Excited lithium ions emit radiation at a wavelength of 670.8 nm in the visible range of the spec

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Excited lithium ions emit radiation at a wavelength of 670.8...

Excited lithium ions emit radiation at a wavelength of $670.8 \mathrm{nm}$ in the visible range of the spectrum. (This characteristic color is often used as a qualitative analysis test for the presence of $\mathrm{Li}^{+} .$ ) Calculate (a) the frequency and (b) the energy of a photon of this radiation. (c) What color is this light?

Key Concepts

Electromagnetic Radiation

Electromagnetic radiation consists of waves that carry energy through space, characterized by a spectrum of wavelengths and frequencies. In the context of atomic spectra, specific wavelengths correspond to transitions between energy levels, resulting in the emission of light with characteristic colors as seen in qualitative tests like those used for identifying lithium ions.

Wavelength and Frequency

Wavelength is the distance between successive peaks of a wave and is inversely proportional to its frequency. The relationship between the speed of light, wavelength, and frequency is given by the equation c = ??, where c is the speed of light, ? is the wavelength, and ? is the frequency. This basic relation allows us to calculate the frequency of electromagnetic radiation if its wavelength is known.

Planck's Relation

Planck's relation establishes the connection between the energy of a photon and its frequency with the formula E = h?, where E is the energy, h is Planck's constant, and ? is the frequency. This principle underlies the concept that light is quantized, and each photon carries a specific amount of energy dependent on its frequency.

Visible Spectrum and Color Identification

The visible spectrum is a segment of the electromagnetic spectrum that can be seen by the human eye, typically spanning wavelengths from about 400 nm to 700 nm. Different wavelengths correspond to different perceived colors. For example, a wavelength of approximately 670.8 nm falls within the red region of the visible spectrum, which is why this light is identified as red.