Finding Small and Hidden Things

Atoms are very, very small! So small that no one can see them, not even with a traditional microscope (there are some new types of microscopes that can see an atom- they are called electron microscopes). Isn’t it incredible, then, that scientists long ago, before modern technology was developed could predict what we would see when we were able to use our fancy electron microscopes to see the atom?

In these two activities, you will investigate ways to identify the size and shape of things that are difficult to measure.

Part 1: The Rutherford Experiment

Explanation

Ernest Rutherford, famous for the “gold-foil experiment,” discovered that the core of an atom is positively charged and named it the nucleus. He did this by shooting beams of positively charged particles called alpha particles at a thin gold foil sheet. After measuring the different angles the particles were deflected, he was able to better determine the shape and size of the nucleus. He calculated that the radius of the nucleus was at least 10,000 times smaller that the radius of the whole atom. This, therefore, accounted for the 99% of the particles that traveled through the gold foil and missed the nucleus. Rutherford built his theory on the few alpha particles that were returned and concluded that the nucleus was also positively charged because the alpha particles were being reflected due to electrical repulsion. Due to this, Rutherford rationalized that the concentration of positive charges and the mass is in the core of the atom.

Figure 1

Procedure

  1. Assemble into groups of two students.
  2. TAPE paper on the top side of the apparatus
  3. Rolla marbledown the ramp into the apparatus in order to discover the shape of the object in the center of the board. Mark the location of the ramp on the paper.
  4. Observe and record the different directions that the marbles are deflected out on the paper.
  5. Continue until you have determined the shape of the object.

Questions

  1. What happens to the marbles when you roll them under the apparatus?
  1. How does this experiment relate to Ernest Rutherford’s discovery of the nucleus of an atom?
  1. Why do some of the marbles pass straight through, and others are deflected back? Explain with respects to Rutherford’s experiment.
  1. Why do some of the marbles shoot back out at different angles, while others come straight back at you?
  1. What is the shape of the object under the apparatus based on the different angles the marbles are deflected out? Where is the object located?
  1. How can you determine what the shape of the object is and where it is located?

Part 2: The Thickness of Aluminum Foil

Explanation

The laboratory tools normally available would not be suitable for the direct measurement of the thickness of a piece of aluminum foil. A ruler’s markings are too far apart to allow any sort of reasonable estimation. As a result, you will need to make other measurements and use them to calculate the thickness of the foil.

The formulas that will enable you to find the thickness of the foil are familiar to you. Remember that density is a property that is expressed as D=m/V. The density of aluminum is known and the mass of a piece of aluminum foil can be measured with a balance. The volume of the aluminum can then be calculated by using the rearranged equation V=m/D.

The volume of a rectangular object is also represented from the simple equation, V = L x W x H, where L = length, W = width, and H = height. Imagine that the regular object is a rectangular shaped piece of aluminum foil. Then the formula might be revised to V = L x W x T, where T = thickness of the foil. Going one step further, the area of the foil can be expressed as A = L x W, so the original formula for volume can be restated as V = A x T. If you combine this equation and the one from density, you will find it easy to calculate the thickness of the aluminum foil.

Procedure

  1. Obtain three rectangular pieces of aluminum foil.
  2. Using a centimeter ruler, carefully measure the length and width of each piece of aluminum foil. Record your measurements. How precise can your measurements be? Think carefully before you record your results, and use the right number of significant figures.
  3. Using a balance, find the mass of each piece of aluminum foil. Record the mass of each piece. Again, be careful to use correct significant figures.

Data

Foil Piece

/

Length

/

Width

/

Mass

1

/

2

3

Questions

(Don’t forget to use Sig Figs!)

  1. For each piece of aluminum foil you used in Part 2, calculate the following:
  2. Area (A)
  1. Volume (V)
  1. Thickness (T)
  1. Convert from thickness of aluminum foil to number of atoms of aluminum using this conversion factor (2.50 x 10-8 cm = 1 aluminum atom)
  1. The actual thickness of aluminum foil is 1.6 x 10-3 cm. Use the percent error equation to calculate your percent error.
  1. While finding the thickness of aluminum foil, what was one source of experimental error and how did it change your results (too high, too low, etc)? Explain thoroughly.

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