When rubidium ions are heated to a high temperature, two lines are observed in its line spectrum at wavelengths (a) \(7.9 \times 10^{-7} \mathrm{m}\) and \((\mathrm{b}) 4.2 \times 10^{-7} \mathrm{m} .\) What are the frequencies of the two lines? What color do we see when we heat a rubidium compound?

Understanding the speed of light is crucial when we delve into the behavior of elements like rubidium under high heat. The speed of light (\(c\)) is a constant at approximately \(3 \times 10^8 \text{ meters per second (m/s)}\) in a vacuum. When calculating the frequency (\(u\)) for the line spectrum of heated rubidium, we use this constant speed and the given wavelengths.

A simple rearrangement of the formula \( c = u \times \text{wavelength} \) allows us to isolate the frequency: \( u = \frac{c}{\text{wavelength}} \). By plugging in the speed of light and the observed wavelengths, we can determine the frequency associated with each spectral line. This calculation underpins much of modern physics and underlines the universal nature of electromagnetic phenomena.

The electromagnetic (EM) spectrum encompasses all types of electromagnetic radiation, which differ from one another in terms of wavelength and frequency. These waves can range from very long radio waves to very short gamma rays. The EM spectrum is continuous and seamless, with the visible light spectrum occupying a narrow band.

Each element, such as rubidium, emits a unique set of wavelengths (line spectrum) when excited. These line spectra are like fingerprints, distinguishing one element from another and allowing scientists to determine the elemental composition of stars and other celestial bodies simply by analyzing the light they emit.

The wavelengths and frequencies of light are inversely related: as the wavelength increases, the frequency decreases, and vice versa. This inverse relationship is fundamental when examining line spectra.

We use the formula \( c = u \times \text{wavelength} \) to describe this relationship quantitatively. In the exercise, frequencies were calculated by dividing the speed of light by each observed wavelength. A shorter wavelength, such as the one observed at \(4.2 \times 10^{-7} \text{m}\), corresponds to a higher frequency and usually places the light toward the blue or violet end of the visible spectrum. Conversely, a longer wavelength, such as \(7.9 \times 10^{-7} \text{m}\), generally corresponds to a lower frequency and red light.

The visible light spectrum is part of the electromagnetic spectrum and is detectable by the human eye. It ranges approximately from \(4.0 \times 10^{-7}\) to \(7.0 \times 10^{-7} \text{m}\), corresponding to the colors violet through red respectively. The two wavelengths given in the exercise fall within this range, implying that the heated rubidium ions emit light within the visible spectrum.

The wavelength of \(7.9 \times 10^{-7} \text{m}\) would typically produce a red hue, while \(4.2 \times 10^{-7} \text{m}\) would appear blue or violet. These vibrant colors are indicative of rubidium's unique electronic transitions and energy levels, showcasing the intrinsic beauty of atomic physics.