Ahydrogen atom has a diameter of about 10 nano meters. a) express this diameter in meters. b) express this diameter in millimeters . c) express this diameter in micrometers. please answer my question thanks.
The Correct Answer and Explanation is:
Given:
Diameter of a hydrogen atom = 10 nanometers (nm)
Part A: Express in meters
1 nanometer (nm) = 1×10−91 \times 10^{-9}1×10−9 meters (m)
So,
10 nm=10×10−9 m=1×10−8 m10 \, \text{nm} = 10 \times 10^{-9} \, \text{m} = 1 \times 10^{-8} \, \text{m}10nm=10×10−9m=1×10−8m
Answer: 1×10−8 m1 \times 10^{-8} \, \text{m}1×10−8m
Part B: Express in millimeters
1 millimeter (mm) = 1×10−31 \times 10^{-3}1×10−3 meters
We already have 1×10−8 m1 \times 10^{-8} \, \text{m}1×10−8m
To convert to millimeters:
1×10−8 m÷1×10−3=1×10−5 mm1 \times 10^{-8} \, \text{m} \div 1 \times 10^{-3} = 1 \times 10^{-5} \, \text{mm}1×10−8m÷1×10−3=1×10−5mm
Answer: 1×10−5 mm1 \times 10^{-5} \, \text{mm}1×10−5mm
Part C: Express in micrometers
1 micrometer (µm) = 1×10−61 \times 10^{-6}1×10−6 meters
We have 1×10−8 m1 \times 10^{-8} \, \text{m}1×10−8m
To convert to micrometers:
1×10−8 m÷1×10−6=1×10−2 µm1 \times 10^{-8} \, \text{m} \div 1 \times 10^{-6} = 1 \times 10^{-2} \, \text{µm}1×10−8m÷1×10−6=1×10−2µm
Answer: 1×10−2 µm1 \times 10^{-2} \, \text{µm}1×10−2µm
Explanation
Unit conversions are essential in science for expressing measurements in different scales. In this question, we are asked to convert the diameter of a hydrogen atom, given in nanometers, to meters, millimeters, and micrometers.
A nanometer is one billionth of a meter, meaning 1 nm=1×10−9 m1 \, \text{nm} = 1 \times 10^{-9} \, \text{m}1nm=1×10−9m. To convert 10 nanometers to meters, we multiply by this factor. The result is 1×10−8 m1 \times 10^{-8} \, \text{m}1×10−8m.
For millimeters, the conversion factor is 1 mm=1×10−3 m1 \, \text{mm} = 1 \times 10^{-3} \, \text{m}1mm=1×10−3m. To convert meters to millimeters, we divide the length in meters by 10−310^{-3}10−3. This gives 1×10−5 mm1 \times 10^{-5} \, \text{mm}1×10−5mm.
Micrometers are also a common unit for small distances, often used in biology or material science. 1 µm=1×10−6 m1 \, \text{µm} = 1 \times 10^{-6} \, \text{m}1µm=1×10−6m. We divide the meters value by 10−610^{-6}10−6, resulting in 1×10−2 µm1 \times 10^{-2} \, \text{µm}1×10−2µm.
These conversions show how small the hydrogen atom is. Even at the scale of micrometers, it only measures hundredths of a micrometer. Such knowledge helps scientists understand atomic and molecular structures, design nanotechnology, or analyze microscopic systems. Accurate conversions between units ensure precise communication of scientific data.
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