The atomic radius of a helium atom is 0.49 Angstroms . What is the diameter in millimeters?
The correct answer and explanation is:
Correct Answer:
The atomic diameter of a helium atom in millimeters is 0.000098 mm.
Explanation:
To calculate the diameter of a helium atom in millimeters, begin by understanding what is given. The atomic radius of helium is 0.49 Ångströms.
An Ångström is a unit of length commonly used to express atomic and molecular dimensions. One Ångström equals 1 × 10⁻¹⁰ meters, or 0.0000000001 meters.
To find the diameter, multiply the radius by 2: Diameter=2×0.49A˚=0.98A˚\text{Diameter} = 2 × 0.49 Å = 0.98 Å
Now convert 0.98 Ångströms to millimeters.
First, convert Ångströms to meters: 0.98A˚=0.98×10−10 meters=9.8×10−11 meters0.98 Å = 0.98 × 10^{-10} \text{ meters} = 9.8 × 10^{-11} \text{ meters}
Next, convert meters to millimeters. Since 1 meter = 1000 millimeters: 9.8×10−11 meters×1000=9.8×10−8 millimeters9.8 × 10^{-11} \text{ meters} × 1000 = 9.8 × 10^{-8} \text{ millimeters}
So, the final answer is: Diameter=0.000000098 mm=9.8×10−8 mm\text{Diameter} = 0.000000098 \text{ mm} = 9.8 × 10^{-8} \text{ mm}
In standard decimal form, that is 0.000098 mm.
This value shows how incredibly small atoms are. Even the full diameter of a helium atom is far below the size visible under an optical microscope. Scientists use specialized instruments like scanning tunneling microscopes to observe atoms at this scale. Converting units like Ångströms to millimeters helps relate atomic measurements to more familiar units, which is important in fields like nanotechnology, physics, and chemistry. It also helps engineers and researchers apply atomic-scale properties in the design of materials and systems at the molecular level.