Problem 11 - Chemistry The Molecular Science

Question

Many marine organisms exhibit bioluminescence, which occurs when excited molecules return to their lowest energy (ground) state by releasing photons in the visible (and other) region of the electromagnetic spectrum. The starfish, Plutonaster bifrons, bioluminesces at \(525 \mathrm{nm}\). (a) What color is the bioluminescence? (b) Calculate the frequency of this bioluminescence.

Step-by-Step Solution

Answer

(a) The color is green. (b) The frequency is \(5.71 \times 10^{14} \text{ Hz}\).

Step 1: Understanding Wavelength Colors

The visible light spectrum ranges from about 400 nm to 700 nm, where each range of wavelengths corresponds to a different color. Wavelengths around 520-565 nm are perceived as green light. Thus, the bioluminescence wavelength of 525 nm falls into the green color range.

Step 2: Calculating Frequency from Wavelength

To calculate the frequency of light, we will use the formula: \( c = \lambda u \), where \( c \) is the speed of light (\(3.00 \times 10^8 \text{ m/s} \)), \( \lambda \) is the wavelength (525 nm, which needs to be converted to meters by multiplying with \(1 \times 10^{-9}\)), and \( u \) is the frequency (in Hz).Rearrange the formula to solve for the frequency: \( u = \frac{c}{\lambda}\). Substituting in the given values, \( u = \frac{3.00 \times 10^8 \text{ m/s}}{525 \times 10^{-9} \text{ m}} = 5.71 \times 10^{14} \text{ Hz}\).

Key Concepts

Electromagnetic Spectrum

The electromagnetic spectrum encompasses a range of all types of electromagnetic radiation that travel at the speed of light. Radiation in this spectrum differs by wavelength and frequency, with radio waves at the longer end and gamma rays at the shorter end. This vast spectrum includes microwaves, infrared light, visible light, ultraviolet light, X-rays, and more.
The spectrum is a way to categorize electromagnetic waves based on these properties:

• Wavelength: The distance between successive peaks of a wave.
• Frequency: The number of waves that pass a point in a given period.

These properties are inversely related. As the wavelength decreases, the frequency increases. Importantly, bioluminescence falls within this spectrum, particularly near visible light, allowing us to perceive it with the human eye.

Wavelength and Frequency

Wavelength and frequency are core concepts in understanding electromagnetic waves. Wavelength refers to the distance between two consecutive points that are in phase on a wave, such as from crest to crest. It is typically expressed in meters, but can also be denoted in nanometers (nm) when referring to visible and other light. In contrast, frequency is the number of waves that pass a fixed point in a second, measured in hertz (Hz).

• Longer wavelengths mean lower frequency and energy.
• Shorter wavelengths mean higher frequency and energy.

The speed of light \(c\) remains constant in a vacuum, allowing us to derive a relationship: \[ c = \lambda u \] where \( \lambda \) is the wavelength and \( u \) is the frequency. This relationship lets us calculate either property if we know the other. For instance, knowing the wavelength of Plutonaster bifrons bioluminescence, we can determine its frequency.

Visible Light Spectrum

The visible light spectrum is a portion of the electromagnetic spectrum that the human eye can detect. This ranges from approximately 400 nm to 700 nm in wavelength. Different colors are perceived at different wavelengths, creating the familiar rainbow from violet to red.

• Violet: Around 400-450 nm.
• Blue: Around 450-495 nm.
• Green: Around 495-570 nm.
• Yellow: Around 570-590 nm.
• Orange: Around 590-620 nm.
• Red: Around 620-700 nm.

Understanding these ranges helps us categorize light emissions, such as bioluminescence, based on their wavelength. For example, Plutonaster bifrons emits light at 525 nm, fitting into the green color range. This knowledge is crucial in fields like marine biology, where such spectral analysis aids in identifying and studying various organisms.