If the density of a certain spherical atomic nucleus is 1.0 x 10 14 g/cm 3 and its mass is 3.5 x 10 -23 g, what is the radius in angstroms? (Å= 10 −10 m)

So here our practice question states, if the density of a certain spherical atomic nucleus is 1.0 times 10 to the 14 grams per centimeters cubed and its mass is 3.5 times 10 to the negative 23 grams, what is the radius in angstroms? Now, one angstrom, which is symbolized by this a with a circle on top equals 10 to the negative 10 meters. So So that's gonna come in handy when we have to do any type of metric prefix conversion associated with angstroms. Now here they're telling us it's a sphere and we're talking about its radius. Now remember the volume equation for sphere is volume equals 4 over 3 times pi times radius cubed. That means we need to isolate radius. The only way to isolate that radius is to figure out what my volume will be. Now, from the information given to us, presented to us, this is only 1 unit by itself, so that has to be our given amount. And then here we have our density, which we've said numerous times at this point, that represents a conversion factor. So let's use those. So we have 3.5 times 10 to the negative 23 grams. We're bringing our conversion factor here. So our conversion factor here, we're going to have grams canceling out, so 1.0 times 10 to the 14 grams has to go on the bottom, and then 1 centimeters cubed has to go on top. Grams here would cancel out, and we'd have centimeters cubed for our volume. So that comes out to 3.5 times 10 to the negative 37 centimeters cubed. So we're going to plug it into the formula. So 3.5 times 10 to the negative 37 centimeters cubed, and that equals 4 over 3 times pi times radius cubed. Alright. So we're going to first multiply both sides by 3 to cancel out this 3. So when I multiply this by 3, I'm going to get 1.05 times 10 to the negative 36 centimeters cubed, and that's equal to 4 times pi times radius cubed. Next, divide both sides by 4. Remember, we're trying to isolate radius here. So when I do that, I'm going to get Oh. We're going to divide it by 4 and pi at the same time. Just kill 2 birds with 1 stone. So that would be radius cubed equals 8.3 556 times 10 to the negative 38 centimeters cubed. But we wanna get rid of centimeters cubed, so we're gonna take the cube root of both sides. So for a lot of you on your calculators, you'll see this symbol, an x with a square root sign. So in your calculator you would hit the button 3, then you would hit this button, in parenthesis, you would put this value of 8.356 times 10 to the negative 38, close parenthesis, and that would give you as your radius 4.37 times 10 to the negative 13 centimeters, but realize here here that we don't want the radius in centimeters, we want it in angstroms. So we have to do a metric prefix conversion. So we're gonna have here 34.37 times 10 to the negative 13 centimeters. Centimeters go on the bottom, our base of meters goes on top. One centi is 10 to the negative 2. So now we have meters, and then let's use this conversion factor here. Meters goes on the bottom, angstroms go on top. One angstrom is 10 to the negative 10 meters. So if you do that correctly, you should get as your answer 4.3 7 times 10 to the negative 5 angstroms. We're going to say here that this number coefficient has 2 sig figs, and 3.5 has 2 sig figs. So the best answer here would be 4.4 times 10 to the negative 5 angstroms. So remember, when dealing with geometric objects, we commonly run into spheres and cubes and cylinders. Their formulas oftentimes do not need to be memorized. They're usually given to you within the question or on a formula sheet. But to be absolutely sure, always consult with your professor. Now remember, even though it's density, we do take components from dimensional analysis to help guide us to our end amount. So keep in mind what we've learned thus far about conversion factors, given amounts, end amounts, and how it all applies to dimensional analysis and, of course, density.

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1. Matter and Measurements4h 29m

What is Chemistry?
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The Scientific Method
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Classification of Matter
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States of Matter
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Physical & Chemical Changes
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Physical Properties
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Intensive vs. Extensive Properties
13m

Temperature (Simplified)
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SI Units (Simplified)
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Metric Prefixes
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7m

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15m

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22m

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12m

Specific Gravity
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2. Atoms and the Periodic Table5h 22m

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Atomic Theory
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11m

Bohr Model (Simplified)
9m

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Electronic Structure
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3m

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Types of Chemical Reactions
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Chirality
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Carboxylic Acid Reactions
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17. Amines40m

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Functional Group Priorities
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Protein Denaturation
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19. Enzymes1h 37m

Intro to Enzymes
3m

Enzyme Classification
34m

Enzyme-Substrate Complex
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Models of Enzyme Action
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Factors Affecting Enzyme Activity
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Enzyme Inhibition
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Enzyme Regulation: Allosteric Control
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Enzyme Regulation: Covalent Modification
14m

20. Carbohydrates1h 46m

Intro to Carbohydrates
4m

Classification of Carbohydrates
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Fischer Projections
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7m

D vs L Enantiomers
9m

Cyclic Hemiacetals
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4m

Cyclic Structures of Monosaccharides
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10m

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Glycosidic Linkage
14m

Disaccharides
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Polysaccharides
8m

21. The Generation of Biochemical Energy2h 9m

Intro to Metabolism
10m

ATP and Energy
12m

Intro to Cofactors
4m

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3m

Coenzymes in Metabolism
15m

Energy Production In Biochemical Pathways
5m

Intro to Citric Acid Cycle
6m

The Citric Acid Cycle
44m

Electron Transport Chain
14m

Oxidative Phosphorylation
7m

Aerobic Respiration Summary
5m

22. Carbohydrate Metabolism2h 31m

Intro to Carbohydrate Metabolism
5m

Intro to Glycolysis
8m

Glycolysis
28m

Glycolysis Regulation
7m

Glycolysis Summary
27m

Pyruvate Oxidation
4m

Anaerobic Respiration
16m

Total Energy from Glucose
10m

Intro to Gluconeogenesis
4m

Gluconeogenesis
37m

23. Lipids2h 26m

Intro to Lipids
6m

Fatty Acids
25m

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6m

Waxes
4m

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12m

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8m

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13m

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7m

Glycerophospholipids
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Sphingomyelins
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7m

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24. Lipid Metabolism1h 45m

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5m

Digestion of Lipids
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Lipoproteins for Transport
6m

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9m

Oxidation of Fatty Acids
21m

Total Energy from Fatty Acids
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Ketone Bodies
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Summary of Lipid Metabolism
12m

25. Protein and Amino Acid Metabolism1h 37m

Digestion of Proteins
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Intro to Amino Acid Catabolism
3m

Amino Acid Catabolism: Amino Group
14m

Amino Acid Catabolism: Carbon Atoms
20m

Intro to Urea Cycle
6m

The Urea Cycle
31m

Review of Metabolism
16m

26. Nucleic Acids and Protein Synthesis2h 54m

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Nitrogenous Bases
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Phosphodiester Bond Formation
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Primary Structure of Nucleic Acids
11m

Base Pairing
10m

DNA Double Helix
6m

Intro to DNA Replication
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Steps of DNA Replication
11m

Types of RNA
10m

Overview of Protein Synthesis
4m

Transcription: mRNA Synthesis
9m

Processing of pre-mRNA
5m

The Genetic Code
6m

Introduction to Translation
7m

Translation: Protein Synthesis
18m

1. Matter and Measurements

Density of Geometric Objects

GOB Chemistry

1. Matter and Measurements

Density of Geometric Objects

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Multiple Choice

If the density of a certain spherical atomic nucleus is 1.0 x 10¹⁴ g/cm³ and its mass is 3.5 x 10^-23 g, what is the radius in angstroms? (Å= 10⁻¹⁰ m)

4.37 x 10⁵ Å

4.37 x 10² Å

4.4 x 10^-5 Å

4.37 x 10^-3 Å

4.4 x 10^-7 Å

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검증된 단계별 안내

Start by using the formula for density, which is density = mass/volume. Here, the density is given as 1.0 x 10^14 g/cm^3 and the mass is 3.5 x 10^-23 g.

Rearrange the formula to solve for volume: volume = mass/density. Substitute the given values into this equation.

The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius. Set the volume you calculated equal to this expression.

Solve the equation (4/3)πr^3 = volume for r, the radius. This will involve isolating r and taking the cube root.

Convert the radius from centimeters to angstroms. Remember that 1 cm = 10^8 angstroms, so multiply the radius in cm by 10^8 to get the radius in angstroms.