The most prominent line in the spectrum of mercury is at 253.652 nm . Other lines are located at

step 1 In this problem, we are given a line spectrum of mercury, with lines at 253 .652 nanometers, 365

The most prominent line in the spectrum of mercury is at...

The most prominent line in the spectrum of mercury is at $253.652 \mathrm{nm} .$ Other lines are located at $365.015 \mathrm{nm}$ $404.656 \mathrm{nm}, 435.833 \mathrm{nm},$ and $1013.975 \mathrm{nm}$ (a) Which of these lines represents the most energetic light? (b) What is the frequency of the most prominent line? What is the energy of one photon with this wavelength? (c) Are any of these lines found in the spectrum of mercury shown in Figure $7.9 ?$ What color or colors are these lines?

The most prominent line in the spectrum of mercury is at $253.652 \mathrm{nm} .$ Other lines are located at $365.015 \mathrm{nm}$ $404.656 \mathrm{nm}, 435.833 \mathrm{nm},$ and $1013.975 \mathrm{nm}$
(a) Which of these lines represents the most energetic light?
(b) What is the frequency of the most prominent line? What is the energy of one photon with this wavelength?
(c) Are any of these lines found in the spectrum of mercury shown in Figure $7.9 ?$ What color or colors are these lines?

Key Concepts

Visible Light and Color Perception

This concept relates to the portion of the electromagnetic spectrum that is visible to the human eye, with specific wavelengths perceived as distinct colors. Understanding which spectral lines fall within the visible range is essential for identifying the colors associated with these lines in an emission spectrum.

Electromagnetic Wave Relationships

This concept explains the interdependence between wavelength, frequency, and energy in electromagnetic radiation, emphasizing that shorter wavelengths correspond to higher frequencies and greater energy. It is fundamental for understanding how changes in the wavelength of light, such as those observed in spectral lines, indicate different energy levels.

Photon Energy and Planck’s Equation

This concept is centered on the quantization of energy described by Planck’s equation, E = hf, where E is the energy of a photon, h is Planck’s constant, and f is the frequency. It is crucial for calculating the energy of a photon from its wavelength, highlighting the inverse relationship between wavelength and energy.

Spectral Lines and Atomic Transitions

This concept involves the emission and absorption of light at specific wavelengths resulting from electrons transitioning between discrete energy levels in atoms. Recognizing these transitions is key to explaining the discrete lines observed in an element's spectrum and to understanding how energy differences manifest as particular colors.

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