High School

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?

**Part A: Cubic micrometers**
Express your answer in cubic micrometers to two significant figures.

**ANSWER:** [tex]6.2 \times 10^{-13} \, \mu m^3[/tex]

**Part B: Cubic nanometers**
Express your answer in cubic nanometers to two significant figures.

**ANSWER:** [tex]6.2 \times 10^{-4} \, \text{nm}^3[/tex]

**Part C: Cubic angstroms**
(1 angstrom = [tex]10^{-10} \, \text{m}[/tex])
Express your answer in cubic angstroms to two significant figures.

**ANSWER:** [tex]6.2 \times 10^{1} \, \text{Å}^3[/tex]

Answer :

Final answer:

The volume of the hydrogen atom can be expressed in different units such as cubic micrometers, cubic nanometers, and cubic angstroms. To convert the volume in meters to these units, we need to use appropriate conversion factors.

Explanation:

The volume of the hydrogen atom is given as 6.2 x 10-51 m3. We are asked to express this volume in different units:

Part A: Cubic micrometers (μm3)

To convert cubic meters to cubic micrometers, we need to multiply by the conversion factor of 1018 since there are 1,000,000,000,000,000,000 cubic micrometers in 1 cubic meter. Therefore, the volume in cubic micrometers is 6.2 x 10-51 m3 * (1018 μm3/m3) = 6.2 x 10-51 + 18 μm3 = 6.2 x 10-33 μm3.

Part B: Cubic nanometers (nm3)

Similarly, to convert cubic meters to cubic nanometers, we need to multiply by the conversion factor of 1027 since there are 1,000,000,000,000,000,000,000,000 cubic nanometers in 1 cubic meter. Therefore, the volume in cubic nanometers is 6.2 x 10-51 m3 * (1027 nm3/m3) = 6.2 x 10-51 + 27 nm3 = 6.2 x 10-24 nm3.

Part C: Cubic angstroms (Å3)

To convert cubic meters to cubic angstroms, we need to multiply by the conversion factor of 1030 since there are 1,000,000,000,000,000,000,000,000,000 cubic angstroms in 1 cubic meter. Therefore, the volume in cubic angstroms is 6.2 x 10-51 m3 * (1030 Å3/m3) = 6.2 x 10-51 + 30 Å3 = 6.2 x 10-21 Å3.

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Final answer:

The volume of a hydrogen atom is approximately 6.2 x 10^-33 cubic micrometers, 6.2 x 10^-24 cubic nanometers, and 6.2 x 10^-21 cubic angstroms.

Explanation:

To convert the volume of a hydrogen atom from cubic meters to cubic micrometers, we can use the conversion factor:

1 cubic meter = 1 x 10^18 cubic micrometers

So, to find the volume in cubic micrometers, we multiply the given volume in cubic meters by the conversion factor:

Volume in cubic micrometers = (6.2 x 10^-51 m) x (1 x 10^18 µm³/m³)

Simplifying the expression, we get:

Volume in cubic micrometers = 6.2 x 10^-33 µm³

To convert the volume of a hydrogen atom from cubic meters to cubic nanometers, we can use the conversion factor:

1 cubic meter = 1 x 10^27 cubic nanometers

So, to find the volume in cubic nanometers, we multiply the given volume in cubic meters by the conversion factor:

Volume in cubic nanometers = (6.2 x 10^-51 m) x (1 x 10^27 nm³/m³)

Simplifying the expression, we get:

Volume in cubic nanometers = 6.2 x 10^-24 nm³

To convert the volume of a hydrogen atom from cubic meters to cubic angstroms, we can use the conversion factor:

1 cubic meter = 1 x 10^30 cubic angstroms

So, to find the volume in cubic angstroms, we multiply the given volume in cubic meters by the conversion factor:

Volume in cubic angstroms = (6.2 x 10^-51 m) x (1 x 10^30 ų/m³)

Simplifying the expression, we get:

Volume in cubic angstroms = 6.2 x 10^-21 ų

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