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) The most energetic light is at 357.9 nm. (b) The color of 425.4 nm light is violet or blue-violet.

Step 1: Identify the Most Energetic Light

The energy of light is inversely proportional to its wavelength according to the equation \( E = \frac{hc}{\lambda} \), where \( E \) is energy, \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength. Therefore, the shortest wavelength corresponds to the most energetic light. Among the wavelengths provided, the shortest is \(357.9 \mathrm{nm}\).

Step 2: Determine the Color of Light at 425.4 nm

The wavelength \(425.4 \mathrm{nm}\) falls within the visible spectrum. Light in this range is typically perceived as violet or blue-violet. Different sources may classify this wavelength slightly differently within the violet and blue-violet spectrum.

Key Concepts

Wavelength

In the realm of light and electromagnetic waves, wavelength is a fundamental concept. It represents the distance between consecutive peaks of a wave. In simpler terms, it's how long a wave is per cycle. Wavelength is often measured in nanometers (nm), particularly when dealing with light.

• Shorter wavelengths have peaks that are closer together.
• Longer wavelengths spread out more compared to shorter ones.

Wavelength is closely linked to energy. According to the equation \[ E = \frac{hc}{\lambda} \] where \( E \) is energy, \( h \) is Planck's constant, and \( \lambda \) is the wavelength. When the wavelength decreases (meaning the peaks are closer together), the energy goes up. This relationship is important in understanding which light is more energetic based on its wavelength alone.

Energy of Light

Energy carried by light is a pivotal aspect of understanding how light behaves and interacts with matter. Light energy increases as its wavelength decreases. This is because the energy (\[ E = \frac{hc}{\lambda} \]) is inversely proportional to the wavelength \( \lambda \).

• Shorter wavelengths, like ultraviolet and x-rays, possess higher energies.
• Longer wavelengths, such as radio waves, have lower energies.

Knowing the energy of light is crucial in fields like chemistry and physics, where energy impacts how substances absorb or emit light during reactions. With shorter wavelengths, light can knock electrons off atoms, which is why higher energy light can be more reactive and potentially damaging.

Visible Spectrum

The visible spectrum refers to the range of light wavelengths that the human eye can detect. It stretches from about 380 nm to 750 nm. This spectrum covers the range of colors we perceive as light, from violet to red.

• Violet and blue are at the short-wavelength end of the spectrum.
• Red is at the longer-wavelength end.

Within this spectrum, each color corresponds to a specific range of wavelengths. When a light source like a lamp or the Sun emits light, it often emits multiple wavelengths. Our eyes perceive these light waves as different colors based on their specific wavelengths. Understanding these basics of the visible spectrum aids in grasping how colors head into wavelengths and impact our perception.

Light Color

Colors of light are directly related to their respective wavelengths in the emission spectrum. Each color we see is tied to a specific range of wavelengths in the visible spectrum. For example:

• Violet light typically ranges from about 380 nm to 450 nm, closely aligning with the example given of 425.4 nm, which is in the violet-blue region.
• Blue and green follow, with blue ranging from 450 nm to 495 nm, and green extending from 495 nm to 570 nm.
• Red, on the other side, marks the longer wavelengths from around 620 nm to 750 nm.

The color of light is critical for many practical applications, such as designing lighting for homes or creating artworks that evoke particular emotions. When working with light, knowing the connection between color and wavelength helps in accurately identifying and manipulating the desired light colors for specific purposes.