Overhead Isotope Detector

Introduction

With few exceptions, the atomic mass listed for each element in the periodic table is an average mass and does not represent the mass of an atom of that element. This is due to the existence of isotopes. Most elements exist in nature in the form of two or more different isotopes. What are isotopes and how can they be detected?

Concepts

• Isotopes
• Mass spectrometer

Background

In 1900, the number of known elements was approximately 80, and they were arranged in rows and columns in the periodic table in order of increasing atomic mass. The prevailing theory at the time stated the periodic properties of elements were a function of their atomic masses. Unfortunately, this led to contradictions in the placements for some elements, notably iodine after the heavier tellurium, and argon before the lighter potassium. In 1913, the English physicist Henry G. J. Moseley, using X-ray diffraction data, showed that atomic number, not mass, determined the properties of elements. But the larger question still remained—Why aren’t the atomic masses of elements always consistent with their corresponding atomic numbers?

Also in 1913, the English physicist J. J. Thomson began experimenting with positively charged beams of ionized neon gas, bending the ion stream in a magnetic field and letting the deflected ions strike a photographic plate. Two distinct patches appeared on the plate, leading Thomson to conclude that neon consisted of atoms with two unique masses, or isotopes. The existence of isotopes, that is, atoms of the same element with the same atomic number, but different masses, explained the apparent anomalies inherent in the atomic mass–based periodic table. It was left to the discovery of the neutron to explain the existence of isotopes.

The purpose of this demonstration is to simulate the separation of charged isotopes in a magnetic field using steel spheres and a magnet. Steel spheres of different masses will be separated based on the degree to which they are deflected when passing over a magnet. The demonstration is performed on an overhead projector stage. Based on the separation, students will determine the mass ratios of the steel sphere “isotopes” and the average atomic mass of the spheres.

Materials

Safety Precautions

No hazards are associated with this demonstration. If performed in a laboratory setting, please follow all laboratory safety guidelines.

Prelab Preparation

Copy and distribute the hand-out materials to each student, including the graph, instruction sheet, example calculation sheet, protractor and ruler.

Model Detector

1. Place the graph paper transparency in the picture frame slot, followed by the glass pane. Secure both in the frame (see Figure 1).
   {12083_Preparation_Figure_1}
2. Place the set pin in the hole of the launching ramp. Take 4 black circle tabs and fold each circle back about one-third on each side so that a double sticky strip is formed.
3. Affix two strips each to the front and back ends of the bottom of the ramp.
4. Carefully press the ramp to the glass pane so that the ramp aligns with the bisecting line of the graph and ends at the intersection of the bisect line and the 0-mm line (point d). See Figure 2.
   {12083_Preparation_Figure_2}
5. Take one of the neodymium magnets and attach another double sticky strip to the bottom. Fix the magnet to the glass stage of the overhead projector, near the center.
6. Place the isotope detector on the overhead with the ramp in the lower right hand corner. Adjust the placement of the detector so that the magnet lies on the 0-mm line of the graph and is slightly right of the bottom edge of the ramp (see Figure 3).
   {12083_Preparation_Figure_3}
7. Take the ⅝" sphere, place it against the ramp stop, and then release it. The ball should curve and hit the side of the frame near the 30-mm line. Adjust the position of the frame to the left or right, keeping the magnet on the 0-mm line as shown, until the correct trajectory occurs. Fix the position of the frame on the overhead projector stage using cellophane tape.

Procedure

1. Start the demonstration using the “uncharged” glass marble. Place the marble against the ramp stop.
2. Tell the students the marble represents the path of an uncharged atom. Release the marble. It is not affected by the magnet and will follow the diagonal line to the corner of the frame.
3. Follow this with the smallest steel sphere. Hold it against the ramp, wait, then release it, and mark with a pencil on the frame where the sphere hits. Have the students label this spot with the letter A on their graphs.
4. Repeat step 3 using the progressively larger steel spheres, labeling the impact sites B, and C, respectively.
5. Place the spheres in a small disposable cup; shake them so they collide with one another. Note: The purpose of this step is to de-magnetize the steel spheres.
6. Repeat steps 3–5 three more times for a total of four trial runs for each sphere.
7. Students should now have four marks on their graphs for each sphere.

Student Worksheet PDF

12083_Student.pdf

Teacher Tips

• Materials in this kit are completely reusable. The demonstration may be performed multiple times year after year. Store materials properly for repeat use.
• The accuracy of this method of determining mass is about 80%. The main source of error is the assumption that the deflected path of the sphere is circular. The actual path is circular under the influence of the magnet, but then the sphere “breaks free” of the magnetic field and travels in a straight line until it hits the edge of the frame.
• When adjusting the placement of the magnet, start with the smallest sphere. Move the spot of the magnet so that the sphere hits the side of the frame no lower than the –20 mm mark. Any lower and the results will be erratic for the position the sphere strikes the frame.
• The purpose for shaking the spheres together in step 5 is to demagnetize any of the spheres that may have become slightly magnetized when rolled passed the magnet.
• For advanced classes, the derivation of the equations needed to calculate the radius for the paths the spheres take can be left to the students.

Sample Data

Answers to Questions

1. Calculate the deflected path radius for each of the three steel spheres.

   See calculations on Sample Graph.

2. If the mass of sphere B is assigned an arbitrary mass number of 8.00, calculate the relative masses of the other two “isotopes.”

   m_A = m_B(m_A/m_B) = 8.00(r_A/r_B) = 8.00 (58.3 mm/108 mm) = 4.32

   m_C = m_B(m_C/m_B) = 8.00(rC/rB) = 8.00 (184 mm/108 mm) = 13.6

3. Assume that the three different size spheres represent isotopes of the same element, and that the relative abundance of each is as follows:

   Sphere 1 – 35%
   Sphere 2 – 7%
   Sphere 3 – 58%

   Based on these abundance values and your calculations of the relative masses of the isotopes, calculate the average atomic mass of the element.

   m_avg = 0.35(4.32) + 0.07(8.00) + 0.58(13.6)

   m_avg = 1.51 + 0.56 + 7.90

   m_avg = 9.97

   {12083_Answers_Figure_7}

Discussion

The overhead isotope detector simulates the basic principle in the design of a mass spectrometer. A schematic of the system is shown in Figure 4.

The system involves a small picture frame with a ramp mounted on it and a magnet secured below the frame. The height of the ramp provides the acceleration due to gravity and because all the steel spheres are launched from the same point, all the spheres have the same velocity as they enter the magnetic field.

The magnetic property of the steel plays the same role as the charge on an ion, causing the path of the sphere to bend in the magnetic field. For steel spheres moving at identical initial velocities in a constant magnetic field, the equation relating mass (m) and radius (r) of curvature is:

To calculate the radius of circular travel for each deflected steel sphere, start by using a protractor to construct a line perpendicular to the diagonal line at d (see Figure 5). Label the end point H.

Next, draw a line from d to A, the point of impact of the deflected sphere with the side of the frame. Find the midpoint of this line segment and label this point G. Drop a perpendicular line from the line segment dA at G. Label the intersection of this perpendicular line and the line segment dH with the letter F. Label the angle formed by AdH as ΘA.

The triangle ▲GdF is a right triangle and of dF, the hypotenuse of the right triangle, is also equal to the radius of the curvature for the path of the steel sphere. In this configuration,

The line segment dF is equal to the the deflected path and dG is equal to ½ dA.

Substituting and rearranging Equation 2 yields:

In this demonstration, the radius of curvature r for each sphere will be calculated from the angle and cord measurements.

References

Special thanks to Irwin Talesnik and John Eix for providing the idea and the instructions for this activity to Flinn Scientific.