Problem 66 - Chemistry and Chemical Reactivity

Question

The most prominent line in the emission spectrum of chromium is found at \(425.4 \mathrm{nm} .\) Other lines in the chromium spectrum are found at \(357.9 \mathrm{nm}, 359.3 \mathrm{nm}\) \(360.5 \mathrm{nm}, 427.5 \mathrm{nm}, 429.0 \mathrm{nm},\) and \(520.8 \mathrm{nm}\) (a) Which of these lines represents the most energetic light? (b) What color is light of wavelength \(425.4 \mathrm{nm} ?\)

Step-by-Step Solution

Answer

(a) 357.9 nm is the most energetic light. (b) 425.4 nm light is blue.

Step 1: Understand Energy and Wavelength Relationship

The energy of light is inversely proportional to its wavelength, according to the formula \(E = \frac{hc}{\lambda}\), where \(E\) is energy, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength. Therefore, shorter wavelengths correspond to higher energy.

Step 2: Compare Wavelengths for Highest Energy

To determine which line represents the most energetic light, compare the wavelengths listed: - 357.9 nm - 359.3 nm - 360.5 nm - 425.4 nm - 427.5 nm - 429.0 nm - 520.8 nm The shortest wavelength is 357.9 nm, which corresponds to the most energetic light.

Step 3: Determine the Color of 425.4 nm Light

The wavelength of 425.4 nm falls within the visible spectrum. It is approximately in the range of violet to blue light. Therefore, light at 425.4 nm is typically perceived as blue.

Key Concepts

Wavelength and Energy Relationship

The relationship between wavelength and energy is fundamental in understanding emission spectra. Energy (E) of photons is related inversely to their wavelength (\(\lambda\)). This means when the wavelength decreases, the energy increases. This relationship is quantified by the equation:\[E = \frac{hc}{\lambda}\]where \(h\) is Planck's constant (6.626 \times 10^{-34} \, \text{J s}), and \(c\) is the speed of light (3.00 \times 10^{8} \text{ m/s}). Thus, shorter wavelengths, like those near 357.9 nm in chromium’s emission spectrum, are the most energetic. Steps for comparing and understanding the emission of different spectra involve looking at their wavelengths and using this formula to calculate energy. Always remember:

• Shorter wavelength → Higher energy
• Longer wavelength → Lower energy

Grasping this concept helps you interpret various phenomena in light and its interaction with matter.

Visible Light Spectrum

The visible light spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. It ranges from roughly 380 nm to 750 nm in wavelength. Different wavelengths within this spectrum correspond to different colors:

• Violet: 380-450 nm
• Blue: 450-495 nm
• Green: 495-570 nm
• Yellow: 570-590 nm
• Orange: 590-620 nm
• Red: 620-750 nm

These colors blend seamlessly into one another, creating the spectrum as we see it. In the context of the chromium emission spectrum, a wavelength of 425.4 nm would fall within the violet to blue range, which is why we perceive it as a blueish hue. Whenever you see light emitting from elements like chromium, each specific wavelength corresponds to one of these colors, making it possible to identify elemental signatures based on color.

Chromium Spectral Lines

Chromium spectral lines are vital for understanding both atomic structure and spectroscopy. The spectrum comprises several specific wavelengths emitted by electrons in the chromium atom as they transition between energy levels. When these electrons release energy, they emit light at characteristic wavelengths, produce specific lines a.k.a. spectral lines. The most prominent lines for chromium, such as those at 357.9 nm and 425.4 nm, reveal essential aspects of its atomic structure. These wavelengths help scientists identify and analyze the element's presence in various samples. The diversity in line intensities and colors (as seen with the multiple lines listed in chromium’s spectrum) indicate different electron transitions. For students, understanding these lines not only involves recognizing the wavelengths themselves but also interpreting what they imply about electron configurations and energy states in atoms. Such insights are crucial for fields like astrophysics and chemical analysis.