Measuring What You Can’t See – Rutherford’s Atom

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Lab Report

Name: ________________________________ Due Date: _____________________ Lab Partners: ______________________________________________________________

Introduction

Objective

Record Data of repeated trials.

Determine the unknown size of an object without direct measurement.

To model Rutherford’s Gold Foil Experiment

If the marble is rolled and the hits and misses recorded, then the calculated diameter of the marble will be

with 25% error of the actual diameter of the marble.

Methods

Materials 7 marbles of equal size

1 visa marker

1 meter stick

masking tape

2 metric rulers

Procedure 1. Use masking tape to make a line 60 cm long on the floor. 2. Use a visa marker to mark X’s on the tape at 5, 15 , 25, 35, 45, and 55 cm (see Fig. 1).

3. Put a marble on each X

4. Measure out 1 meter from the center of the masking tape line. Mark this spot by putting a small piece of

masking tape on the floor. Put a single marble on this spot. (see Fig. 1)

5. One team member (A) will sit behind the line of marbles, a second team member (B) will sit behind the

single marble and the third (or fourth) team member (C and D) will be the recorder.

6. Without looking, the team member (B) sitting behind the spot will randomly roll the single marble toward

the line of marbles.

7. Team member (A) will return the bombarding marble back to

the team member (B) for another trial and replace the marble

if it was hit and moved from an “X”. Team member(s) (C and

D) will record using “slash marks” if the marble was a hit or

miss in Data Table 1.

8. Continue for 30 trials.

9. Trials are complete, rotate positions and repeat steps 5-9

until each team member has made 30 trials.

10. When all team members have completed 30 trials each,

measure the diameter of the marble by placing a metric ruler perpendicular to the top of a meter stick at

the 10 cm marking. Place a marble next to the ruler. Place a second metric ruler on the opposite side of the

sphere in a vertical position (see Fig. 2) Remove marble and measure the

distance between the two rulers.. Record this diameter on Data Table 2

under Actual Diameter.

Measuring What You Can’t See – Rutherford’s Atom

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Lab Report

Results

Data Table 1: Number of hits and misses for individual team member shooting a marble at six target marbles.

Team Member Hits Misses

Member A (30 trials)

Member B (30 trials)

Member C (30 trials)

Member D (30 trials)

TOTAL = ______trials TOTAL = TOTAL =

Data Table 2: Actual and calculated. diameters for a marble based on the individual team members trials.

Total number of Trials = ____________________

Calculations: 1. Calculate the diameter of the marble using the following formula. Show your work below and circle your

final answer.

𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 = 𝐿𝑒𝑛𝑔𝑡𝑕 𝑜𝑓 𝑚𝑎𝑠𝑘𝑖𝑛𝑔 𝑡𝑎𝑝𝑒 × (# 𝑜𝑓 𝑕𝑖𝑡𝑠)

2 × # 𝑜𝑓 𝑚𝑎𝑟𝑏𝑙𝑒𝑠 𝑜𝑛 𝑓𝑖𝑒𝑙𝑑 × (# 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠)

2. Record the diameter on Data Table 2 under Calculated Diameter.

3. Next calculate the % error using the following formula. Show your work below and circle your final

answer.

% 𝑒𝑟𝑟𝑜𝑟 =𝐴𝑐𝑡𝑢𝑎𝑙 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 − 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟

𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟𝑥 100

Actual Diameter(cm) (from step 10 in procedures)

Calculated Diameter(cm) (See calculations below)

Measuring What You Can’t See – Rutherford’s Atom

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Lab Report

DAY 2 of Activity

1. Share your actual and calculated diameters with the rest of the class by writing them on the white board.

2. Copy down everyone’s actual and calculated diameters into Data Table 3.

3. Using the data in Data Table 3 and a computer, make a histogram (bar graph) of the data.

4. Find the percent error using the median values (average data) for the actual and calculated diameters. The

equation is provided below and again – show all work in the space provided.

Show your work below and circle your final answer.

Data Table 3: Actual and calculated diameters for a marble for the entire class.

Group #

Actual Diameter

(cm)

Calculated Diameter

(cm)

Group #

Actual Diameter

(cm)

Calculated Diameter

(cm)

1

6

2

7

3

8

4

9

5

AVERAGE

DATA

Percent Error of Average Data % 𝑒𝑟𝑟𝑜𝑟 =𝐴𝑣𝑔 .𝐴𝑐𝑡𝑢𝑎𝑙 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 −𝐴𝑣𝑔 . 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟

𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟𝑥 100

Measuring What You Can’t See – Rutherford’s Atom

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Lab Report

Discussion 1. List at least 3 things on which the hit/miss ratio depends.

a. b. c.

2. What would happen to your data if the size of the marbles were twice as large as the ones you used? 3. How does the number of trials affect the result? (Be sure to use the % error data in explaining your answer).

4. Would 1 million trials cause the calculated diameter of the marble to be any closer to the actual diameter? Explain.

5. How does this lab relate to the gold foil experiment?