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A proton has a radius of approximately 1 × 10 -13 cm and a mass of 1.7 × 10 − 24 g. a. Determine the density of a proton. For a sphere, V = ( 4 / 3 ) π r 3 ; 1 cm 3 = 1 mL; π =3 .14 . b. By assuming that black holes have the same density as protons, determine the mass (in kilograms) of a black hole and the size of a sand particle. A typical sand particle has a radius of 1 × 10 − 4 m.

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Chemistry In Focus

7th Edition
Tro + 1 other
Publisher: Cengage Learning,
ISBN: 9781337399692

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Section
BuyFindarrow_forward

Chemistry In Focus

7th Edition
Tro + 1 other
Publisher: Cengage Learning,
ISBN: 9781337399692
Chapter 2, Problem 46E
Textbook Problem
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A proton has a radius of approximately 1 × 10 -13 cm and a mass of 1.7 × 10 24 g.

a. Determine the density of a proton. For a sphere, V = ( 4 / 3 ) π r 3 ;  1 cm 3 = 1  mL;  π =3 .14 .

b. By assuming that black holes have the same density as protons, determine the mass (in kilograms) of a black hole and the size of a sand particle. A typical sand particle has a radius of 1 × 10 4 m.

Interpretation Introduction

Interpretation:

The density of a proton and the mass of a black hole is to be calculated.

Concept Introduction:

Density of a substance is a measure of compactness of that substance. It is defined as the mass of a substance present in per unit of its volume. The unit of density is derived when the unit of mass is divided by the unit of volume. Its most common units are g/cm3 and g/mL.

Density = Mass Volume

As 103g = 1 kg, conversion factor for g into kg is as:

1 kg103g

Explanation of Solution

a) The density of a proton having radius of approximately 1×1013cm and a mass 1.7×1024g.

Calculation of volume of a proton is as:

Volume of a proton = 43πr3

Substitute the given values in the above equation as:

Volume of a proton = 43×3.14 ×(1×1013cm)3Volume of a proton = 4×1039cm3 

Therefore, the volume of a proton is 4×1039cm3 .

Calculation of density of a proton is as follows:

Density of proton = Mass of protonVolume of proton 

Substitute the given values in the above equation as:

Density of a proton = 1.7×1024 g4×1039 cm3 Density of a proton = 4×1014 g/cm3.

Thus, the density of a proton is 4×1014 g/cm3.

b) The mass of a black hole and the size of a sand particle, radius of sand particle is 1×104m.

The volume of a black hole is as follows:

Radius of the black hole = 1×104m1m = 100 cm

So,

Radius of the black hole = 1×104m×100 cmmRadius of the black hole = 1×102 cm

Volume of the black hole = 43πr3

Substitute the given values in the above equation as:

Volume of the black hole = 43×3

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