# 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:

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\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 **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle m_e, e, \varepsilon_0, h,}**
and **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\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: **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle R_M = \frac{R_\infty}{1+m_e/M},}**
where **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle M}**
is the atomic mass of the nucleus. We can use the relation **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\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 (**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle n_1,}**
and **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle n_2}**
are the quantum numbers for the electrons transitioning). For the Balmer series we will be using **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle n_1 = 2}**
, and the accepted values for the transitions are (and are from this Wikipedia Page:

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