How to Calculate a Balmer Series Wavelength
A Balmer series provides the wavelengths of the spectral line emissions of the hydrogen atom. A spectral line emission occurs when the photons of a particular wavelength are emitted at a significantly greater rate than the photons with the nearby frequencies. The Balmer series was discovered by Johann Balmer in 1885 when he noticed a mathematical relationship among the hydrogen spectral lines.
Instructions
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1
Observe the wavelengths of light for the hydrogen emission spectrum lines that are in the visible spectrum. There are four of these lines with observed wavelengths of 410 nanometers (nm), 434 nm, 486 nm and 656 nm.
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2
Find a relationship between these four wavelengths in order to predict the locations of hydrogen spectral lines that aren't in the visible spectrum. Use the Balmer series, which is Y = B(m^2 / (m^2 - 4)) where Y is the wavelength of the spectral line, B is a constant value of approximately 364.56 nm, and m is an integer greater than 2.
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3
Calculate the first four values in the Balmer series for m = 3, 4, 5 and 6. This gives us the values of 656 nm, 486 nm, 434 nm and 410 nm respectively. Note that this correlates with the observed wavelengths of the spectral emission lines given in Step 1.
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4
Use the Balmer series to predict the wavelengths of the hydrogen spectral emission lines that are below the visible spectrum. The next three wavelengths in the Balmer series are 397 nm, 388.9 nm and 383.5 nm. These spectral lines have been confirmed by observation.
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5
Examine the results of additional wavelengths in the Balmer series. These spectral lines become progressively closer together and more difficult to identify. Note that the wavelengths in the Balmer series converge at the wavelength B (364.56 nm).
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