Part C: Propagation using your Station 4 measurements

Part C: Propagation using your Station 4 measurements

You measured the angle of the red hydrogen emission line with the spectrometer. Now you will calculate sin(θ) and propagate your uncertainty through the calculation.

1. Convert your angle measurement and its uncertainty from degrees to radians. Show your work.
2. Calculate sin(θ) for your best estimate of θ.
3. Calculate sin(θ+ ∆θ). What is ∆(sin θ)?
4. Report sin(θ) in correct form and justify your rounding.
5. The grating spacing d is printed on your spectrometer. Record its value.
6. The wavelength of the red emission line is related to the angle by the grating equation: λ = dsin(θ). Calculate λ using your value of sin(θ).
7. Propagate the uncertainty in sin(θ) through this calculation to find ∆λ. Note: d is given, not measured — treat it as exact for now.
8. Report your wavelength result in correct form and justify your rounding.
9. You will compare this result to the known wavelength of the red Balmer line in Part 5. Before you do — does your result seem reasonable? What order of magnitude do you expect for a wavelength of visible light?