Demonstration at a glance...

In this demonstration...

• Demonstration Overview

• Materials and Equipment
• Preparation Tasks
• The Demonstration
• Learning Objectives and Standards
• Additional Information and Resources

Review relationship of Computational Thinking to the electron configuration of elements in the Periodic Table.

9 to 14 minutes

Open the ECT Pseudocode Guide

1 minute

Overview

2 to 5 minutes

Part 1: Using Computational Thinking with electron orbitals and energy shells

15 to 20 minutes

Part 2: Developing an algorithm to assign electrons to orbitals with energy shells

10 to 30 minutes

Notes to the Teacher:

Chemistry often involves processes that cannot be observed directly. Computational thinking becomes all the more critical in this field where observations and data must be analyzed for patterns to develop laws and theories. At the end of this demonstration students should see how they can model phenomena with computational thinking, like scientists before them, in order to make predictions and better understand their world.

Notes to the Teacher:

The likelihood of an atom to react or bond to an atom is determined by its electrons. Knowing the energy levels and configuration can provide useful insight. In this experiment we are going to use computational thinking to derive this information from the periodic table.

Use the following information to present an overview of orbitals within energy shells.

Computational Thinking Connections:

Decomposition

The periodic table (http://www.webelements.com/) is divided up into periods (rows) and groups (columns). Each element can be uniquely described using the four quantum numbers (http://wikipedia.org/wiki/Principal_quantum_number). For the purposes of this model, we only need to focus on two: the principle quantum number (n) which describes the number of energy levels in which an electron can reside for that element, and the azimuthal quantum number (ℓ) which refers to one of the four orbital states [s, p, d, and f] starting at 0 within each energy level.

Pattern Recognition

• An electron’s energy level, n, is always a positive integer.
• The number of possible subshells or orbital states for an energy level is equal to the energy level number, n

• For example, the elements in third row of the periodic table (n = 3) have three subshells or orbital states [s, p, and d] although not all of these subshells will be occupied for elements at the beginning of the row.

• The number of orbitals of each orbital state or subshell is 2ℓ + 1
• The maximum number of electrons in an orbital is 2.
• Therefore, the number of electrons associated with a subshell or orbital state is 2(2ℓ + 1)

• for s, ℓ = 0 → maximum number of electrons = 2(2*0 + 1) = 2
• for p, ℓ = 1 → maximum number of electrons = 2(2*1 + 1) = 6
• for d, ℓ = 2 → maximum number of electrons = 2(2*2 + 1) = 10
• for f,  ℓ = 3 → maximum number of electrons = 2(2*3 + 1) = 14

Abstraction

• The Aufbau principle (http://wikipedia.org/wiki/Aufbau_principle) states that electrons will fill up shells at the lowest energy possible.
• Hund’s Rule (http://wikipedia.org/wiki/Hund%27s_rule) states that, to increase the atom’s stability, electrons will fill up empty shells at lower levels before filling up partially-filled shells.

Algorithm Design

Madelung developed an energy ordering rule that predicts which subshell electrons will inhabit within each energy shell.   It is called the n + ℓ ordering rule (See See Wikipedia article -- Aufbau_principle -- The_Madelung_energy_ordering_rule)

Notes to the Teacher:

Use the following information to walk your class through pseudocode that describes how electrons can be assigned to orbitals within energy shells.

Algorithm Development:

This algorithm is based off the on Madelung’s n + ℓ energy ordering rule.

In particular,

• The number of electrons to be assigned to orbitals is equal to the atomic number (Z) of the element
• The number of subshells at each energy level is equal to the number of the energy level (n)
• Subshells at each energy level are represented by an azimuthal quantum number,  ℓ, starting at ℓ = 0, which corresponds to the s subshell
• Thus ℓ ranges from 0 to n-1
• The number of orbitals in each subshell is 2ℓ + 1
• The maximum number of electrons in an orbital is 2
• Thus, the maximum number of electrons associated with a subshell is 2(2ℓ + 1)

Steps of algorithm:

1. Start with energy level 1 and azimuthal quantum number 0 (n = 1 and ℓ = 0)
2. Set electrons-in-this-subshell = 0
3. If there is room for another electron in this subshell (electrons-in-this-subshell < 2(2ℓ + 1))

1. Add 1 to electrons-in-this-subshell

4. Else move to a new subshell

1. Set electrons-in-this-subshell = 0
2. If ℓ > 0 then move down and to the left by adding 1 to n and subtracting 1 from  ℓ (keeping n +  ℓ unchanged)
3. Else increase sum of n+ ℓ by 1 as follows:

1. Set ℓ to n
2. Set n to 1
3. Find an available subshell that maintains the current value of n+ ℓ but conforms to ℓ < n

             i.e.  While  ℓ >= n subtract 1 from  ℓ and add 1 to n

5. Repeat steps 3 and 4 until the number of electrons assigned to subshells is equal to the atomic number (Z)

This pattern of assigning electrons to subshells is often represented by the following diagram that is the traditional way of representing the Madelung energy ordering rule (http://wikipedia.org/wiki/Aufbau_principle#The_Madelung_energy_ordering_rule). Each red diagonal arrow represent equal values of n+ ℓ and each arrow corresponds to a value of n+ℓ  that is one greater than the arrow above. Line 4.b. of the algorithm corresponds to moving down and to the left along one these arrows.  In addition, lines 4.c.i through iii corresponds to following a tail of an arrow looking for an available subshell, e.g. following the fourth red arrow to subshell 3p after filling subshell 3s at the end of the third arrow.

While the Madelung energy ordering rule and this algorithm work for many elements (especially in the lower energy levels), it has many instances where the experimental data does not agree with its predictions.

Notes to the Teacher:

• The above discussion of experimental data sometimes being different from what a model predicts illustrates how a model helps us where it can, but also exposes where we need to learn more. Models and algorithms are refined in light of more data.
• The algorithm above assigns electrons to subshells within energy levels but does not directly generate the standard electron configuration notation for the assignment, e.g. the assignment of 6 electrons of carbon is represented by 1s2 2s2 2p2. How could the algorithm above be enhanced so that it produced the electron configuration using the standard notation as its output?  You could discuss this question with your class to help them better understand how the values of n and ℓ relate to electron configuration notation.

Learning Objectives

Standards

LO1: Student should be able to show how the formula for the number of electrons associated with each orbital state forms as a sequence associated with ℓ = 0, 1, 2, 3

Core Subject

CCSS MATH.F.BF.2: Write arithmetic and geometric sequences both recursively and

with an explicit formula, use them to model situations, and translate

between the two forms.

Computer Science

CSTA L3B.CT.8: Use models and simulations to help formulate, refine, and test scientific hypotheses.

LO2: Student should be able to explain how the position of an element in the Periodic Table is associated with the number of electronics in each orbital state in the outermost electron shell.

Core Subject

NGSS HS-PS1-1: Use the periodic table as a model to predict the relative properties of elements based on the patterns of electrons in the outermost energy level of atoms.

Computer Science

AUSTRALIA 8.4 (Collecting, managing and analyzing data): Analyse and visualise data using a range of software to create information; and use structured data to model objects or events.

CSTA L3A.CT.8: Use modeling and simulation to represent and understand natural phenomena.

UK 4.2: Develop and apply their analytic, problem-solving, design, and computational thinking skills.

LO3: Student should be able to explain how an algorithm produces a particular result.

Computer Science

AUSTRALIA 4.4 (Processes and production skills: Creating digital solutions by: defining): Define simple problems, and describe and follow a sequence of steps and decisions (algorithms) needed to solve them

CSTA L1:6.CT.1: Understand and use the basic steps in algorithmic problem-solving (e.g., problem statement and exploration, examination of sample instances, design, implementation and testing).

UK 2.3: Use logical reasoning to explain how some simple algorithms work and to detect and correct errors in algorithms and programs.

Term

Definition

For Additional Information

Electron

A negatively charged particle that resides outside of the nucleus in an atom. An atom in its elemental form has an equal number of electrons and protons (atomic number Z)

http://en.wikipedia.org/wiki/Electron 

Energy level

The amount of energy associated with an electron, which is always a positive integer

http://en.wikipedia.org/wiki/Atom#Energy_levels 

Orbital state

A state of an electron associated with particular angular momentum

http://en.wikipedia.org/wiki/Atomic_orbital 

Concept

Definition

Decomposition

Breaking down data, processes or problems into smaller, manageable parts

Pattern Recognition

Observing patterns and regularities in data

Abstraction

Identifying and extracting relevant information to define main idea(s)

Algorithm Design

Creating an ordered series of instructions for solving similar problems

Contact info

For more info about Exploring Computational Thinking (ECT), visit the ECT website (g.co/exploringCT)

Credits

Developed by the Exploring Computational Thinking team at Google and reviewed by K-12 educators from around the world.

Last updated on

06/26/2015

Copyright info

Except as otherwise noted, the content of this document is licensed under the Creative Commons Attribution 4.0 International License, and code samples are licensed under the Apache 2.0 License.