The diameter of a hydrogen atom is about \( 1.04 \times 10^{-10} \) meters، A protein molecule has an overall length of 2000 times (or \( 2 \times 10^{3} \) times) the diameter of a hydrogen atom. What is the length of the protein molecule, in meters, if it were written in scientific notation? \( 2.08 \times 10^{-13} \) meters \( 2.08 \times 10^{-7} \) meters \( 2.08 \times 10^{-12} \) meters \( 2.08 \times 10^{-8} \) meters

To find the length of the protein molecule, we multiply the diameter of a hydrogen atom by 2000 (which is \( 2 \times 10^{3} \)). The calculation looks like this: \[ \text{Length of protein} = 2000 \times (1.04 \times 10^{-10} \text{ meters}) = 2 \times 10^{3} \times 1.04 \times 10^{-10} \text{ meters} \] When we compute this, we first multiply the coefficients: \[ 2 \times 1.04 = 2.08 \] Next, we add the exponents of 10: \[ 10^{3} \times 10^{-10} = 10^{-7} \] Putting it all together, we get: \[ \text{Length of protein} = 2.08 \times 10^{-7} \text{ meters} \] So the answer is \( 2.08 \times 10^{-7} \) meters. Did you know that the sizes of atoms and molecules are typically measured in picometers (10^-12 meters) or nanometers (10^-9 meters) because they are so small? The hydrogen atom's size gives us a peek into the atomic world, where size is minuscule but crucial for understanding chemical reactions! For more trivia, it’s interesting to note that proteins, made up of long chains of amino acids, are vital for life. Their functions range from catalyzing metabolic reactions to replicating DNA. Scientists constantly study their structure and interactions to better understand biology and develop medicines!