Cesium was discovered in natural mineral waters in \(1860 \mathrm{by}\) R. W. Bunsen and G. R. Kirchhoff using the spectroscope they invented in \(1859 .\) The name came from the Latin caesius ("sky blue") because of the prominent blue line observed for this element at \(455.5 \mathrm{~nm} .\) Calculate the frequency and energy of a photon of this light.

Understanding the frequency and energy of light is fundamental to the field of spectroscopic analysis. In simple terms, the frequency of light is the number of waves that pass a point in one second. It is measured in Hertz (Hz) and is inversely proportional to the wavelength—the distance between successive crests of a wave. The energy of a photon of light is directly related to its frequency through Einstein's equation,

\[ E = h u \]
where \( E \) is the energy of the photon, \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \) Joule\textperiodcentered seconds), and \( u \) is the frequency. The higher the frequency of the light, the greater the energy of each photon.

For example, in the exercise involving cesium's blue light, once the frequency is calculated using the speed of light and the given wavelength, the energy of a single photon can be determined. This is crucial for applications such as determining the chemical composition of substances and understanding atomic structures in spectroscopy.

A spectroscope is an instrument that disperses light into its component wavelengths, producing a spectrum. It typically consists of a slit through which light enters, a collimating lens or mirror that renders the light rays parallel, a dispersive element such as a prism or diffraction grating that separates the light into different wavelengths, and a viewing or recording device. The principles of spectroscopy allow scientists to determine the composition of distant stars and the concentration of elements in various materials.

In the historical context of the exercise, Bunsen and Kirchhoff used their invention of the spectroscope to discover cesium. The characteristic blue line they observed corresponds to a unique wavelength, and thus a specific frequency and energy, which are intrinsic properties of cesium's emitted photons when it is heated or excited. This technique is still in use today in various forms for chemical analysis and research.

The speed of light, denoted by \( c \), is a fundamental physical constant and is the fastest speed at which all conventional matter and information in the universe can travel. It is valued at approximately \( 3.0 \times 10^8 \) meters per second (\(m/s\text{)\). Understanding the speed at which light travels is crucial for calculations involving light's frequency and energy.

The relationship between wavelength \(\lambda\), frequency \(u\), and the speed of light is given by the equation

\[ c = \lambdau \]
This equation means that the product of the frequency and the wavelength of light will always equal the speed of light. In the provided exercise, students use this principle to calculate the frequency of light emitted by cesium, turning a given wavelength (in nanometers) into the speed of light units (meters per second) to solve for the frequency.