised and solved a mathematical equation describing the behavior of the electron in a hydrogen atom. The modern description of the electrons in atoms, called the quantum mechanical model, came from the mathematical solutions to the Schrödinger equation.
Explain that like the Bohr model, the quantum mechanical model of the atom restricts the energy of electrons to certain values.
Click to reveal the text describing similarity to the Bohr model.
Explain that the quantum mechanical model does not specify an exact path that the electron takes around the nucleus.
Click to reveal the text describing differences from the Bohr model.
Explain that the quantum mechanical model determines the allowed energies an electron can have and how likely it is to find the electron in various locations around the nucleus of an atom.
Click to show the windmill.
Explain that the quantum mechanical description of how electrons move around the nucleus is similar to a description of how the blades of a windmill rotate. The windmill blades in the photo have some probability of being anywhere in the blurry region they produce in the picture, but you cannot predict their exact location at any instant.
Click to show the schematic of an atom.
Explain that in the quantum mechanical model of the atom, the probability of finding an electron within a certain volume of space surrounding the nucleus can be represented as a fuzzy, cloudlike region, as shown. The cloud is more dense where the probability of finding the electron is high and is less dense where the probability of finding the electron is low. There is no boundary to the cloud because there is a slight chance of finding the electron at a considerable distance from the nucleus. Therefore, attempts to show probabilities as a fuzzy cloud are usually limited to the volume in which the electron is found 90 percent of the time.

8. Probability Distribution
Probability Distribution An atomic orbital is a region of space where there is a high probability (90%) of finding an electron.
Probability
Explain that solutions to the Schrödinger equation give the energies, or energy levels, an electron can have. For each energy level, the Schrödinger equation also leads to a mathematical expression, called an atomic orbital, that describes the probability of finding an electron at various locations around the nucleus. An atomic orbital is represented pictorially as a region of space in which there is a high probability of finding an electron (approximately 90 percent probability). An atomic orbital is a probability distribution.
Explain that to better understand a probability distribution, students will see an animation of ten particles that rebound randomly off molecules or atoms (not shown) until they descend into one of the funnels. Each funnel determines the final position on the x-axis of the particle that falls into it. The larger funnels are more likely to capture more particles, so the probability of finding a particle under the large funnel is greater than under a small funnel.
Click to show the animation.
Ask: Based on this animation, what is the probability of finding a particle at x = 4?
Answer: Out of ten particles, four of them finished their random trajectory at x = 4, so the probability of finding a particle at x = 4 is 4/10 or 0.4.
Click to label the probability.
Ask: Based on this animation, what is the probability of finding the particle at x > 3?
Answer: Out of ten particles, four of them finished at x = 4, two at x = 5, and one at x = 6, so a total of = 7 particles finished their random trajectories at x > 3. The probability of finding a particle at x > 3 is therefore 7/10 = 0.7.
These probabilities are described by a curve, which is called the probability distribution.
Click to show the probability distribution.
Emphasize that this is a one-dimensional probability distribution. Later in the lesson, three-dimensional probability distributions will be seen.
0.4 x 1 2 3 4 5 6
Distance
Red curve is probability distribution.

9. Atomic Orbitals
Energy levels of electrons are labeled by principal quantum numbers (n). The values have different shapes and energy levels as they increase in value.
n = 1,2,3,4…
Different sublevels in the orbital are denoted by letters
(s, p,d,f).

10. Atomic Orbital for n = 1 s sublevel (d, 0, 0) (0, −d, 0)
The energy levels of electrons in the quantum mechanical model are labeled by principal quantum numbers (n) inherited from the Bohr model.
Click to show the text for principal quantum number.
The principal quantum number can be any positive integer (n = 1, 2, 3, 4, and so on). For n = 1, a single atomic orbital is possible, which is a spherically symmetric orbital as shown on the screen. It is called an “s” orbital.
Tell students: Let’s examine the probabilities of finding the electron at two different points around the nucleus.
Click to show two points.
Ask: How does the probability of finding the electron a distance −d on the y-axis compare to the probability of finding an electron a distance +d on the x-axis?
Answer: Because the wave function is spherically symmetric, these probabilities are equal because they are the same distance from the origin.
Ask: What is the probability of finding the electron outside the atomic orbital pictured on the screen?
Answer: The pictorial representation of the atomic orbital shows the volume in which there is a 90 percent chance of finding the electron, so outside this region there is a 10 percent chance of finding the electron.

11. Atomic Orbitals for n = 2 p sublevels s sublevel
Remind students that as for the Bohr model, electrons in n = 2 orbitals in the quantum model have higher energy than electrons in the n = 1 orbital.
Explain that for each principal energy level greater than 1, there are several orbitals with different shapes and at different energy levels. These energy levels within a principal energy level constitute energy sublevels.
Explain that different atomic orbitals are denoted by letters. We have already seen the s orbital, which is spherical.
Click to label the s sublevel.
Explain that for n = 2, electrons can also occupy “p” orbitals, which are higher in energy than the (n = 2) s orbital.
Click to reveal the p sublevels.
Ask: For the py orbital, what is the probability of finding an electron on the z-axis?
Answer: It is essentially zero. The py orbital does not cross the z-axis except at the origin, but the py orbital goes to zero at the origin.
For advanced students, ask: How does the electron in a p orbital get from one lobe of the orbit to the other if it has zero probability to be at the origin (which it must cross to get from lobe to the other)?
Answer: We cannot think of electrons in the same way as we think of macroscopic particles. The only description currently available for quantum-sized particles like electrons is their wave function, which only gives the probability of where a point-like electron would be found if we were to look for it (for example, by scattering another electron from it). In fact, the electron is not a point-like particle, but has wave characteristics as well, so you can say that the electron is actually partly in both lobes at the same time! The quantum world is nothing like the macroscopic world and does not always obey our intuition, which was constructed based on the macroscopic world.

12. Atomic Orbitals for n = 3 d sublevels p sublevels s sublevel
Explain that for n = 3, a third sublevel is possible, called the “d” level.
Click to show the d sublevels.
Emphasize the number of sublevels is equal to the principle quantum number n.
Ask: How are the orientations of the d xy and d x2−y2 orbitals similar? How are they different?
Answer: Both lie in the xy plane. The lobes of the d xy orbital lie between the x- and y-axes. Those of the d x2–y 2 orbital lie along the x- and y-axes.
Tell students that the next-higher orbital is the f orbital, which has a more complicated shape than the d orbital. The f orbital is possible for n greater than or equal to 4.

13. Principle energy level Maximum number of electrons
Summary of Energy Levels and Sublevels Maximum number of electrons in an orbit can be determined by the 2n2 rule.
Principle energy level
Number of sublevels
Types of sublevels
Maximum number of electrons
n = 1
n = 2
n = 3
n = 4
4s (1 orbital), 4p (3 orbitals),
4d (5 orbitals), 4f (7 orbitals) 1 2 3 4
1 s (1 orbital) 2 8 18 32
2s (1 orbital), 2p (3 orbitals)
3s (1 orbital), 3p (3 orbitals),
3d (5 orbitals)
Ask: How many sublevels does each principle energy level have?
Answer: The number of sublevels is the same as the principle quantum number n of the principal energy level.
Click to reveal the response.
Ask: What type of sublevels does the n = 1 principal energy level have, and how many orbitals are in the sublevels?
Answer: It has an s sublevel with a single orbital.
Ask: What type of sublevels do the n = 2 principal energy level and n = 3 energy level have, and how many orbitals are in the sublevels?
Answer: They each have an s sublevel with a single orbital and a p sublevel with three orbitals. In addition, the n = 3 principal energy level has a d sublevel with five orbitals.
Explain that the lowest principal energy level (n = 1) has only one sublevel, called 1s. The second principal energy level (n = 2) has two sublevels, 2s and 2p. The 2p sublevel is of higher energy than the 2s sublevel and consists of three p orbitals of equal energy. Thus, the second principal energy level has four orbitals (one 2s and three 2p orbitals). The third principal energy level (n = 3) has three sublevels. These are called 3s, 3p, and 3d. The 3d sublevel consists of five d orbitals of equal energy. Thus, the third principal energy level has nine orbitals (one 3s, three 3p, and five 3d orbitals).
Ask: How many orbitals are in the n = 4 principal energy level, and what are the orbitals called?
Answer: The fourth principal energy level (n = 4) has four sublevels, called 4s, 4p, 4d, and 4f. The 4f sublevel consists of seven f orbitals of equal energy. The fourth principal energy level, then, has sixteen orbitals (one 4s, three 4p, five 4d, and seven 4f orbitals).
Explain that the principal quantum number always equals the number of sublevels within that principal energy level. The number of orbitals in a principal energy level is equal to n2. As you will learn in the next lesson, a maximum of two electrons can occupy an orbital. Therefore, the maximum number of electrons that can occupy a principal energy level is given by the formula 2n2.
Ask: What is the maximum number of electrons that can go into each principal energy level?
Answer: A maximum of two electrons can exist in the n = 1 principal energy level. For n = 2, the maximum number of electrons is 2 × 22 = 8. For n = 3, the maximum number of electrons is 2 × 32 = 18. For n = 4, the maximum number of electrons is 2 × 42 = 32.

19. Electron Configuration chart