"The hydrogen atom has a volume of approximately [tex]6.2 \times 10^{-31} \, \text{m}^3[/tex]. What is this volume in each unit?

(a) cubic picometers
(b) cubic nanometers
(c) cubic angstroms"

(Note: 1 angstrom = [tex]10^{-10} \, \text{m}[/tex])

Question

High School

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Answer :

mmrizvi034 mmrizvi034 · Answer 1 · 2023-09-15T18:52:30-04:00

Final Answer:

(a) The volume of the hydrogen atom is approximately [tex]\(6.2 \times 10^{-5}\)[/tex] cubic picometers.

(b) The volume of the hydrogen atom is approximately [tex]\(6.2 \times 10^{-25}\)[/tex] cubic nanometers.

(c) The volume of the hydrogen atom is approximately [tex]\(6.2 \times 10^{-31}\)[/tex] cubic angstroms.

Explanation:

To convert the given volume of the hydrogen atom [tex](\(6.2 \times 10^{-31}\)[/tex] m³) into different units, we need to use conversion factors:

(a) To convert cubic meters to cubic picometers, we multiply by [tex]\(10^{30}\) (since \(1 \text{ m}^3 = 10^{30} \text{ pm}^3\)).[/tex]

(b) To convert cubic meters to cubic nanometers, we multiply by [tex]\(10^{27}\) (since \(1 \text{ m}^3 = 10^{27} \text{ nm}^3\)).[/tex]

(c) To convert cubic meters to cubic angstroms, we multiply by [tex]\(10^{24}\) (since \(1 \text{ m}^3 = 10^{24} \text{ Å}^3\)).[/tex]

After applying these conversion factors, we get:

(a) [tex]\(6.2 \times 10^{-5}\)[/tex]cubic picometers,

(b) [tex]\(6.2 \times 10^{-25}\)[/tex] cubic nanometers, and

(c) [tex]\(6.2 \times 10^{-31}\)[/tex] cubic angstroms.