Station 4: Angle Measurement and the Hydrogen Spectrum

Station 4: Angle Measurement and the Hydrogen Spectrum

Learning objectives: 2, 5

You will find a cardboard box spectrometer with a protractor and a hydrogen discharge tube.

Part A: Getting to know the instrument

  1. Look at the protractor on the spectrometer. What is the smallest division marked on it?
  2. Look at the spacing between divisions. Can you estimate between them? How finely do you think you can read this instrument?
  3. Based on your answers, what is the smallest uncertainty you could honestly claim when reporting an angle measured with this spectrometer?

The smallest division on an analog instrument is called the least count. The smallest uncertainty you can honestly claim when using an instrument is called the Instrument Limit of Error, or ILE. For analog instruments like a protractor, the ILE is equal to the least count or some fraction of it — your judgment about how finely you can read the scale determines which.

Part B: Making a measurement

  1. Turn on the hydrogen discharge tube and look through the spectrometer. You should see several colored emission lines. Find the bright red line — it is the easiest to locate and the brightest in the visible spectrum.
  2. Carefully align the spectrometer with the red line and read the angle from the protractor. Record your measurement in the form (measurement ±ILE) with appropriate units.
  3. Have each group member make the measurement independently without looking at each other’s values. Record all measurements.
  4. Look at your group’s measurements. Do they all agree exactly? If not, what do you think is causing the variation — is it the instrument, the person making the measurement, or something else?
  5. Later in this activity you will use this measurement to calculate sin(θ) and propagate your uncertainty through that calculation. For now, record your best estimate of θ and its ILE carefully — you will need them.