To know the relationship in between atomic spectra and the electronic structure of atoms.

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The principle of the photon emerged from testing with thermal radiation, electromagnetic radiation emitted together the an outcome of a source’s temperature, i m sorry produces a consistent spectrum the energies.The photoelectric effect listed indisputable proof for the existence of the photon and thus the particle-like behavior of electromagnetic radiation. However, much more direct evidence was necessary to verify the quantized nature of power in all matter. In this section, we describe how monitoring of the interaction of atoms v visible light listed this evidence.

## Line Spectra

Although objects at high temperature emit a consistent spectrum that electromagnetic radiation, a various kind of spectrum is observed once pure samples of individual elements are heated. Because that example, as soon as a high-voltage electrical discharge is passed v a sample the hydrogen gas at short pressure, the resulting individual isolated hydrogen atoms brought about by the dissociation the H2 emit a red light. Unequal blackbody radiation, the shade of the light emitted by the hydrogen atoms does no depend greatly on the temperature that the gas in the tube. Once the emitted light is passed with a prism, just a couple of narrow lines of certain wavelengths, called a line spectrum, room observed rather than a consistent range of wavelengths (Figure $$\PageIndex1$$). The irradiate emitted by hydrogen atom is red because, that its four characteristic lines, the most intense heat in that spectrum is in the red part of the visible spectrum, in ~ 656 nm. With sodium, however, us observe a yellow color due to the fact that the most intense currently in the spectrum are in the yellow section of the spectrum, at about 589 nm.

Figure $$\PageIndex1$$: The emissions of light by Hydrogen Atoms. (a) A sample that excited hydrogen atom emits a properties red light. (CC BY-SA 3.0 Unported; scientific research Made Alivevia Wikipedia)(b) when the irradiate emitted by a sample that excited hydrogen atom is split 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 in ~ 656 nm. (CC BY-SA 3.0;Jan Homannvia Wikipedia)

Such emission spectra were observed for plenty of other aspects in the so late 19th century, which gift a major an obstacle because classic physics was unable to describe them. Part of the explanation is detailed by Planck’s equation: the monitoring of just a few values that λ (or $$u$$) in the line spectrum expected that just a couple of values of E to be possible. Thus the energy levels the a hydrogen atom had to be quantized; in various other words, only states the had particular values of power were possible, or allowed. If a hydrogen atom might have any worth of energy, then a constant spectrum would have been observed, similar to blackbody radiation.

In 1885, a Swiss math teacher, Johann Balmer (1825–1898), showed that the frequencies the the lines observed in the visible region of the spectrum that hydrogen right a straightforward equation that can be expressed as follows:

\< u=constant\; \left ( \dfrac12^2-\dfrac1n^^2 \right ) \label6.3.1\>

where n = 3, 4, 5, 6. Together a result, these lines are well-known as the Balmer series. The sweden physicist john Rydberg (1854–1919) ultimately restated and expanded Balmer’s result in the Rydberg equation:

\< \dfrac1\lambda =\Re\; \left ( \dfrac1n^2_1-\dfrac1n^2_2 \right ) \label6.3.2\>

where $$n_1$$ and also $$n_2$$ are positive integers, $$n_2 > n_1$$, and also $$\Re$$ the Rydberg constant, has actually a value of 1.09737 × 107 m−1.

Johann Balmer (1825–1898)

A mathematics teacher in ~ a secondary school because that girls in Switzerland, Balmer was 60 year old as soon as he created the record on the spectral currently of hydrogen that made the famous.

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

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Like Balmer’s equation, Rydberg’s simple equation explained the wavelength of the visible lines in the emissions spectrum the hydrogen (with n1 = 2, n2 = 3, 4, 5,…). An ext important, Rydberg’s equation additionally predicted the wavelength of other series of currently that would certainly be it was observed in the emission spectrum the hydrogen: one in the ultraviolet (n1 = 1, n2 = 2, 3, 4,…) and also one in the infrared (n1 = 3, n2 = 4, 5, 6). Unfortunately, scientists had actually not yet developed any theoretical justification because that an equation of this form.