To understand the relationship in between atomic spectra and the digital structure the atoms.

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The photoelectric effect noted indisputable proof for the presence of the photon and also thus the particle-like habits of electromagnetic radiation. The ide of the photon, however, arised from testing with thermal radiation, electromagnetic radiation emitted together the an outcome of a source’s temperature, i beg your pardon produces a continuous spectrum of energies. Much more direct evidence was essential to verify the quantized nature that electromagnetic radiation. In this section, we describe how trial and error with visible light provided this evidence.


Line Spectra

Although objects at high temperature emit a continuous spectrum of electromagnetic radiation, a various kind the spectrum is observed as soon as pure samples of individual facets are heated. Because that example, as soon as a high-voltage electrical discharge is passed v a sample of hydrogen gas at short pressure, the resulting individual secluded hydrogen atoms resulted in by the dissociation the H2 emit a red light. Unlike blackbody radiation, the shade of the irradiate emitted through the hydrogen atoms does not depend substantially on the temperature of the gas in the tube. As soon as the emitted irradiate is passed through a prism, only a couple of narrow lines, referred to as a line spectrum, which is a spectrum in which light of only a certain wavelength is emitted or absorbed, fairly than a constant range of wavelength (Figure (PageIndex1)), quite than a continuous range that colors. The light emitted through hydrogen atoms is red because, the its 4 characteristic lines, the many intense heat in its spectrum is in the red part of the visible spectrum, at 656 nm. With sodium, however, us observe a yellow color since the most intense present in the spectrum space in the yellow part of the spectrum, at about 589 nm.

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Figure (PageIndex1): The emissions of irradiate by Hydrogen Atoms. (a) A sample of excited hydrogen atom emits a characteristic red light. (b) as soon as the irradiate emitted through a sample that excited hydrogen atom is separation into its component wavelengths by a prism, 4 characteristic violet, blue, green, and red emissions lines can be observed, the many intense of which is at 656 nm.

Such emission spectra were observed for numerous other facets in the late 19th century, which presented a major challenge because classical physics was unable to explain them. Component of the explanation is noted by the monitoring of only a couple of values the λ (or ν) in the heat spectrum expected that just a couple of values that E were possible. Hence the energy levels that a hydrogen atom had to it is in quantized; in various other words, only states that had specific values of power were possible, or allowed. If a hydrogen atom might have any worth of energy, then a continuous spectrum would have actually been observed, similar to blackbody radiation.

In 1885, a Swiss mathematics teacher, Johann Balmer (1825–1898), verified that the frequencies of the lines observed in the visible region of the spectrum that hydrogen right a an easy equation that can be expressed together follows:

< u=constant; left ( dfrac12^2-dfrac1n^^2 ight ) label(PageIndex1)>

where n = 3, 4, 5, 6. As a result, this lines are known as the Balmer series. The swedish physicist john Rydberg (1854–1919) subsequently restated and expanded Balmer’s an outcome in the Rydberg equation:

< dfrac1lambda =Re; left ( dfrac1n^2_1-dfrac1n^2_2 ight ) label(PageIndex2)>

where (n_1) and (n_2) are confident integers, (n_2 > n_1), and ( Re ) the Rydberg constant, has a value of 1.09737 × 107 m−1.


Johann Balmer (1825–1898)

A mathematics teacher at a second school for girls in Switzerland, Balmer to be 60 years old when he wrote the record on the spectral currently of hydrogen the made him famous.

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Balmer published only one other paper on the topic, which showed up when he to be 72 years old.