Introduction

In this app last section left us with a planetary model of the atom that takes into account the existence of the nucleus, but which is inherently unstable. To recap, the model proposes that the centrifugal force of the revolving electron just exactly balances the attractive force of the nucleus. However, the issue is that the electrons—being electrically charged—must radiate energy as they move in a circular orbit. This is because Maxwell’s equations of electromagnetism predict that accelerating electric charges must emit electromagnetic waves. If the electrons radiate energy, they would lose velocity, thus spiraling into the nucleus.

Even if an electron’s orbit could somehow be stabilized, a related puzzle became a real quandary: it had been known since the late nineteenth century that excited atoms of a single element do not radiate a continuous spectrum. Instead, they produce a discontinuous spectrum of many lines. That is, as shown in Figure 77, instead of a smooth spectrum containing all colors, the light emitted by excited atoms consists of some number of discrete waves of different wavelengths. Each element has an individual, characteristic line spectrum, called its emission spectrum.

Figure 77 (a) The spectrum of light produced by white light is continuous, containing all colors of the visible spectrum. (b) The light produced by excited hydrogen is discontinuous, having just a few, well-defined spectral lines.

In 1862, Anders Ångström discovered three lines in the spectrum of hydrogen, and later found a fourth line. By 1871, he had measured all four wavelengths to a high degree of accuracy: one red line (6,562.852 Å = 656.2852 nm), one blue-green line (4,861.33 Å = 486.133 nm), and two violet lines (4,340.47 Å = 434.047 nm and 4,101.74 Å = 410.174 nm).

H_α, H_β, H_γ, and H_δ are the official designations for the four hydrogen lines of the visible portion of the spectrum. However, there are others in other parts of the electromagnetic spectrum. The group of visible hydrogen spectral lines is called the Balmer Series in honor of the Swiss mathematical physicist Johann Jakob Balmer, who was able to calculate the four visible lines’ wavelengths using one formula, now called the Balmer Formula.