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## Calculate the Energy!

Days Needed less than 1

### Objective

Students will review what has been learned so far about the basic structure of an atom. Students will then calculate the energy differences in different energy states of the Bohr atom of Hydrogen. They will then compare these energy levels with observed Hydrogen lines in a laboratory spectrum.

### Science and Math Standards

 NCTM NSES Content Standard 2: - Mathematics as Communications Content Standard A: - Evidence, models, and explanation Content Standard 4: - Mathematics as Connections Content Standard C: - Structure of atoms

### Pre-requisites

Math Students should be familiar with basic algebra.
Science Students should understand the structure of atoms and the relationship between energy and light, and how atoms emit light.
Students should have read the background sections on the Properties of Light and Atoms and Light Energy.

### Introduction

We can use tools like the periodic table of elements to figure out exactly how many protons, neutrons, and electrons at atom has. Understanding the structure and function of an atom is very important in understanding spectroscopy. Spectroscopy is one of the most useful tools for unlocking the mysteries of supernovae and their remnants.

### Engagement

Edible Subatomic Particles -

Materials needed:

• large plastic easter eggs, enough for one per student, or one per group.
• gumballs or m&ms of two different colors
• tic tacs
• ping pong balls (same amount as easter eggs)

1. A large plastic egg (atom) is given, one per person - each egg contains a split ping pong ball (nucleus) with a set number of either gumballs or m&m type candies (neutrons and protons) inside. Be sure to use different colors for protons and neutrons. Put smaller hard candy (like tic tacs, for instance) in the egg, but so they can move freely around the ping pong ball. They will be the electrons. Make sure there are the same amount of protons as electrons (unless you want an ionized atom!) You may want to give each student an "atom" of a different "element" by varying the number of sub-atomic particles in each students egg.

2. Without opening the egg, and using the scientific method, have the students determine the components within: number, size, movement, weight/mass, sound.

3. Have the students open the eggs - now report on the contents specifically as to number and size only. Can the student deduce what element they have an atom of? Make sure to point out that the electrons are not in perfect orbits around the nucleus. Like real electrons, they form a sort of electron cloud. Now is a good time to bring in information about the quantum mechanical nature of the atom. For example, originally, each electron orbital was pictured as having a specific radius, much like a planetary orbit in the solar system. However, the modern view is not so simple. Though each orbital does have a precise energy, the electron is now envisioned as being smeared out in an "electron cloud" surrounding the nucleus.

### Exploration

In the background section on "Atoms and Light Energy", the students should have learned that there are many energy states within an atom. The class is now going to calculate the energies differences between some of the different levels the atom. This will tie directly in to the concept of a spectrum.

Print out the Student Worksheet for the class. Have students eat remains of atom while completing on the worksheet.

• Student Worksheet
• Solution for Student Worksheet

### Evaluation

Students should show calculations of energy levels. These calculations and answers to the questions on the Student Handout, as well as the closure excercise, provide material for assessing the students' understanding of the concept that energy transitions lead to emission of observed light at particular wavelengths.

### Closure

Students should write a three minute paper describing how this excercise explains line emission from atoms such as hydrogen.