Many chemistry conferences have held a 50 -Trillion Angstrom Run (two significant figures). How long is this run in kilometers and in miles? (
The Correct Answer and Explanation is:
Correct Answer:
50 trillion angstroms is equal to:
- 5.0 kilometers
- 3.1 miles
Step-by-Step Conversion:
1. Understand the units:
- 1 angstrom (Å) = 1×10−101 \times 10^{-10}1×10−10 meters
- 1 kilometer = 1×1031 \times 10^31×103 meters
- 1 mile = approximately 1.609 kilometers
2. Convert angstroms to meters:
We are given 50 trillion angstroms, which is:50×1012 A˚=5.0×1013 A˚50 \times 10^{12} \, \text{Å} = 5.0 \times 10^{13} \, \text{Å}50×1012A˚=5.0×1013A˚
Now convert angstroms to meters:5.0×1013×10−10=5.0×103 meters5.0 \times 10^{13} \times 10^{-10} = 5.0 \times 10^3 \, \text{meters}5.0×1013×10−10=5.0×103meters
So, the run is 5000 meters.
3. Convert meters to kilometers:
5000 m=5.0 km5000 \, \text{m} = 5.0 \, \text{km}5000m=5.0km
4. Convert kilometers to miles:
5.0 km÷1.609≈3.1 miles5.0 \, \text{km} \div 1.609 \approx 3.1 \, \text{miles}5.0km÷1.609≈3.1miles
Explanation
The 50-Trillion Angstrom Run is a fun and scientifically themed way to describe a relatively short race distance, but in very tiny units. An angstrom is a unit used primarily in atomic and molecular sciences to express extremely small distances, such as the size of atoms or the length of chemical bonds. One angstrom equals one ten-billionth of a meter, or 1×10−101 \times 10^{-10}1×10−10 meters.
To understand how long this run really is, we must convert angstroms to more familiar units like kilometers or miles. First, multiplying 50 trillion (50 × 101210^{12}1012) angstroms by the length of one angstrom (1 × 10−1010^{-10}10−10 meters) gives 5000 meters. This is the same as 5.0 kilometers because 1000 meters equal 1 kilometer.
For those who use miles as a more familiar unit of distance, we convert kilometers to miles by dividing by the conversion factor of approximately 1.609. So, 5.0 kilometers is equal to about 3.1 miles.
Therefore, despite the huge-sounding number “50 trillion,” the actual run is just 5 kilometers or 3.1 miles—comparable to a typical 5K run held in many local community races or charity events. It’s a humorous way to combine science with athletics, showing how scientific units can be applied in creative, engaging contexts that still make real-world sense when properly converted.
