The purpose of this lab experiment is to perform a modified Rutherford scattering experiment using macroscopic objects.

In 1910 Sir Ernest Rutherford and his students conducted a famous experiment whereby the basic construction of the atom became evident. He applied what was then known about collisions with macroscopic objects to collisions at atomic dimensions, and proved that atoms must have a central, highly compact nucleus of positive charge surrounded by a cloud of negatively charged electrons. We will perform a modified Rutherford experiment in that it presents the general technique used to determine unknown properties of a scattering target.

	Figure 1. Three scatterers off a flat surface. Notice how the scattering angle, , is not dependent on the impact parameter, .		Figure 2. Three scatterers off a circular surface. Notice how the scattering angle, , is dependent on the impact parameter, .

Consider two immovable surfaces, one flat and one round, as shown in Figures 1 and 2. As shown in the Figures, three particles traveling on parallel paths impact the target's surface, but each particle has a unique impact parameter, . We can detect in what directions each particle rebounds from the surface. After colliding with the target, the particles are deflected, or scattered, from their initial direction by some scattering angle, . You should note from Figure 1 that the flat surface is characterized by having each particle scatter from the surface at the same angle: the value of is independent of .

Particles impacting the circular surface, however, scatter according to a precise mathematical relationship between their impact parameter, , and their scattering angle, . We will use a scattering apparatus to indirectly measure the radius of a plastic target. An air gun is used to discharge steel shot at the target, which is rigidly fixed in the center of large metal rim of radius as shown in Figure 3. By lining the metal rim with a carbon strip, the impact position of the scattered particles can be recorded and the scattering angle may be determined. The air gun can be set at various impact parameters by adjusting the travel screw shown in Figure 8.

Figure 3. A diagram of the scattering apparatus.

If the target's radius is , then from Figure 3 we find

(1)

From Figure 3 it can also be shown that the arclength may be represented by

(2)

where and are given in radians, and is the known radius of the metal rim enclosing the scattering apparatus. You should be able to convince yourself of this relationship if you recall the that the arclength, , that subtends an angle, , of a circle of radius, , is given by the formula .

Therefore, if values for and can be deduced or indirectly measured, we can determine the value for . From Figure 3, we see that and are related by and Equation 1 then becomes

(3)

Using the trigonometric identity, , Equation 3 simplifies to

(4)

Thus a relationship between the target's radius, the impact parameter and the scattering angle is established for circular targets.

During this experiment, keep in mind that like Rutherford before you, the dimensions of your target are to remain "invisible". That is, in this experiment you are not allowed to directly measure the target's diameter or radius! However, you do know, a priori, that the scattering target is exactly centered within the metal ring and you may use that fact to assist your investigation.

1. Determine the radius of the scattering target. Remember, you are not allowed to directly measure the target's radius, except when determining the accuracy of your experimental results.

(Figure 4.) The scattering apparatus -- circular target, metal rimmed wall, and air gun. (Figure 5.) The circular target. (Figure 6.) The air gun. (Figure 7.) A box of steel shot -- the scatterer, or particle, for this experiment. Use only one BB! (Figure 8.) The mechanism used to move the air gun left and right. (Figure 9.) The steel shot is being loaded into the air gun chamber. (Figure 10.) The air gun chamber is being closed. Do not forget this important step! (See the Hints and Cautions section.) (Figure 11.) Squeezing the bulb will eject the steel shot. Be careful -- the particle will be moving with a large velocity. Notice how the student's thumb is covering the vent hole. Also, it is important to squeeze the bulb with a consistent force throughout the experiment. (Figure 12.) The carbon paper strip. (Figure 13.) The metal rimmed wall is lined with the carbon paper. (Figure 14.) Raw data from the carbon paper. This data corresponds to one impact parameter, b. Notice the dispersion in the data points and the experimenter's estimation of the impact point. Meter stick Vernier caliper Scissors Sticky tape

[Click on images to enlarge.] 4 5 6 7 8 9 10 11 12 13 14

1. Caution!!! Do not place your arms, hands or face into the scattering apparatus as the velocity of the steel shot is quite large.

2. Caution!!! When inserting the steel shot into the air gun chamber, be certain to rotate the chamber closed before firing the gun. Failure to do so may result in the projectile exiting the chamber and impacting your face!

3. The success of this experiment is greatly dependent on the force with which the air gun bulb is squeezed. To produce reproducible results, be consistent with the force with which you squeeze the bulb.

4. Do not be discouraged if your data looks very scattered. Try your best to pinpoint the average impact point for each impact parameter value. Remember, scattering experiments are expected to show a distribution of impact points.

5. Before beginning the experiment, verify that your air gun shoots straight by firing the steel shot so that it misses the target. The impact points should be close together. If not, alert your TA before proceeding!

6. Keep track of your steel shot (the BB).

1. A much more complicated (and realistic) scattering experiment
2. Clemson Physics Lab Tutorials

Each lab group should download the Lab Report Template and fill in the relevant information as you perform the experiment. Each person in the group should print-out the Questions section and answer them individually. Since each lab group will turn in an electronic copy of the lab report, be sure to rename the lab report template file. The naming convention is as follows:

For example the group at lab table #5 working on the Ideal Gas Law experiment would rename their template file as "5 Gas Law.doc".

Each student should download the questions. Each person in the group should print out the questions and answer them individually. Discussing the questions as a group is acceptable, but each student is responsible for turning in answers that represent their own work, not the work of others.

These Nudge Questions are to be answered by your group and checked by your TA as you do the lab. They should be answered in your lab notebook.

Objective 1 Nudges

1. What are the units for angles, arclengths and displacements in this experiment?
2. What assumptions must you make regarding the target, air gun and metal rim for this experiment? Are these assumptions valid?
3. What is the radius of the large metal rim?
4. How many pieces of carbon paper should you use for this experiment?
5. How far around the metal rim should you wrap the carbon paper?
6. Are your results dependent on the force with which you fire the air gun?

7. How will you determine the position of the gun when = 0?
8. Is it necessary to place a mark on the carbon paper at the = 0 position?
9. How will you measure the impact parameter, ? Is this the most accurate method?
10. How many launches will you make for each ?
11. How many values for will you use for this experiment?
12. Is it necessary for each impact parameter, , to be equally spaced?

13. How will you determine the value for angle as shown in Figure 3? How is related to ?
14. How is related to , the arclength subtended by angle ?
15. Can you directly measure from the markings on the carbon paper?
16. How are the arclengths, and , related to the impact position points on the carbon paper?
17. How is the arclength related to , and ?

18. What parameters will you plot to determine the radius of the target, ?
19. How does your indirect measurement of the target radius, , compare to the direct measurement?
20. What are the uncertainties in your measurements?
21. What is the uncertainty in your value for ?

• Read the Hints and Cautions section!
• Hand out only one steel shot per lab group -- otherwise, the floor will be covered in BB's!

Vernier caliper tutorial.