Question

The light that plants absorb to perform photosynthesis has a wavelength that peaks near \(675 \mathrm{~nm}\). Express this distance in (a) millimeters and (b) meters.

Short answer

675 nm is 0.000675 mm and 6.75 x 10^-7 m.

Step-by-step solution

Understand the Problem

We need to convert the wavelength of light from nanometers to millimeters and meters. The given wavelength is 675 nanometers.

Convert Nanometers to Millimeters

Remember that 1 millimeter (mm) is equal to 1,000,000 nanometers (nm). To convert from nanometers to millimeters, we use the conversion factor:\[ 1 \text{ mm} = 1,000,000 \text{ nm} \].Divide the given wavelength by 1,000,000:\[ 675 \text{ nm} \times \frac{1 \text{ mm}}{1,000,000 \text{ nm}} = 0.000675 \text{ mm} \].

Convert Nanometers to Meters

Remember that 1 meter (m) is equal to 1,000,000,000 nanometers (nm). To convert from nanometers to meters, we use the conversion factor:\[ 1 \text{ m} = 1,000,000,000 \text{ nm} \].Divide the given wavelength by 1,000,000,000:\[ 675 \text{ nm} \times \frac{1 \text{ m}}{1,000,000,000 \text{ nm}} = 6.75 \times 10^{-7} \text{ m} \].

Key concepts

Converting Nanometers to Millimeters

Converting units can sometimes feel tricky, but understanding the basics makes it a lot simpler. Let's break down how to convert nanometers (nm) to millimeters (mm). A nanometer is incredibly small, specifically one billionth of a meter—so more commonly, we convert it into larger units like millimeters for easier comprehension.
A critical piece of information here is that:

• 1 millimeter equals 1,000,000 nanometers.

To convert nanometers to millimeters, you'll need to divide the nanometer value by 1,000,000 because you're finding out how many of these tiny units fit in one millimeter.
For instance, for a wavelength of 675 nm, the conversion would be:

• \[ 675 \text{ nm} \times \frac{1 \text{ mm}}{1,000,000 \text{ nm}} = 0.000675 \text{ mm} \]

This means that the light wavelength is just 0.000675 millimeters. Breaking it down into such steps helps you grasp the magnitude of these tiny measurements.

Converting Nanometers to Meters

To express distances measured in nanometers into meters, we need to consider the scale. A nanometer is one billionth of a meter, meaning:

• 1 meter equals 1,000,000,000 nanometers.

This conversion helps us understand just how small a wavelength measured in nanometers truly is. To convert from nanometers to meters, take the nanometer value and divide it by 1,000,000,000.
Let's consider the example where the wavelength is 675 nm. The conversion would look like this:

• \[ 675 \text{ nm} \times \frac{1 \text{ m}}{1,000,000,000 \text{ nm}} = 6.75 \times 10^{-7} \text{ m} \]

Here, the result shows that the wavelength is a mere fraction of a meter: 0.000000675 meters or 6.75 x 10^-7 in scientific notation. This illustrates the tiny scale on which photochemistry, such as photosynthesis, operates.

Understanding Photosynthesis Light Wavelength

Photosynthesis is an incredible natural process, where plants convert light energy into chemical energy. This transformation primarily uses the light spectrum's visible portion. Plants are especially adapted to absorb certain wavelengths of light with high efficiency, mainly blue (around 430 nm) and red (around 675 nm).
The 675 nm wavelength is significant because it's within the red light spectrum, crucial for photosynthesis. It optimizes the light-harvesting ability of plants' chlorophylls, especially in the chloroplasts of plant cells.
Recognizing the conversion of photosynthetic wavelengths from nanometers to other units helps in various scientific contexts, such as:

• Understanding plant growth conditions.
• Designing artificial light sources for growing plants indoors.

In summary, converting measurement units enables easier analysis and application across multiple scientific and practical applications, offering deeper insight into natural and artificial processes.