How to Calculate the Theoretical Value of a Hydrogen Spectrum
Hydrogen is the simplest and most common atom in the universe, consisting of one proton and one electron. This electron emits a photon with a specific wavelength when it transitions to a lower energy level. This means that hydrogen emits electromagnetic radiation that corresponds to every possible electron transition for a hydrogen atom. These series of wavelengths are known as the hydrogen emission spectrum and can be predicted with great accuracy.
Instructions
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1
Familiarize yourself with the Rydberg formula. This equation is given as 1/y = R(1/(n')^2 -- 1/n^2) where y is the wavelength of the emitted photon, R is a constant called the Rydberg constant, n' is the initial energy level and n is the final energy level.
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2
Solve the Rydberg formula for the wavelength. From 1/y = R(1/(n')^2 -- 1/n^2), 1/y = R[(n^2 -- (n')^2)/((n')^2(n^2))] -> y = 1/ R[(n^2 -- (n')^2)/((n')^2(n^2))] = (n')^2(n^2)/ R[(n^2 -- (n')^2]. Thus, y = (n')^2(n^2)/ R[(n^2 -- (n')^2].
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3
Derive the Rydberg constant as R = m(e^4)/8(p^2)(h^3)c, where m is the rest mass of the electron, e is the elementary charge, p is the permittivity of free space, h is Planck's constant and c is the speed of light. Rydberg's constant evaluates to approximately 1.0973 x 10^7 1/meters.
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4
Calculate the hydrogen emission wavelengths for an initial electron energy level of n' = 1. For the formula y = (n')^2(n^2)/ R[(n^2 -- (n')^2], calculate the values for the wavelength y, where n' = 1 and n = 2, 3, 4.....
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5
List the values of y for the specific series given in step 4. These wavelengths are 122 nanometers (nm) for n = 2, 103 nm for n = 3 and 97.2 nm for n = 4 and so on. This series converges at 91.1 nm. This series for the hydrogen emission spectrum is known as the Lyman series, and the series for each initial energy level of the electron may be similarly calculated.
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