Physics307L:People/Mondragon/Notebook/071121

calibration
using mercury to calibrate. center of slit, measuring clockwise

so the calibration curve is $$real\,wavelength=1.204205321\times measured\,value-76.8339591$$

the hydrogen spectrum
mean value for Rydberg constant=$$1.1061*10^{7}\,\mathrm{m}^{-1}$$ standard deviation $$4.6*10^{4}\,\mathrm{m}^{-1}$$

CALCULATIONS
heres the excel file Section above has numbers from the excel file.

here is a more careful analysis

Linefit says the calibration data fits the line $$actual\,wavelength=(1.204205 \pm 0.042636)*measured\,wavelength-(76.833959 \pm 22.932003)nm$$

Error propagation
No data on measurement error was ever taken, so, for any measurement of wavelength the error on the calculated actual value will be
 * $$actual\,wavelength\,error=0.042636*measured\,wavelength+22.932003nm$$

The calculated Rydberg constant is related to the measured wavelength value thusly

$$ \begin{align} \frac{1}{\lambda} &= R_\mathrm{H}\left(\frac{1}{2^2} - \frac{1}{n^2}\right), n=3,4,5,...\\ R_\mathrm{H}     &=  \frac{1}{\left(\frac{1}{2^2} - \frac{1}{n^2}\right)\lambda}\\ R_\mathrm{H}     &=  \frac{1}{\left(\frac{1}{2^2} - \frac{1}{n^2}\right)(m*\lambda_m+b)}\\ \end{align}$$ Where $$\lambda_m$$ is the wavelength measured by the instrument, $$m$$ is the slope of the calibration curve, and $$b$$ is the y intercept of the curve. Because of the uncertainty in the fit, the calculated value of the Rydberg constant will have uncertainty.

$$\Delta R_\mathrm{H} = \frac{1}{\left(\frac{1}{2^2} - \frac{1}{n^2}\right)(m*\lambda_m+b)^2}(\Delta m*\lambda_m+\Delta b)= R_\mathrm{H} \frac{\Delta m*\lambda_m+\Delta b}{m*\lambda_m+b}=R_\mathrm{H} \frac{\Delta \lambda}{\lambda}$$

The uncertiainty in RH is just RH times the relative uncertainty in the calculated wavelength.

Average for Rydberg constant= $$ 1.10592*10^7\,\mathrm{m}^{-1}$$. Uncertainty of average = $$9.64*10^5\,\mathrm{m}^{-1}$$. Accepted value = $$10 967 758.341 \pm 0.001\,\mathrm{m}^{-1}$$