Sebastian Balmer Series/Balmer Series Lab Data - September 15, 2010
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
Setup
Background
The Rydberg constant is given by the following equation which can be found here:
[math]\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}, }[/math] where [math]\displaystyle{ m_e, e, \varepsilon_0, h, }[/math] and [math]\displaystyle{ c }[/math] 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: [math]\displaystyle{ R_M = \frac{R_\infty}{1+m_e/M}, }[/math] where [math]\displaystyle{ M }[/math] is the atomic mass of the nucleus. We can use the relation [math]\displaystyle{ \frac{1}{\lambda} = R_\infty \left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right) }[/math] in order to predict the Rydberg constant by measuring the wavelength of emission for known energy state transitions ([math]\displaystyle{ n_1, }[/math] and [math]\displaystyle{ n_2 }[/math] are the quantum numbers for the electrons transitioning). For the Balmer series we will be using [math]\displaystyle{ n_1 = 2 }[/math], and the accepted values for the transitions are (and are from this Wikipedia Page:
