The average radius of a molecule of lysozyme, an enzyme in tears, is \(1430 \mathrm{pm}\). What is its radius in nanometers (nm)?

To convert picometers to nanometers, we need to understand the relationship between these units. A picometer (pm) is one of the smallest units of length and is equal to one trillionth of a meter, while a nanometer (nm) is one billionth of a meter.

Recall that 1 nanometer (nm) represents 1000 picometers (pm). Knowing this, we can easily convert any value in picometers to nanometers by dividing by 1000.

For example, to convert 1430 pm to nm:

• Set up the conversion factor: \[ 1 \text{ nm} = 1000 \text{ pm} \]


• Divide the number of picometers by 1000: \[ 1430 \text{ pm} \times \frac{1 \text{ nm}}{1000 \text{ pm}} = 1.43 \text{ nm} \]

This gives us the equivalent value in nanometers, which is the necessary conversion for various scientific measurements.

Lysozyme is an enzyme found in many bodily fluids like tears and saliva. It plays a crucial role in preventing bacterial infections by breaking down the cell walls of bacteria—essentially acting as part of the body's immune defense.

The average radius of a lysozyme molecule is 1430 picometers (pm). To have a better understanding of its size at a more manageable scale, we convert this radius to nanometers (nm).

Using the previous conversion, we find that the radius is 1.43 nm:

• Initial radius: 1430 pm
• Convert using factor: \[ 1430 \text{ pm} \times \frac{1 \text{ nm}}{1000 \text{ pm}} = 1.43 \text{ nm} \]

This size is incredibly small, showcasing the molecular scale at which lysozymes operate to protect us. This tiny radius gives insight into the efficiency and effectiveness of lysozymes in fighting off bacterial invaders.

Basic chemistry calculations often involve unit conversions, as we saw with converting picometers to nanometers. These conversions are critical for understanding and working with different chemical substances and their properties.

Here are a few tips for handling these kinds of calculations:

• Always identify the units you are starting with and the units you need to convert to. This sets a clear goal for your calculation.


• Use correct conversion factors. Make sure to know the relationship between the units correctly, such as 1 nm = 1000 pm.


• Set up the conversion factor as a fraction to help you easily cancel out the units and perform the calculation. In the case of picometers to nanometers: \[ 1430 \text{ pm} \times \frac{1 \text{ nm}}{1000 \text{ pm}} = 1.43 \text{ nm} \]


• Double-check your calculations to avoid errors. Simple mistakes can lead to incorrect answers.

By practicing these strategies, basic chemistry calculations can become straightforward and manageable, allowing for a deeper understanding of the material.