Home Next Previous Contents

2. Rutherford Scattering Experiment

2.1 Theory

Rutherfordís experiment consisted of bombarding a very thin foil with monoenergetic alpha (α) particles (doubly ionized helium nuclei) as shown in Fig. 1. According to the plum pudding model, the α particles would barely be deflected as it passed through the foil because the coulomb repulsion is spread out over the positive pudding. In other words, the α particles would pass straight through the foil. Rutherford found instead that a small percentage of α particles were deflected as much as 180 degrees. The only way to explain such deflections was to assume that the positive charge and virtually all of the atomís mass was highly concentrated at the center of the atoms in the foil. Only a high concentration of charge would produce the necessary coulomb force for the observed large angle scattering to occur.


Figure 1: Scattering Geometry

Assuming point charges and a pure coulomb repulsion, Rutherford calculated that the number of α particles, N(θ), that are deflected into an angle θ after passing through the foil is:

  Eq. (1)

The constant K = (1/4πε0)2 (zZe2/2Mv2)2, where ε0 = 8.85 x 10-12 F/m, z = number of protons in alpha particles (2), Z = number of protons in the atoms making up the foil (that is, the atomic number of the foil element), M = mass of the alpha particles, and v = the velocity of the alpha particles. This Eq. (1) is known as the Rutherford Scattering Formula.

2.2 Equipment & Apparatus

Figures 2 and 3 show the experimental setup and specific positions of the following equipment.


Figure 2: Experiment Setup and electrical connections for Rutherford Scattering.
They include a scattering chamber (with shut off valve), pump(not shown), discriminator/preamplifier, AC adapter, and counter.

Equipment List

  1. Americium Source: Emits α particles (energies ~ 5.48 MeV)
  2. Slit and Foil Holder: Holds the foil and slit in place
  3. Slit: Defines the beam width and divergence of the α particles. The large slit size will increase the countrate at the expense of angular precision.
  4. Foil: There are two types of foils used in this experiment: A gold foil 2μm thick and an aluminum foil 7μm thick.
  5. Swivel holder: Adjustment for incident angle
  6. Wire from detector (located in Scattering Chamber) to deliver the signal from the detector to the discriminator/preamplifier
  7. Discriminator/Preamplifier: Converts the current signal from the detector to a voltage pulse and sets a high pass filter to reject voltage pulses below the discriminator level.
  8. Adapter: Supplies power for the discriminator.
  9. Counter: Counts the number of voltage pulses (i.e., α particles) intercepted by the detector at each angle
  10. Clock: The clock is used to set the gate interval so that the number of counts per interval is the count rate from the detector.
  11. Scattering Chamber: This is the vacuum chamber where the scattering takes place.
  12. Vacuum pump: Pumps the scattering chamber to prevent collisions of the α particles with background gas atoms.


Figure 3: Scattering Chamber Lid includes source, swivel arm, swivel arm holder, slit and foil.

2.3 Precautions

  1. Never handle the Americium source! Be sure to discuss proper radiation procedures with the instructor before using the Americium source
  2. Never touch the foils!
  3. Protect the detector from light! Cover the chamber with a black cloth before turning on the detector power supply.
  4. Keep the power off while the vacuum chamber is open.
  5. Never try to open the scattering chamber unless the pump is off, the power is off and the chamber has been vented.

2.4 Procedure

Important - Never touch the foil itself!

Part A: Check out counting system.

  1. Ask instructor to attach the Americium source as shown in Figure 3. Move the swivel arm holding the Americium source to the 180* position.
  2. Put the 1 mm slit in front of the gold foil. Secure the foil and slit in swivel holder (2).
  3. Place the scattering chamber lid on the scattering chamber, while making sure that the gasket stays in place.
  4. Open the valve on the side of the scattering chamber which goes to the vacuum pump.
  5. Turn on the vacuum pump.
  6. Wait 5 to 10 minutes for the vacuum to form in the chamber.
  7. Cover the lid of the scattering chamber with a black cloth, or turn out the lights (the detector is light sensitive).
  8. Plug in the adapter to the discriminator preamplifier.
  9. Position the knob on the scattering chamber lid to angle zero (this corresponds to firing the beam of alpha particles perpendicular to the foil).
  10. Start the counter simultaneously with the clock. Flicking the rightmost switch upward on the counter will cause the counter to start counting the number of α particles which reach the detector in the scattering chamber. To stop counting, press the same switch downward. Just to the right of the counter screen is a flat, square black button. This button zeroes the counter, but it also stops the counter! Approximately 1 to 2 alpha particles per minute will be back scattered.
  11. Obtain and register the time it takes to count a given number of α particles. Repeat the measurement 10 or 20 times. Calculate the mean number of counts and the standard deviation of the counts in a fixed time interval. The standard deviation should be equal to <n>1/2.

Part B. Measuring the angle dependency of N(θ).

In the following procedure, you will measure the number of alpha particles that are deflected through an angle θ into the detector. The procedure will be repeated for both the Au and Al foils.

  1. Put the 1 mm slit in front of the gold foil. Secure the foil and slit in swivel holder (2). Either remove swivel holder (5) or rotate it out of the way. It is no longer needed.
  2. Place the scattering chamber lid on the scattering chamber, while making sure that the gasket stays in place.
  3. Open the valve on the side of the scattering chamber which goes to the vacuum pump.
  4. Turn on the vacuum pump.
  5. Wait 5 to 10 minutes for the vacuum to form in the chamber.
  6. Cover the lid of the scattering chamber with a black cloth, or turn out the lights (as the detector is light sensitive).
  7. Plug in the adapter to the discriminator preamplifier.
  8. Position the knob on the scattering chamber lid to angle zero (this corresponds to firing the beam of alpha particles perpendicular to the foil).
  9. Obtain and register the time it takes to count a given number of α particles n(θ) at θ = 0, 5, 10, 15, 20, 25, and 30 degrees. For the best statistics you should count long enough to get 10-100 counts. Also, since you will need to scale the count rates taken in step 10, you should count for a particularly long time at 30°. Note- it will be necessary to experimentally locate the actual zero point (θ0) of θ every time you change foils or slits! You must therefor measure the countrate for angles less than zero to find the peak rate.
  10. Exchange the 1mm slit for the 5mm slit and repeat the above procedure (steps 1 through 9), except when repeating step 9, use angles θ = 30, 40, 50, and 60 degrees. Again, count for a long enough time at 30° to calculate the conversion factor accurately in step 11. The large slit is used to increase the countrate since N(θ) is decaying as sin-4(θ/2).
  11. Calculate the conversion factor, k, to scale the countrate from the 5mm and 1mm slits:

      Eq. (2)

    For scale the measured values for θ > 30°, divide the counting rates determined for θ = 40°, 50°, etc. by the conversion factor k.

  12. Change to the aluminum foil and repeat the above procedure (steps 1 through 11).
  13. Calculate the counting rate N(θ) = n(θ) / Δt for each measurement.
  14. Plot log[ N(θ)] against log[sin(θ-θ0)] for the gold and aluminum foils. Be sure to include error bars on both N(θ) and θ. If you are unsure how to do this, ask the instructor.
  15. Your curve in step 14 should be a straight line. Show that the slope of this line is consistent with the Rutherford Scattering Formula

Part C: Calculate the atomic number of aluminum.

Compare the scattering rates of the gold and aluminum foils for a scattering angle of 10 degrees. From the Rutherford scattering formula the atomic numbers of Au and Ag are related to their atomic numbers as:

  Eq. (3)

where d = thickness of foil, Z = atomic number, and N = counting rate.


Home Next Previous Contents
School of Physics at Georgia Tech
837 State Street, Atlanta, GA 30332-0430 USA, Phone:(404) 894-5201, Fax:(404) 894-9958