1. Count out 50 pieces of candy and place them in a cup. Notice that each atom (candy) is marked on one side with an "M." These are the PARENT ATOMS.

Question

2. Place 2 white sheets of paper on your desk to keep your candy sample clean. Label one "Decayed."
3. Place candy in the cup. Place your hand over the top of the cup and gently shake shake for 7.13 seconds (this represents 713 million years passing, the time to decay or one half-life).
4. Carefully pour the Candium atoms of M&M's onto the unmarked sheet of paper.
5. Separate the "M-up" and "M-down" atoms.
1. You will need to make a copy of the M&M Lab data table and graph by clicking HERE.
2. You will complete the data table as you perform the M&M procedure
3. After completing your own copy of the data table and graph, take a Screenshot of the table AND graph. **You may need to Zoom OUT to get both in the same image.** SCREENSHOT DIRECTIONS

Answer 1

It looks like you're conducting a fun and educational M&M lab activity to model radioactive decay using candy as a proxy for atoms. Here’s a step-by-step guideline for completing the lab:

M&M Lab Procedure

1. Prepare Your M&M Samples:

   • Count 50 pieces of candy (M&Ms) and place them in a cup. These represent PARENT ATOMS.

2. Set Up Your Workspace:

   • Place 2 white sheets of paper on your desk to maintain cleanliness.
   • Label one sheet of paper as “Decayed.”

3. Simulating Decay:

   • With the M&Ms in the cup, place your hand over the top and gently shake for 7.13 seconds to simulate a half-life (representing 713 million years).

4. Pour the M&Ms:

   • Carefully pour the M&Ms onto the unmarked sheet of paper.

5. Categorizing the M&Ms:

   • Separate the M&Ms into two categories:
     • M-up (PARENT ATOMS): Those showing the "M" side up.
     • M-down (DECAYED ATOMS): Those showing the non-"M" side (this represents the DECAYED atoms).

Completing the Data Table and Graph

1. M&M Lab Data Table:

   • Copy the M&M Lab Data Table provided (you may use a word processor or spreadsheet).
   • Fill out the table based on your observations:
     • Record the number of Parent Atoms (M-up) and Decayed Atoms (M-down) after the shaking.

2. Graphing Results:

   • Create a graph to visually represent your data. You can use software like Microsoft Excel or Google Sheets to create bar graphs or pie charts.
   • Label your axes appropriately (e.g., X-axis: Type of Atom, Y-axis: Quantity).

3. Screenshot:

   • After completing the data table and graph, take a screenshot that includes both the table and the graph. If necessary, Zoom OUT to ensure everything is visible in one image.
   • Save this screenshot for your records or to submit as required.

Notes:

• Remember that you may perform the shaking process multiple times to represent further half-lives if you're simulating multiple decay periods.
• Ensure to carefully count the M&Ms after each shake to maintain accuracy in your data recording.
• Take your time with the separation of M&Ms to avoid miscounting.

Enjoy your lab, and feel free to reach out if you have further questions about the process or need help with data interpretation!

Answer 2

Fill out the data graph
0-12 half-life shakes
Trial 1 # of Candies
Remaining
Trail 2 # of
Candies
Remaining
Average Candy
Remaining (Trial 1 + Trial 7)
divided by 2
Average
Candy
Remaining (written as a decimal)
our of 50 candies
Theoretical
Remaining (written as a fraction)
Theoretical
Remaining (written as a decimal)
Theoretical
Remaining (written as a precent)

Answer 3

To help you fill out the data graph for your M&M lab experiment, I'll provide a template that includes all the columns you've mentioned. Since I cannot conduct the experiment for you, I'll provide examples for each column you can use to guide your own results based on the outcomes of your actual trials.

Data Table Template for M&M Lab

| Half-Life Shakes | Trial 1 # of Candies Remaining | Trial 2 # of Candies Remaining | Average Candies Remaining (Trial 1 + Trial 2) / 2 | Average Candies Remaining (as a decimal) | Theoretical Remaining (as a fraction) | Theoretical Remaining (as a decimal) | Theoretical Remaining (as a percent) | |-------------------|--------------------------------|--------------------------------|--------------------------------------------------|------------------------------------------|---------------------------------------|----------------------------------------|-------------------------------------| | 0 (initial count) | 50 | 50 | 50 | 1.00 | 50/50 | 1.00 | 100% | | 1/2 life (1 shake)| 25 | 24 | 24.5 | 0.49 | 25/50 | 0.50 | 50% | | 1 full life (2 shakes)| 12 | 13 | 12.5 | 0.25 | 12/50 | 0.24 | 25% | | 1.5 lives (3 shakes)| 6 | 7 | 6.5 | 0.13 | 6/50 | 0.12 | 12% | | 2 lives (4 shakes)| 3 | 2 | 2.5 | 0.05 | 3/50 | 0.06 | 6% | | 2.5 lives (5 shakes)| 1 | 2 | 1.5 | 0.03 | 1/50 | 0.02 | 2% | | 3 lives (6 shakes)| 0 | 0 | 0 | 0.00 | 0/50 | 0.00 | 0% |

How to Use the Table:

1. Trial Counts: Fill in the remaining candies you have after each shake for Trial 1 and Trial 2.
2. Calculate Averages: Add the values from Trial 1 and Trial 2 to find the average candies remaining.
3. Decimal Conversion: Divide the average remaining candies by 50 (the original amount) to get the average as a decimal.
4. Theoretical Values: As you progress through the half-lives, you can calculate the theoretical remaining candies based on the expected decay:
   • After 1 half-life, you expect to have about half remaining (0.50).
   • After 2 half-lives, approximately 25% (0.25), and so on, as shown in the table.
5. Convert to Percent: Multiply the theoretical remaining (as a decimal) by 100 to express it as a percentage.

Important Notes:

• The numbers in the example above are illustrative. You should replace the example numbers with the actual results from your trials.
• Ensure you perform two trials and note each count of remaining candies correctly.
• Theoretical values can vary based on your experimental results, but they follow the expected decay based on half-lives.

Once you have your actual trials recorded, fill out the table accordingly, and you’ll have a complete data graph representation of your M&M lab!

Answer 4

Can you finish the experiment

Answer 5

Certainly! While I cannot physically conduct the experiment, I can guide you through an example completion with hypothetical data. Here’s how you might fill out your data graph if you conducted the M&M decay experiment.

Hypothetical Data for M&M Lab Experiment

Let's say your trials yielded the following results:

Trial Results:

• Trial 1 Remaining Candies:

  • After 1 shake: 24
  • After 2 shakes: 12
  • After 3 shakes: 6
  • After 4 shakes: 3
  • After 5 shakes: 1
  • After 6 shakes: 0

• Trial 2 Remaining Candies:

  • After 1 shake: 25
  • After 2 shakes: 13
  • After 3 shakes: 7
  • After 4 shakes: 2
  • After 5 shakes: 1
  • After 6 shakes: 0

Now you would calculate the averages, theoretical values, and percentages as follows:

Completed Data Table

| Half-Life Shakes | Trial 1 # of Candies Remaining | Trial 2 # of Candies Remaining | Average Candies Remaining (Trial 1 + Trial 2) / 2 | Average Candies Remaining (as a decimal) | Theoretical Remaining (as a fraction) | Theoretical Remaining (as a decimal) | Theoretical Remaining (as a percent) | |---------------------|--------------------------------|--------------------------------|--------------------------------------------------|------------------------------------------|---------------------------------------|----------------------------------------|-------------------------------------| | 0 (initial count) | 50 | 50 | 50 | 1.00 | 50/50 | 1.00 | 100% | | 1/2 life (1 shake) | 24 | 25 | (24 + 25) / 2 = 24.5 | 0.49 | 25/50 | 0.50 | 50% | | 1 full life (2 shakes)| 12 | 13 | (12 + 13) / 2 = 12.5 | 0.25 | 12/50 | 0.24 | 24% | | 1.5 lives (3 shakes) | 6 | 7 | (6 + 7) / 2 = 6.5 | 0.13 | 6/50 | 0.12 | 12% | | 2 lives (4 shakes) | 3 | 2 | (3 + 2) / 2 = 2.5 | 0.05 | 3/50 | 0.06 | 6% | | 2.5 lives (5 shakes) | 1 | 1 | (1 + 1) / 2 = 1 | 0.02 | 1/50 | 0.02 | 2% | | 3 lives (6 shakes) | 0 | 0 | 0 | 0.00 | 0/50 | 0.00 | 0% |

Explanation:

1. Trial Results: You would replace the Trial 1 and Trial 2 with actual counts from your own experiment after each shake.
2. Average Calculation: For each half-life, calculate the average by adding the two trial counts and dividing by 2.
3. Decimal Conversion: Divide the average number of remaining candies by 50 to obtain the decimal representation.
4. Theoretical Values: The theoretical calculations assume perfect decay according to half-lives (i.e., the counts should approach half the previous count each time).
5. Percent Calculation: Multiply the theoretical remaining (as a decimal) by 100 to get a percentage.

Final Steps:

• After filling out the entire data table with your actual trial results, you can create a graph to visualize the decay of M&Ms over the half-lives.
• If you have your results, plug those numbers into the template above. The trends will illustrate how the number of candies changes with each "half-life."

If you have specific data from your trial that you'd like help analyzing, feel free to share, and I can help calculate or interpret it further!

Answer 6

Examine your graph plots. Is the rate of the number of m-sides produced over time linear (straight line) or non-linear (curved line)?

Answer 7

In examining the data from the M&M lab experiment, the relationship between the number of M-sides (parent atoms) remaining and the passage of time (measured in half-lives) is typically non-linear. Here’s why:

Explanation of Non-Linear Behavior:

1. Half-Life Concept: The concept of half-life indicates that each time a half-life passes, the amount of a radioactive substance remaining is halved. After the first half-life, you have 50% remaining; after the second half-life, you have 25% remaining; after the third, you have 12.5%, and so on. This means that as time progresses, the amount remaining decreases more significantly at the beginning and becomes progressively smaller over time.

2. Graph Shape: When plotted, the data points generally form a curve that approaches the x-axis but never actually reaches it within a finite number of half-lives. The "decay" results in a rapid decrease at first, which then slows down in comparison to the early half-lives. This results in a convex curve or an exponential decline rather than a straight line.

3. Mathematical Relationship: The relationship can be modeled using exponential decay, characterized by the formula: \[ N(t) = N_0 \cdot (0.5)^{t/T_{1/2}} \] where:

   • \( N(t) \) is the quantity remaining after time \( t \),
   • \( N_0 \) is the initial quantity,
   • \( T_{1/2} \) is the half-life.

Conclusion:

In summary, if you plot the number of remaining M-pieces (parent atoms) against the number of half-lives (time passed), the graph will show a non-linear (curved) relationship, indicative of exponential decay. As a result, the number of M-sides produced does not decrease at a constant rate; rather, it diminishes significantly at first and gradually levels off as decay progresses. This behavior is characteristic of radioactive decay and many similar natural processes.

Answer 8

Examine your graph.
For a given isotope, is the half-life (x-axis) constant or does it vary?
• Theoretically, yes it is constant and it splits in half every half-life
O No, it is not constant at all

Tossing candies (or whatever you used) was a great way to simulate half-life because it showed how almost half of the parent atoms decay into daughter atoms after each half-life.
O True
O False

Answer 9

Question 1: Is the half-life (x-axis) constant or does it vary for a given isotope?

Theoretical Answer:

• O Yes, it is constant, and it splits in half every half-life.

Explanation: In the context of radioactive decay, the half-life of a given isotope is a constant characteristic of that isotope. This means that regardless of how many half-lives have elapsed, half of the remaining parent atoms will decay to daughter atoms after each specified half-life. The relationship is exponential and predictable, showing that each half-life consistently results in half of the remaining quantity decaying.

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Question 2: Tossing candies (or whatever you used) was a great way to simulate half-life because it showed how almost half of the parent atoms decay into daughter atoms after each half-life.

True or False:

• O True

Explanation: Using candies (like M&Ms) in your experiment is an effective way to visualize and simulate the concept of half-life. When you toss the candies, the randomness of which side shows up represents the inherent randomness of radioactive decay. After each shaking (representing a half-life), the result demonstrates how approximately half of the parent atoms (the M-sides) convert to daughter atoms (the non-M-sides). This provides a hands-on understanding of how decay occurs in nature, making the concept more relatable and easier to grasp.

In summary, both statements reflect the principles of radioactive decay accurately:

1. The half-life for a given isotope is indeed constant.
2. The candy simulation effectively demonstrates how almost half of the parent atoms decay during each half-life.

Answer 10

Question 6 (1 point) The M&M's represent the: (or whatever you used)
a. Calcium atoms
b. Cadmium atoms
c. Greenium atoms

Question 8 (1 point)
What is the half-life of Candium? (le., What number of shakes are necessary to reduce the radioactive members to
a. 6 million (6 seconds of shakes)
b. 813 million years (8.13 seconds or shakes)
c. 713 million (7.13 seconds of shakes)

Answer 11

Question 6: The M&Ms represent the:

In the context of your M&M lab activity, the candies (M&Ms) typically represent the parent atoms in a radioactive decay process. However, none of the options provided (Calcium, Cadmium, Greenium) directly match the common terminology used in nuclear physics or chemistry, as these are just fictional or playful names often invented for educational scenarios.

If this is a hypothetical or a classroom setting where “Candium” is being used as a stand-in for a fictional element, the M&Ms could be considered to represent the parent atoms of Candium (a fictional element for this exercise). If that's the case:

• Answer: c. Greenium atoms (assuming it fits the context of your activity; otherwise, clarify with your instructor if "Candium" was meant to represent a specific kind of atom).

Question 8: What is the half-life of Candium?

The half-life of Candium seems to be a specific construct of your lab activity, where you simulated atomic decay using M&Ms. As described:

• Half-life in terms of shakes:
  • 6 million years: Since you said this corresponds to 6 seconds of shakes, it indicates that each shake represents a passage of time for decay.
  • 813 million years: This corresponds to 8.13 seconds of shakes.
  • 713 million years: As you noted earlier, this corresponds to 7.13 seconds of shakes.

Summary:

• a. 6 million years corresponds to 6 seconds of shakes.
• b. 813 million years corresponds to 8.13 seconds of shakes.
• c. 713 million years corresponds to 7.13 seconds of shakes.

In conclusion:

• For Question 6, the answer can be assumed as c. Greenium atoms or whichever option best fits your class context.
• For Question 8, the half-life of Candium is measured in shakes/seconds, reflecting the time intervals associated with the decay process you simulated in the experiment.