# Equipment

• Spectrometer - Adam Hilger; London, England; Serial: 12610
• Spectrum Tube Power Supply - Model: SP200 (5000V;10mA; Electro-Technic Products)
• Mercury Tube
• Hydrogen Tube
• Deuterium Tube

# Background

The Rydberg constant is given by the following equation which can be found here:

$\displaystyle R_\infty = \frac{m_e e^4}{8 \varepsilon_0^2 h^3 c} = 1.097\;373\;156\;852\;5\;(73) \times 10^7 \ \mathrm{m}^{-1},$ where $\displaystyle m_e, e, \varepsilon_0, h,$ and $\displaystyle c$ are the mass of an electron, the charge of an electron, the permittivity of free space, Planck's constant, and the speed of light respectively. After reading the Wikipedia article about the Rydberg constant, I learned that when dealing with Hydrogen we must use the reduced mass version of the Rydberg constant given by: $\displaystyle R_M = \frac{R_\infty}{1+m_e/M},$ where $\displaystyle M$ is the atomic mass of the nucleus. We can use the relation $\displaystyle \frac{1}{\lambda} = R_\infty \left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$ in order to predict the Rydberg constant by measuring the wavelength of emission for known energy state transitions ($\displaystyle n_1,$ and $\displaystyle n_2$ are the quantum numbers for the electrons transitioning). For the Balmer series we will be using $\displaystyle n_1 = 2$ , and the accepted values for the transitions are (and are from this Wikipedia Page: