PHYS 3310L – Electron Charge-to-Mass Ratio

Electron Charge-to-Mass Ratio

Before you begin: retrieve your pre-lab from D2L and compare your equation derivations and error propagation setups with your lab partners. If your equations differ, work through the physics together and agree on the correct forms before touching the apparatus. Record the outcome of your comparison in your shared lab notebook. Then begin the experiment.

Your Task Today

In 1897, J.J. Thomson measured the charge-to-mass ratio of the electron using a beam of cathode rays deflected by electric and magnetic fields. Today you will make the same measurement using a modern commercial instrument, evaluated against a standard set by NIST.

By the end of today’s lab session you will have:

  • Aligned the apparatus to minimize the effect of Earth’s magnetic field
  • Produced a stable, circular electron beam at multiple accelerating voltages and coil currents
  • Measured the radius of the electron beam for nine trials
  • Calculated e/m and its propagated uncertainty for each trial
  • Determined whether the BroLight BEM-5017 meets the NIST acceptance criterion

The NIST acceptance criterion: The device is considered acceptable if (1) the propagated uncertainty is less than 8% of the measured value and (2) the accepted value e/m = 1.758820 × 1011 C/kg falls within ±σe/m of your measured value. Both conditions must be satisfied. Your memo must make a definite statement about whether each trial meets this criterion.

Record everything in your shared lab notebook — what you do, what you observe, what surprises you, and how you reason through problems.

Section 1: Getting to Know the Apparatus

Before connecting anything or powering on, examine the apparatus and identify each component. You will need to describe the apparatus accurately in your memo.

  1. Identify and record in your lab notebook:
    • The glass tube containing the electron gun and helium gas
    • The filament (cathode) and anode inside the tube
    • The two Helmholtz coils and their orientation relative to the tube
    • The mirrored scale and its purpose
    • The accelerating voltage terminals and the Helmholtz coil terminals on the platform
    • The two power supplies and what each controls

Record the manufacturer, model number, and any relevant apparatus parameters in your lab notebook.

  1. Make a labeled sketch of the apparatus from the perspective of looking directly into the Helmholtz coils. Your sketch should show:
    • The two Helmholtz coils
    • The direction of the magnetic field B
    • The circular electron beam path
    • The beam radius r
    • The coil radius R

Use any tool you choose. Include this sketch in your memo.

  1. In your lab notebook, write the measurement equation you derived in the pre-lab and your fully evaluated error propagation equation. You will use both throughout the lab session.

Section 2: Minimizing Earth’s Magnetic Field

Earth’s magnetic field introduces a systematic error into this experiment. It adds to (or subtracts from) the Helmholtz field, shifting the electron beam’s circular path away from what the coil current alone would produce. Before taking any data, you must orient the apparatus to minimize this effect.

Why this matters: Earth’s magnetic field is approximately 5 × 10−5 T — about 5% of the typical Helmholtz field in this experiment. If not minimized, it will shift your measured radius systematically in one direction, producing a consistent bias in all nine of your e/m values. Unlike random error, this cannot be reduced by taking more measurements.

  1. Use the compass provided to determine the direction of Earth’s magnetic field in your lab space. Record the direction in your lab notebook.
  2. Orient the apparatus so that the axis of the Helmholtz coils points in the direction of Earth’s magnetic field. In this orientation, Earth’s field runs parallel to the coil axis — the same direction as the Helmholtz field — rather than perpendicular to the electron beam, which would deflect the beam out of the plane of the coils. Record the final orientation in your lab notebook.
  3. Even after alignment, Earth’s field is not completely eliminated as a source of error. Explain in your lab notebook why a small residual contribution remains and what type of error it introduces.

Section 3: Setting Up the Apparatus

The apparatus has been partially wired by your instructor. Verify the connections before powering on:

  1. Check that the following connections are in place:
    • The positive terminal of the 200 V DC supply connected to the Accelerating Voltage positive terminal on the platform
    • The negative terminal of the 200 V DC supply connected to the Accelerating Voltage negative terminal
    • Both AC 6.3 V terminals connected to the Filament terminals on the platform
    • The Helmholtz coils connected in series to the constant-current power supply, with current flowing through both coils in the same direction

Do not modify any connections. If something looks wrong, alert your instructor.

  1. With both power supplies off and all voltage controls fully counterclockwise, push both power switches to the ON position.
  2. Wait approximately five minutes for the filament to heat up. Do not adjust any controls during this time. While you wait, review your pre-lab derivation and error propagation equations with your partners.

Section 4: Getting a Stable Beam

  1. On the accelerating voltage supply, set the voltage range switch to 0–200 V. Slowly increase the accelerating voltage to approximately 160 V. You should see the electron beam appear as a faint blue-green line inside the tube.
  2. If no beam appears, work through the following before changing anything:
    • Has the filament had enough time to warm up?
    • Is the accelerating voltage set correctly?
    • Is the voltage range switch set to 0–200 V?

Diagnose before adjusting.

  1. Slowly increase the current to the Helmholtz coils. Watch the beam — it should curve and, as the current increases, form a complete circle. If the beam deflects downward rather than upward, swap the connections on the coil power supply terminals. If the beam forms a spiral rather than a circle, rotate the tube gently in its socket until the beam closes into a circle.
  2. Once you have a stable circular beam, take a moment to observe it carefully. Sketch what you see in your lab notebook. Note the color, brightness, and sharpness of the beam. Does the beam match your pre-lab prediction?
  3. Adjust the accelerating voltage to optimize the focus and brightness of the beam. Record the voltage at which the beam appears sharpest. This is a good starting point for your first set of measurements.

Expected observations — Section 4

The beam should appear as a blue-green glowing circle. The color is characteristic of excited helium emission. The beam is brightest at higher accelerating voltages (faster electrons, more helium excitation) and at lower coil currents (larger radius, longer path through the gas). At very high currents the circle becomes very small and may be difficult to measure accurately.

A good beam for measurement is: clearly visible, forming a closed circle (not a spiral), with edges sharp enough to locate on the mirrored scale to within 1–2 mm. The beam may be slightly brighter on the outside edge than the inside — this is normal.

Section 5: Measuring the Radius

Measuring the radius of the electron beam accurately is the most important and most error-prone step in this experiment. Read this section carefully before making any measurements.

Parallax elimination: The mirrored scale is mounted at the back of the apparatus. Because the beam is inside the glass tube and the scale is behind it, viewing the beam from an angle causes a parallax error — the beam appears to be at a different position than it actually is. To eliminate parallax:

  • Look through the tube at the electron beam
  • Move your head until the beam and its reflection in the mirror are aligned — they appear as one
  • Read the position of the beam on the scale only when the beam and its reflection coincide

Measuring diameter, not radius: Measure the position of the beam on both the left and right sides of the mirrored scale. The difference between the two readings is the diameter of the circular path. The radius is half the diameter.

  1. Practice the parallax elimination technique before recording any data. Measure the beam position on both sides of the scale, calculate the diameter, and record the radius. Have each group member make the measurement independently and compare. Do your values agree? If not, practice until they do.
  2. Estimate the uncertainty in your radius measurement, σr. Consider: how precisely can you locate the edge of the beam on the scale? The beam has a finite width — where exactly is its center? Record your reasoning for your uncertainty estimate in your lab notebook.

Section 6: Taking Data

You will take 9 measurements systematically: 3 accelerating voltages, each with 3 different Helmholtz coil currents.

Target accelerating voltages: approximately 120 V, 160 V, and 200 V.

For each voltage: adjust the Helmholtz coil current to produce three different circular beam radii. Choose currents that give well-separated, clearly visible radii across the full range of the mirrored scale. Do not exceed 2 A through the Helmholtz coils.

  1. For each of the 9 trials, record the following in your lab notebook:
    • Accelerating voltage V and its uncertainty σV
    • Helmholtz coil current IH and its uncertainty σIH
    • Left and right beam positions on the mirrored scale
    • Diameter of the beam path (difference of left and right readings)
    • Radius r (half the diameter) and its uncertainty σr

Record raw readings, not derived quantities — you will calculate e/m and its uncertainty separately.

  1. For each uncertainty, record your reasoning. Do not just write a number — explain how you estimated it. Is each uncertainty primarily systematic or random?
  2. As you take data, watch for any trends. Does the beam radius change in the direction you expect when you increase the voltage? When you increase the current? If something looks wrong, diagnose it before continuing.

Section 7: Calculating e/m and Propagating Uncertainty

  1. For each of the 9 trials, calculate e/m using the equation you derived in the pre-lab. Use the constant k = 7.80 × 10−4 T/A. Use SI units throughout — convert all measurements to meters, volts, and amperes before calculating.
  2. For each trial, propagate the uncertainty using the equation you derived in the pre-lab. Calculate σe/m for each trial and express it as both an absolute uncertainty and a percentage of your measured value.
  3. For each trial, determine whether the NIST acceptance criterion is met:
    • Is σe/m/(e/m) < 8%?
    • Does the accepted value 1.758820 × 1011 C/kg fall within e/m ± σe/m?

Record your determination (pass/fail) for each trial.

  1. Organize your results in a data table. Include all quantities listed in questions 17 and 20. Your table should be formatted clearly enough to appear in a professional memo — think about column headers, units, significant figures, and readability.

Section 8: Checking for Trends

  1. Look across your 9 values of e/m. Do they cluster around the accepted value, or do you see a systematic offset in one direction? If there is a systematic offset, what might cause it?
  2. Compare your e/m values across the three accelerating voltages. Is there a trend — does e/m increase, decrease, or stay roughly constant as V increases? If there is a trend, what does it suggest about a possible systematic error?
  3. Compare your e/m values across the three coil currents for a fixed voltage. Is there a similar trend? What does this suggest?
  4. Which of your 9 trials has the smallest percentage uncertainty? Which has the largest? What experimental conditions produced the best and worst precision?

Section 9: Reflecting on the Experiment

  1. Based on your 9 trials, what is your overall conclusion about the BroLight BEM-5017? Does it meet the NIST acceptance criterion? Are there conditions — specific voltages or currents — under which it performs better or worse?
  2. List the sources of systematic error in this experiment. For each one, state whether it makes your measured e/m too high or too low, and whether you were able to minimize it or only acknowledge it.
  3. Earth’s magnetic field was minimized by alignment but not eliminated. Estimate its residual contribution to your measurement. Is it large enough to affect your NIST determination?
  4. If you were designing a follow-up experiment to improve the precision of this measurement, what would you change? Which uncertainty source would you prioritize reducing, and why?

Your Memo

Your group will produce a professional technical memo addressed to Dr. Mease R. Carefully, Director, Standards Division, NIST. One group member serves as lead author. The lead author role rotates across the semester.

Your memo must include:

  • A brief description of the apparatus and the principle of the measurement
  • Your labeled sketch of the apparatus
  • The measurement equation with a brief explanation of how it was derived
  • Your complete data table, including all measured quantities, their uncertainties, calculated e/m values, propagated uncertainties, and pass/fail determinations for each trial
  • A discussion of sources of uncertainty and systematic error — including Earth’s magnetic field
  • A definite conclusion about whether the BroLight BEM-5017 meets the NIST acceptance criterion, supported by your data and uncertainties
  • An author contributions statement

Lead with your conclusion. Dr. Carefully needs to know immediately whether the device passes — do not make her read to the end to find out.

Format: Professional memo, maximum two pages plus the data table. Submit as a PDF to D2L one week after your group completes this experiment.

Learning Objective Alignment

Use this table when building your grade proposal to identify which parts of this assignment provide evidence for each learning objective.

Section / QuestionLearning Objectives
Section 1, Questions 1–3 1, 3
Section 2, Questions 4–6 2, 4
Section 3, Questions 7–9 3
Section 4, Questions 10–14 3, 4
Section 5, Questions 15–16 3, 5
Section 6, Questions 17–19 3, 5
Section 7, Questions 20–23 5, 6
Section 8, Questions 24–272, 4, 5
Section 9, Questions 28–31  2, 4, 5, 6
Memo 7, 8, 9