Physics307L:People/Josey/Balmer and Rydberg

Balmer Series
For this experiment, my lab partner, Kirstin, and I observed and measured the spectrum lines from the Balmer series for both hydrogen and deuterium. The Balmer series is a specific series of spectral lines that result form the moving of electrons from a higher energy state to the n=2 energy state in hydrogen. When this occurs, the electron releases a photon with a very specific energy that can be determined by the following formula:

$$ \frac {1} {\lambda} = \frac {1} {R} (\frac {1} {n^2} - \frac {1} {m^2}) $$

Where λ is the wavelength of the light, R is the Rydberg constant, and both n and m are principle quantum numbers that represent the original state, m, and the final state, n, of the electron. By measuring the wavelengths of the spectral lines and solving for the above equation, we determined that the Rydberg constant for hydrogen is 1.0962 (9) * 107 m-1, and 1.0975 (6) * 107 m-1 for deuterium. We were then able to compare this to the accepted values by calculating the Rydberg constant as a function of the mass of the nucleus:

$$R_M = \frac{R_\infty}{1+m_e/M},$$

where R$$_\infty$$ is given by:

$$ R_\infty = \frac{m_e e^4}{8 \varepsilon_0^2 h^3 c} = 1.097\;373\;156\;852\;5\;(73) \times 10^7 \ \mathrm{m}^{-1} $$

This gives values of:

$$R_{Hydrogen}= 10967758.3406 m^{-1}\ \ $$

$$R_{Deuterium}=10970746.1986 m^{-1} \ \ $$

for hydrogen and deuterium. Comparing our measured results to the accepted values, we found that we were less than 0.1% off of the accepted value for the constant, leading us to conclude that we were successful in our experiment.

primary notebook for this lab