Problem 64 - 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 line. (b) Light at 425.4 nm appears blue.

Step 1: Identify the Most Energetic Wavelength

The energy of light is inversely proportional to its wavelength. The shorter the wavelength, the higher the energy. Therefore, find the wavelength with the smallest value from the given wavelengths: 357.9 nm, 359.3 nm, 360.5 nm, 427.5 nm, 429.0 nm, and 520.8 nm. The smallest wavelength is 357.9 nm.

Step 2: Determine the Color of Light at 425.4 nm

To find the color of light with a wavelength of 425.4 nm, refer to the visible light spectrum. Wavelengths in the range of approximately 380-450 nm are perceived as blue to violet colors. The wavelength 425.4 nm falls within this range, indicating that it appears blue.

Key Concepts

Chromium in the Emission Spectrum

Chromium is a fascinating element found in the transition metals section of the periodic table. Transitions in the atomic energy levels of chromium atoms emit characteristic colors of light, which form what is known as an emission spectrum. Every element has a unique emission spectrum determined by its arrangement of electrons, and chromium is no exception. When energy is supplied to chromium, its electrons become excited and cause it to emit light at specific wavelengths as they return to their ground state.
This light emission appears in distinct lines, each corresponding to a particular wavelength, in the emission spectrum.

• These lines signify transitions between different energy levels of chromium's electrons.
• Each line's position in the spectrum is unique to chromium, much like a fingerprint.
• Understanding these lines helps scientists identify the presence of chromium in a sample using spectroscopic techniques.

The most notable line in chromium's emission spectrum, as given, is observed at 425.4 nm.

Understanding Wavelength

The concept of wavelength is crucial in the study of light and plays a vital role in determining the properties of light emitted by different elements. Wavelength is defined as the distance between successive peaks of a wave and is usually measured in nanometers (nm) for light waves.
It's important to understand that:

• Wavelength is inversely related to energy: shorter wavelengths carry more energy than longer ones.
• In the electromagnetic spectrum, different ranges of wavelengths correspond to different types of light, such as ultraviolet or visible light.
• Each element emits light at characteristic wavelengths that appear as lines in the emission spectrum.

In the exercise, chromium's emission lines include those as short as 357.9 nm, which possesses the highest energy among the listed values due to its smaller wavelength.

The Energy of Light

The energy of light waves is a core concept when discussing emission spectra. It's vital because it helps explain why certain wavelengths appear in an element's emission spectrum. Energy (E) of light is related to its frequency (u) and wavelength (lambda), according to the equation:\[ E = h u = \frac{hc}{\lambda} \]where h is Planck's constant and c is the speed of light.
From this relationship, we can draw some key conclusions:

• The energy of light is directly proportional to its frequency.
• Since frequency is inversely proportional to wavelength—shorter wavelengths result in higher energies.
• That is why the line with the smallest wavelength, 357.9 nm for chromium, is the most energetic.

Understanding this principle helps predict which emission lines correspond to high energy levels in any given spectrum.

Exploring the Visible Light Spectrum

The visible light spectrum is a small part of the electromagnetic spectrum that is perceivable to the human eye. It ranges from approximately 380 nm (violet) to 750 nm (red). Different colors are seen based on the wavelength of the light:

• Violet/blue light from around 380 to 450 nm.
• Green light around 500 to 570 nm.
• Red light from 620 to 750 nm.

In the context of the exercise, the problem asks about the color of light at a wavelength of 425.4 nm. This wavelength falls within the blue region of the visible spectrum, indicating that chromium emits blue light at this wavelength.
Understanding the visible spectrum is important for identifying the colors associated with different wavelengths and helps us interpret the emission lines of elements like chromium in terms of observable color.