How many atoms are in a human body? If you lined the atoms in a human up, how long would the line be? (The volume of human is 2.4ft3, the volume of an oxygen atom: 1.66 ×10-30 m3, the average diameter of the atoms in the human body is 1.52 x 10-3 nm/atom.)
The Correct Answer and Explanation is :
Number of Atoms in a Human Body
- Volume of a Human Body:
The volume of the human body is given as ( 2.4 \, \text{ft}^3 ). Converting this to cubic meters:
[
2.4 \, \text{ft}^3 \times 0.0283168 \, \text{m}^3/\text{ft}^3 = 0.0679 \, \text{m}^3
] - Volume of a Single Atom:
The volume of an oxygen atom is ( 1.66 \times 10^{-30} \, \text{m}^3 ). Assuming similar dimensions for the average atom in the human body, this value will be used. - Number of Atoms:
The total number of atoms in the body is approximately the total volume of the body divided by the volume of a single atom:
[
\frac{0.0679 \, \text{m}^3}{1.66 \times 10^{-30} \, \text{m}^3/\text{atom}} \approx 4.09 \times 10^{28} \, \text{atoms}.
]
Length of a Line of Atoms
- Average Diameter of an Atom:
The average diameter of atoms in the human body is ( 1.52 \times 10^{-3} \, \text{nm} = 1.52 \times 10^{-12} \, \text{m} ). - Length of the Line:
If all ( 4.09 \times 10^{28} ) atoms were lined up, the total length would be:
[
\text{Total Length} = 4.09 \times 10^{28} \, \text{atoms} \times 1.52 \times 10^{-12} \, \text{m/atom}.
]
[
\text{Total Length} \approx 6.21 \times 10^{16} \, \text{m}.
] - Converting to Light-Years:
One light-year is approximately ( 9.461 \times 10^{15} \, \text{m} ).
[
\frac{6.21 \times 10^{16} \, \text{m}}{9.461 \times 10^{15} \, \text{m/light-year}} \approx 6.56 \, \text{light-years}.
]
Explanation
Atoms are incredibly small, and the human body is composed of a vast number of them due to its volume and density. By dividing the human body’s volume by the typical atomic volume, we estimate around ( 4.09 \times 10^{28} ) atoms. If these atoms were lined up, their collective length would stretch over 6.56 light-years. This visualization underscores the astonishing scale difference between atomic dimensions and macroscopic structures. Such calculations reveal the density of matter and the staggering number of components in living organisms.