Estimate the number of nuclei that are present in a 50 -kg human body.

Name: Problem 33, Chapter 27: College Physics
Uploaded: 2021-09-18T16:49:57-08:00
Duration: 5 min 18 s
Channel: Declan Nell
Description: Estimate the number of nuclei that are present in a 50 -kg human body.

Estimate the number of nuclei that are present in a 50 -kg...

Key Concepts

Mole Concept and Avogadro's Number

The mole is a fundamental unit in chemistry that connects the macroscopic and microscopic worlds by providing a way to count large numbers of particles. Avogadro’s number, approximately 6.022×10^23, specifies how many atoms, molecules, or nuclei are contained in one mole of substance, making it essential for converting mass into an estimated number of particles.

Atomic Nucleus

The nucleus is the dense, central component of an atom that contains protons and neutrons. Understanding the nucleus is crucial because the question specifically asks for the number of nuclear cores in the human body, which involves considering how many atoms—and hence, nuclei—are present in a given mass.

Estimation Techniques in Physics

Estimation techniques involve making reasonable approximations and assumptions to simplify complex calculations. In problems like estimating the number of nuclei in a 50-kg human body, concepts such as average atomic mass and the predominant elements in the body are used to perform a ballpark calculation, which is a common practice in physics and chemistry to manage large numbers.

Transcript

00:01 Hello, and in this question here, we're asked to estimate the number of atoms in the human body, okay? and we're told here, there's the number of nuclei, but obviously each atom has one nuclei, so we calculate the number of atoms, okay? so we're told here that we're going to, you do this for a 50 kilogram body, okay? and, well, how could we go about this? so we're going to make the approximation, okay, that a human body, okay, is 75 % water, and 25 % carbon.

00:35 Now, of course, this is not true at all.

00:38 There's a huge variety of elements that a human body is comprised of.

00:43 But for the sake of this question and the sake of simplicity, we're just going to say that it's 75 % water and 25 % carbon to give us a rough estimate for how many nuclei there are in a human body.

00:55 So this means, okay, the total mass of water is equal to 37 .5 kilograms.

01:01 And the total mass of carbon in the body is equal to 12 .5 kilograms.

01:08 Okay.

01:10 So from here, how could we calculate the number of nuclei in the body? well, the total number of nuclei will be the total number of carbon atoms, plus the number of water molecules.

01:28 However, in one more water molecule, there's going to be three atoms.

01:31 So there's going to be two hydrogen, one oxygen.

01:34 So we're going to multiply the number of water molecules by three, as there are three atoms in one water molecule.

01:40 So if we can calculate the number of water molecules and the number of carbon atoms will be able to determine the number of nuclei within a human body.

01:49 Okay? well, what is the number of carbon atoms? well, this is just the mass of the carbon, so the total mass of carbon in the body, divided by the mass of a single carbon nucleus, plus, or a single carbon atom, i should say, plus the total mass, we're going to have a factor of three, three times the total mass of water in the body, divided by the mass of water, or a single molecule of water.

02:16 So we have the total mass of carbon water, we just need the mass of a single molecule or atom.

02:22 And by googling it, we get the mass of carbon is equal to, the mass of a single carbon is equal to 12 .0 .0 .0.

02:32 0107 u excuse me where u is the atomic unit of mass and has a value of 1 .67 times 10 to the power of minus 27 kilograms okay and so this gives that the mass of a single carbon is equal to 2 .0057 times 10 to the power of minus 26 kilograms okay and we also need the mass of a single water molecule and if you google this you'll get a value of a value of a value of a of 18 .0152 to 8 grams per mole.

03:10 Okay? and one mole, okay? so one mole contains six times 10 to the power of 23 atoms, okay? so if we divide this weight here by the number of atoms, the number of molecules will be able to calculate the mass of a single molecule, okay? so this means the mass of a single molecule of water, so we're dividing this figure here by this figure to get the mass of a single molecule of water.

03:41 And this means that the mass of a single water molecule is equal to 3 times 10 to the power of minus 26 kilograms.

03:51 Okay, cool...

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