An atom consists of electrons, protons, and neutrons. Each electron has a charge of -1, each proton has a charge of +1, and each neutron has no charge. If 3 electrons are removed from each of 4 atoms, what is the combined net change to the charge of the 4 atoms?

Question

Complete the steps below to solve this problem and others like it.

Part A
Three electrons are removed from each of 4 atoms. Write an expression to represent the net change on the charge for the group of atoms.

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Part B
Simplify the expression obtained in part A and explain what the answer represents.

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Part C
Here’s a similar problem. Write an expression for the net change in charge if two electrons are added to each of six atoms in a group. Also, write an expression that represents removing two protons each from a group of six atoms.

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Part D
Simplify the two expressions in part C.

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Part E
How are the two products in part D related?

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Part F
Think about multiplying any two rational numbers. Based on this activity and your previous work, write a set of rules for finding the sign of the product based on the sign of the two numbers being multiplied.

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Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.

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Answer 1

Part A

To find the net change on the charge for the group of atoms when 3 electrons are removed from each of 4 atoms, we can represent this with the following expression:

\[ \text{Net Change} = \text{Number of Atoms} \times \text{Electrons Removed per Atom} \times \text{Charge per Electron} \]

Substituting the values:

\[ \text{Net Change} = 4 \text{ atoms} \times 3 \text{ electrons} \times (-1) \text{ charge/electron} \]

Part B

Now, we simplify the expression from Part A:

\[ \text{Net Change} = 4 \times 3 \times (-1) = 12 \times (-1) = -12 \]

This result represents a net charge change of -12, indicating that the overall charge of the 4 atoms has decreased by 12 units due to the removal of electrons. Since electrons have a negative charge, removing them results in a net positive charge increase but is expressed as a net negative change.

Part C

For the similar problem, we want to find the net change in charge if two electrons are added to each of six atoms in a group and represent removing two protons each from a group of six atoms.

1. Adding two electrons to each of six atoms: \[ \text{Net Change (Electrons Added)} = 6 \text{ atoms} \times 2 \text{ electrons} \times (-1) \text{ charge/electron} \]

2. Removing two protons from six atoms: \[ \text{Net Change (Protons Removed)} = 6 \text{ atoms} \times 2 \text{ protons} \times (+1) \text{ charge/proton} \]

Part D

Now we can simplify both expressions:

1. For the addition of electrons: \[ \text{Net Change (Electrons Added)} = 6 \times 2 \times (-1) = 12 \times (-1) = -12 \]

2. For the removal of protons: \[ \text{Net Change (Protons Removed)} = 6 \times 2 \times (+1) = 12 \times (+1) = +12 \]

Part E

The two products from Part D show that adding electrons (which has a charge of -12) effectively increases the negative charge, while removing protons (which has a charge of +12) effectively decreases the positive charge. In essence, they represent opposite processes with equal magnitude: one increases negative charge and the other decreases positive charge.

Part F

When multiplying two rational numbers, the following rules can be applied regarding the sign of the product:

1. When both numbers are positive, the product is positive.
2. When one number is positive and the other is negative, the product is negative.
3. When both numbers are negative, the product is positive.

These rules help in determining the sign of the product based on the signs of the two numbers being multiplied.

Self-Evaluation

I would rate my work a 5. I thoroughly explained each part of the problem, providing clear mathematical expressions and interpretations of their meanings. I learned how to systematically approach charge changes in atoms and clarify mathematical rules regarding signs in products, though I initially felt challenged in ensuring the consistency of the reasoning throughout the exercise.