WEBVTT
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Calculate the wavelength in the first line in the Lyman series.
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The Rydberg constant π
sub π» equals 1.09737 times ten to the seventh inverse meters.
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State your answer to four significant figures.
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We want to solve for a wavelength weβll call π.
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Weβre told in this statement the value of a constant called the Rydberg constant.
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Knowing this, we can begin our solution by recalling the mathematical relationship for the Lyman series.
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This series expresses the wavelength of photons that are created when electrons in a hydrogen atom transition from higher-energy levels down to the π equals one energy level.
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The wavelength of the emitted photon depends on the starting energy level only, since all the electrons end up down at the π equals one level.
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In our statement, weβre told we wanna solve for the wavelength in the first line in the Lyman series.
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That means weβre transitioning from π equals two to π equals one.
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The Lyman seriesβ mathematical relationship says that one over the wavelength π equals the Rydberg constant π
sub π» times one divided by the final π value squared, which for the Lyman series is one minus one divided by the initial π value squared.
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In our case, because weβre looking for the first line in the series, π sub πͺ is two, and therefore our expression in parentheses simplifies to one minus one-fourth or three-fourths.
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We rearrange this equation then for π and we find that π equals four divided by three times π
sub π».
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Plugging in for π
sub π», the Rydberg constant, when we enter these values on our calculator, we find that π, to four significant figures, is 121.5 nanometers.
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That is the wavelength of the first line in the Lyman series.