Estimate the number of nucleons found in the body of a \(75-\mathrm{kg}\) person.

Assuming that a person's body is about 70% water, we can estimate the mass of water in the body as follows: Mass of water = 0.7 x Mass of the person So in a 75 kg person: Mass of water = 0.7 x 75 kg = 52.5 kg

We know that the molecular weight of water (H₂O) is approximately 18 g/mol. To find the number of moles of water in the body, we can use the mass and molecular weight: Number of moles of water = Mass of water / Molecular weight of water Converting the mass of water to grams (1 kg = 1000 g): Mass of water = 52.5 kg x 1000 g/kg = 52500 g Number of moles of water = 52500 g / 18 g/mol = 2916.67 moles

In order to estimate the number of nucleons in the body, we first need to find the number of water molecules. We can use Avogadro's number (\(6.022 \times 10^{23} \text{ molecules/mol}\)) to find the number of water molecules: Number of water molecules = Number of moles of water x Avogadro's number Number of water molecules = 2916.67 moles x \(6.022 \times 10^{23} \text{ molecules/mol}\) ≈ \(1.75 \times 10^{26}\) water molecules

Each water molecule consists of 2 hydrogen atoms and 1 oxygen atom. The respective atomic weights of hydrogen and oxygen are approximately 1 and 16, which represent the number of nucleons (protons + neutrons) in each atom. So, in each water molecule, there are 18 nucleons. Now, to estimate the total number of nucleons in the body, we will multiply the number of water molecules by the number of nucleons per water molecule: Total number of nucleons = Number of water molecules x Nucleons per water molecule Total number of nucleons = \(1.75 \times 10^{26}\) water molecules x 18 nucleons/water molecule ≈ \(3.15 \times 10^{27}\) nucleons Therefore, the estimated number of nucleons found in the body of a 75 kg person is approximately \(3.15 \times 10^{27}\).