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Use the concepts in this chapter to obtain an estimate for the number of atoms in the universe. Make the following assumptions: (a) Assume that all
of the atoms in the universe are hydrogen atoms in stars. (This is not a ridiculous assumption because over three-fourths of the atoms in the universe
are in fact hydrogen. Gas and dust between the stars represent only about 15% of the visible matter of our galaxy, and planets compose a far tinier
fraction.) (b) Assume that the sun is a typical star composed of pure hydrogen with a density of 1.4 g/cm and a radius of 7 x 108m. (c) Assume
that each of the roughly 100 billion stars in the Milky Way galaxy contains the same number of atoms as our sun. (d) Assume that each of the 10
billion galaxies in the visible universe contains the same number of atoms as our Milky Way galaxy.
Express your answer using one signififcant figure.

Sagot :

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Answer:  1.22x10^78 H atoms per Universe

Explanation:  Lots of conversions, so watch for errors.

Mass of Sun:

 V=(4/3)πr²

 V = (4/3)(π)(7x10⁸m)² = 1.44x10²⁷ m³  or 1.44x10³³ cm³

 Mass of Sun:  (1.44x10³³ cm³)*(1.4g/cm³) = 2.02x10³³ g/sun

Suns/Milky Way = 1x10¹¹ suns/galaxy

Suns/Universe =   (1x10¹¹ suns/galaxy)*(1x10¹⁰galaxies/universe) = 1x10²¹ suns/universe

Assunming all mass ins in the suns, mass of the universe is:

(1x10²¹ suns/universe)*(2.02x10³³ g/sun) = 2.02x10⁵⁴g/universe

Molar mass of H is 1 g/mole

1 mole = 6.02x10²³H atoms

H atoms/universe = (2.02x10⁵⁴g/universe)*(1 g H atoms/mole)*(6.02x10²³H atoms/mole) = 1.22x10⁷⁸ H atoms per universe.

Answer:

Number of atoms in the universe is [tex]\[1.201\times {{10}^{79}}\][/tex]

Explanation:

Calculate number of atoms in universe using CGS unit.

Step 1

Calculate mass of sun  

[tex]\[\text{Mass of sun = Density }\times \text{ Volume}\][/tex]

Step 2

Insert the value of density and radius to calculate mass of sun

[tex]& \text{Mass of sun = 1}\text{.4}\times \frac{4}{3}\pi {{\left( 7\times {{10}^{10}} \right)}^{3}} \\ & \text{Mass of sun}=2.011\times {{10}^{33}}g \\ \end{align}[/tex]

Average atomic mass of hydrogen atom is [tex]\[1.008amu\][/tex]

Avogadro’s number is number of atoms in 1 mole of hydrogen.

Step 3

Calculate number of Hydrogen [tex]\[\left( {{N}_{H}} \right)\][/tex]atoms in sun

[tex]& {{N}_{H}}=\frac{\text{Mass of sun}}{\text{Molar mass of Hydrogen atom}}\times \text{Avogadro }\!\!'\!\!\text{ s }\text{Number} \\ & {{N}_{H}}=\frac{2.011\times {{10}^{33}}}{1.008}\times 6.02\times {{10}^{23}} \\ & {{N}_{H}}=1.201\times {{10}^{57}} \\[/tex]

Step 4  

Calculate number of atoms[tex]\[\left( {{N}_{A}} \right)\][/tex] in our Milky Way galaxy

[tex]& {{N}_{A}}=\text{Number of stars}\times \text{Number of atoms in sun} \\ & {{N}_{A}}=1.00\times {{10}^{11}}\times 1.202\times {{10}^{57}} \\ & {{N}_{A}}=1.201\times {{10}^{68}} \\[/tex]

   

Step 5

Calculate number of atom in observable universe [tex]\[\left( {{N}_{Ao}} \right)\][/tex]

[tex]& {{N}_{Ao}}=\text{Number of galaxies }\times \text{ Number of atoms in our galaxy} \\ & {{N}_{Ao}}=1.00\times {{10}^{11}}\times 1.201\times {{10}^{68}} \\ & {{N}_{Ao}}=1.201\times {{10}^{79}} \\[/tex]

Learn more about universe here:  

https://brainly.com/question/17525451

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