(a) Find the number of electrons and the number of each species of quarks in 1 L of water. (b) M

(a) Find the number of electrons and the number of each...

Key Concepts

Avogadro's Number and the Mole Concept

This concept involves the idea that one mole of a substance contains a fixed number of entities, about 6.02 × 10^23, which allows one to convert between macroscopic amounts of material and the number of molecules or atoms it contains. It forms the basis for estimating the number of individual particles, such as electrons or atoms, in a given mass or volume of a substance.

Molecular Composition

Understanding the molecular composition involves knowing the constituent atoms and their arrangement within a molecule. For example, water is composed of two hydrogen atoms and one oxygen atom. This knowledge is critical for determining counts of electrons and for further breaking down the structure into subatomic particles.

Subatomic Particle Structure

This concept covers the organization of atoms into subatomic particles such as electrons, protons, and neutrons. It entails knowing that electrons orbit the nucleus, and that the nucleus contains protons and neutrons. This structure is essential for computing the number of electrons and the more complex internal structure of the nucleus.

Quark Composition of Nucleons

Protons and neutrons, collectively known as nucleons, are not fundamental particles but are made up of quarks bound together by the strong force. Typically, a proton is composed of two up quarks and one down quark, while a neutron is composed of one up quark and two down quarks. This concept is necessary to determine the number of individual quarks present in a body of matter.

Order-of-Magnitude Estimation

Order-of-magnitude estimation is a method used for approximating quantities to the nearest power of ten. This approach is useful in physics when exact values are difficult to obtain, enabling one to make reasonable approximations, such as estimating the total number of fundamental particles in a given mass or volume of material.

Assumptions in Estimative Reasoning

Making assumptions is crucial when data is incomplete or when simplifications are necessary to solve complex problems. These assumptions might include approximations of average atomic masses, the typical composition and density of biological tissue, or uniformity in molecular structure. Clarity in these assumptions is key to ensuring that the estimations are as accurate and justifiable as possible.

Transcript

00:01 We begin by noting that there are 1 ,000 grams of water in one liter of water, and also that there are 10 protons and 8 neutrons in each molecule of water.

00:13 So there are two hydrogen atoms in each molecule of water and one oxygen atom in each molecule of water.

00:21 You have eight protons per oxygen atom and eight neutrons in each oxygen atom.

00:28 And you only have two, well, for each hydrogen atom, you have one proton, but no neutrons.

00:34 And you've got two hydrogen atoms in every molecule.

00:37 So therefore, you have 10 protons and eight neutrons per water molecule.

00:42 So now the number of protons in one liter of water can be calculated in the following way.

00:49 Let me scroll down.

00:53 We have 1 ,000 grams.

00:55 We have avogadro's number, which is going to be 6 .02 times 10 to the 23rd molecules per 18 grams times 10 protons per molecule.

01:07 The molecule unit cancels, the gram unit cancels, and we now have 3 .34 times 10 to the 26 protons in 1 ,000 grams.

01:19 Similarly, we can calculate the number of neutrons.

01:22 In these 1 ,000 grams of water.

01:38 And so instead of 10 protons, we have 8 neutrons, and we get a number that's similar.

01:45 It's really just 80 % of the other value, and that's 2 .68 times 10 to 26 neutrons.

01:55 Just as we had 3 .34 times 10 of the 26 protons, assuming the water is neutral in charge, we'll have also 3 .34 times 10 of the 26 protons.

02:05 Electrons also.

02:07 So we've calculated the number of protons, neutrons, and electrons in the 1 ,000 grams of water, or the one liter of water.

02:16 So now we can go ahead and calculate the number of quarks in the water as well.

02:23 So we know that for every proton, we're going to have two up quarks and a down quark.

02:28 And for every neutron, we're going to have two down quarks and an up quark.

02:33 So we're going to use the number of protons and the number of neutrons that we just calculated to get the number of up quarks and the number of down quarks.

02:43 And so the way we do this is, for instance, for the number of up quarks, we're going to multiply the number of protons by two because for every proton there are two up quarks, and then we're going to add the number of neutrons because for every neutron there's one up quark.

03:02 So we take twice the number of up quarks, as you see here, and we say two, because there's two up quarks in every proton, and we multiply the number of protons...

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