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.

Table of contents

Skip topic navigation

1. Matter and Measurements4h 29m

What is Chemistry?
7m

The Scientific Method
9m

Classification of Matter
16m

States of Matter
8m

Physical & Chemical Changes
19m

Chemical Properties
8m

Physical Properties
5m

Intensive vs. Extensive Properties
13m

Temperature (Simplified)
9m

Scientific Notation
13m

SI Units (Simplified)
5m

Metric Prefixes
24m

Significant Figures (Simplified)
11m

Significant Figures: Precision in Measurements
7m

Significant Figures: In Calculations
19m

Conversion Factors (Simplified)
15m

Dimensional Analysis
22m

Density
12m

Specific Gravity
9m

Density of Geometric Objects
19m

Density of Non-Geometric Objects
8m

2. Atoms and the Periodic Table5h 22m

The Atom (Simplified)
9m

Subatomic Particles (Simplified)
12m

Isotopes
17m

Ions (Simplified)
22m

Atomic Mass (Simplified)
18m

Atomic Mass (Conceptual)
12m

Periodic Table: Element Symbols
6m

Periodic Table: Classifications
11m

Periodic Table: Group Names
8m

Periodic Table: Representative Elements & Transition Metals
7m

Periodic Table: Elemental Forms (Simplified)
6m

Periodic Table: Phases (Simplified)
8m

Law of Definite Proportions
9m

Atomic Theory
9m

Rutherford Gold Foil Experiment
9m

Wavelength and Frequency (Simplified)
5m

Electromagnetic Spectrum (Simplified)
11m

Bohr Model (Simplified)
9m

Emission Spectrum (Simplified)
3m

Electronic Structure
4m

Electronic Structure: Shells
5m

Electronic Structure: Subshells
4m

Electronic Structure: Orbitals
11m

Electronic Structure: Electron Spin
3m

Electronic Structure: Number of Electrons
4m

The Electron Configuration (Simplified)
22m

Electron Arrangements
5m

The Electron Configuration: Condensed
4m

The Electron Configuration: Exceptions (Simplified)
12m

Ions and the Octet Rule
9m

Ions and the Octet Rule (Simplified)
8m

Valence Electrons of Elements (Simplified)
5m

Lewis Dot Symbols (Simplified)
7m

Periodic Trend: Metallic Character
4m

Periodic Trend: Atomic Radius (Simplified)
7m

3. Ionic Compounds2h 18m

Periodic Table: Main Group Element Charges
12m

Periodic Table: Transition Metal Charges
5m

Periodic Trend: Ionic Radius (Simplified)
5m

Periodic Trend: Ranking Ionic Radii
8m

Periodic Trend: Ionization Energy (Simplified)
9m

Periodic Trend: Electron Affinity (Simplified)
8m

Ionic Bonding
6m

Naming Monoatomic Cations
6m

Naming Monoatomic Anions
5m

Polyatomic Ions
25m

Naming Ionic Compounds
11m

Writing Formula Units of Ionic Compounds
7m

Naming Ionic Hydrates
6m

Naming Acids
18m

4. Molecular Compounds2h 18m

Covalent Bonds
6m

Naming Binary Molecular Compounds
6m

Molecular Models
4m

Bonding Preferences
6m

Lewis Dot Structures: Neutral Compounds (Simplified)
8m

Multiple Bonds
4m

Multiple Bonds (Simplified)
6m

Lewis Dot Structures: Multiple Bonds
10m

Lewis Dot Structures: Ions (Simplified)
8m

Lewis Dot Structures: Exceptions (Simplified)
12m

Resonance Structures (Simplified)
5m

Valence Shell Electron Pair Repulsion Theory (Simplified)
4m

Electron Geometry (Simplified)
8m

Molecular Geometry (Simplified)
11m

Bond Angles (Simplified)
11m

Dipole Moment (Simplified)
15m

Molecular Polarity (Simplified)
7m

5. Classification & Balancing of Chemical Reactions3h 17m

Chemical Reaction: Chemical Change
5m

Law of Conservation of Mass
5m

Balancing Chemical Equations (Simplified)
13m

Solubility Rules
16m

Molecular Equations
18m

Types of Chemical Reactions
12m

Complete Ionic Equations
18m

Calculate Oxidation Numbers
15m

Redox Reactions
17m

Spontaneous Redox Reactions
8m

Balancing Redox Reactions: Acidic Solutions
17m

Balancing Redox Reactions: Basic Solutions
17m

Balancing Redox Reactions (Simplified)
13m

Galvanic Cell (Simplified)
16m

6. Chemical Reactions & Quantities2h 34m

Empirical Formula
21m

Molecular Formula
20m

Calculating Molar Mass
9m

Mole Concept
36m

Mass Percent
4m

Stoichiometry
23m

Limiting Reagent
19m

Percent Yield
20m

7. Energy, Rate and Equilibrium3h 40m

Nature of Energy
6m

First Law of Thermodynamics
7m

Endothermic & Exothermic Reactions
7m

Bond Energy
14m

Thermochemical Equations
12m

Heat Capacity
19m

Thermal Equilibrium (Simplified)
8m

Hess's Law
23m

Rate of Reaction
11m

Energy Diagrams
12m

Chemical Equilibrium
7m

The Equilibrium Constant
14m

Le Chatelier's Principle
20m

Solubility Product Constant (Ksp)
17m

Spontaneous vs Nonspontaneous Reactions
7m

Entropy (Simplified)
9m

Gibbs Free Energy (Simplified)
18m

8. Gases, Liquids and Solids3h 27m

Pressure Units
6m

Kinetic Molecular Theory
14m

The Ideal Gas Law
18m

The Ideal Gas Law Derivations
13m

The Ideal Gas Law Applications
6m

Chemistry Gas Laws
17m

Chemistry Gas Laws: Combined Gas Law
12m

Standard Temperature and Pressure
14m

Dalton's Law: Partial Pressure (Simplified)
13m

Gas Stoichiometry
18m

Intermolecular Forces (Simplified)
19m

Intermolecular Forces and Physical Properties
11m

Atomic, Ionic and Molecular Solids
10m

Heating and Cooling Curves
30m

9. Solutions4h 27m

Solutions
6m

Solubility and Intermolecular Forces
17m

Solutions: Mass Percent
6m

Percent Concentrations
10m

Molarity
18m

Osmolarity
15m

Parts per Million (ppm)
13m

Solubility: Temperature Effect
8m

Intro to Henry's Law
4m

Henry's Law Calculations
12m

Dilutions
12m

Solution Stoichiometry
14m

Electrolytes (Simplified)
13m

Equivalents
11m

Molality
15m

The Colligative Properties
15m

Boiling Point Elevation
16m

Freezing Point Depression
9m

Osmosis
16m

Osmotic Pressure
10m

Vapor Pressure Lowering (Raoult's Law)
16m

10. Acids and Bases3h 10m

Acid-Base Introduction
11m

Arrhenius Acid and Base
6m

Bronsted Lowry Acid and Base
21m

Acid and Base Strength
17m

Ka and Kb
16m

The pH Scale
16m

Auto-Ionization
9m

pH of Strong Acids and Bases
9m

Acid-Base Equivalents
14m

Acid-Base Reactions
7m

Gas Evolution Equations (Simplified)
6m

Ionic Salts (Simplified)
11m

Buffers
11m

Henderson-Hasselbalch Equation
16m

Strong Acid Strong Base Titrations (Simplified)
13m

11. Nuclear Chemistry56m

Types of Radiation
5m

Alpha Decay
8m

Beta Decay
11m

Gamma Emission
6m

Electron Capture
3m

Positron Emission
5m

Radioactive Half-Life
8m

Measuring Radioactivity
6m

BONUS: Lab Techniques and Procedures1h 38m

Laboratory Materials
29m

Experimental Error
12m

Distillation & Floatation
12m

Chromatography
6m

Filtration and Evaporation
4m

Extraction
17m

Test for Ions and Gases
14m

BONUS: Mathematical Operations and Functions47m

Multiplication and Division Operations
6m

Addition and Subtraction Operations
6m

Power and Root Functions
6m

Power and Root Functions
20m

The Quadratic Formula
7m

12. Introduction to Organic Chemistry1h 34m

Introduction to Organic Chemistry
7m

Structural Formula
8m

Condensed Formula
9m

Skeletal Formula
6m

Functional Groups in Chemistry
11m

Naming Alkanes
4m

The Alkyl Groups
9m

Naming Alkanes with Substituents
13m

Naming Cyclic Alkanes
6m

Naming Other Substituents
8m

Alkane Reactions
7m

13. Alkenes, Alkynes, and Aromatic Compounds2h 12m

Spatial Orientation of Bonds
3m

Intro to Hydrocarbons
16m

Isomers
14m

Chirality
15m

Naming Alkenes
11m

Naming Alkynes
9m

Intro to Addition Reactions
4m

Halogenation Reaction
4m

Hydrogenation Reaction
3m

Hydrohalogenation Reaction
7m

Hydration Reaction
10m

Naming Benzene
19m

Benzene Reactions
10m

14. Compounds with Oxygen or Sulfur1h 6m

Naming Alcohols
16m

Naming Ethers
13m

Naming Thiols
6m

Alcohol Reactions: Dehydration Reactions
9m

Intro to Redox Reactions
8m

Alcohol Reactions: Oxidation Reactions
7m

Reactions of Thiols
4m

15. Aldehydes and Ketones1h 1m

Naming Ketones
12m

Naming Aldehydes
12m

Tollens' and Benedict's Test
12m

Reduction of Aldehydes and Ketones
11m

Hemiacetal and Acetal Formation
11m

16. Carboxylic Acids and Their Derivatives1h 11m

Naming Carboxylic Acids
16m

Naming Esters
15m

Naming Amides
10m

Carboxylic Acid Reactions
4m

Ester Reactions: Esterification
4m

Ester Reactions: Acid-Catalyzed Hydrolysis
3m

Ester Reactions: Saponification
3m

Amide Formation
4m

Amide Hydrolysis
8m

17. Amines39m

Classifying Amines
3m

Naming Amines
12m

Naming Ammonium Salts
10m

Functional Group Priorities
8m

Amine Reactions
4m

18. Amino Acids and Proteins1h 51m

Intro to Amino Acids
6m

Amino Acid Three Letter Codes
5m

Amino Acid One Letter Codes
14m

Amino Acid Classifications
21m

Peptides
12m

Primary Protein Structure
4m

Secondary Protein Structure
17m

Tertiary Protein Structure
11m

Quaternary Protein Structure
10m

Summary of Protein Structure
7m

19. Enzymes1h 37m

Intro to Enzymes
3m

Enzyme Classification
34m

Enzyme-Substrate Complex
6m

Models of Enzyme Action
5m

Factors Affecting Enzyme Activity
12m

Enzyme Inhibition
8m

Enzyme Regulation: Allosteric Control
5m

Enzyme Regulation: Feedback Control
6m

Enzyme Regulation: Covalent Modification
14m

20. Carbohydrates1h 41m

Intro to Carbohydrates
4m

Classification of Carbohydrates
4m

Fischer Projections
4m

Enantiomers vs Diastereomers
7m

D vs L Enantiomers
9m

Cyclic Hemiacetals
8m

Intro to Haworth Projections
4m

Cyclic Structures of Monosaccharides
11m

Mutarotation
4m

Reduction of Monosaccharides
10m

Oxidation of Monosaccharides
7m

Glycosidic Linkage
14m

Disaccharides
7m

Polysaccharides
2m

21. The Generation of Biochemical Energy2h 8m

Intro to Metabolism
10m

ATP and Energy
12m

Intro to Cofactors
4m

Intro to Coenzymes
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
13m

Oxidative Phosphorylation
7m

Aerobic Respiration Summary
5m

22. Carbohydrate Metabolism2h 22m

Intro to Carbohydrate Metabolism
5m

Intro to Glycolysis
8m

Glycolysis
28m

Glycolysis Summary
27m

Pyruvate Oxidation
3m

Anaerobic Respiration
16m

Total Energy from Glucose
10m

Intro to Gluconeogenesis
4m

Gluconeogenesis
37m

23. Lipids2h 26m

Intro to Lipids
6m

Fatty Acids
25m

Physical Properties of Fatty Acids
6m

Waxes
4m

Triacylglycerols
12m

Triacylglycerol Reactions: Hydrogenation
8m

Triacylglycerol Reactions: Hydrolysis
13m

Triacylglycerol Reactions: Oxidation
7m

Glycerophospholipids
15m

Sphingomyelins
13m

Steroids
15m

Cell Membranes
7m

Membrane Transport
10m

24. Lipid Metabolism1h 45m

Intro to Lipid Digestion
5m

Digestion of Lipids
6m

Lipoproteins for Transport
6m

Glycerol Metabolism
14m

Intro to Fatty Acid Oxidation
9m

Oxidation of Fatty Acids
21m

Total Energy from Fatty Acids
14m

Ketone Bodies
14m

Summary of Lipid Metabolism
12m

25. Protein and Amino Acid Metabolism1h 37m

Digestion of Proteins
5m

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

Intro to Nucleic Acids
4m

Nitrogenous Bases
16m

Nucleoside and Nucleotide Formation
9m

Naming Nucleosides and Nucleotides
13m

Phosphodiester Bond Formation
7m

Primary Structure of Nucleic Acids
11m

Base Pairing
10m

DNA Double Helix
6m

Intro to DNA Replication
20m

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

Previous problemNext problem

Struggling with GOB Chemistry?

Join thousands of students who trust us to help them ace their exams!Watch the first video

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

Previous problemNext problem

Verified step by step guidance

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.