A nanometer(nm ) is one billionth of a meter (1 nm=10-9m). If 100 million atoms make a row 1 cm in length what is the diameter of one in nanometers?
length= .01m/100E6= 1E-2*1E-8=1E-10m=.1E-9
so 1/10 of a nanometer.
To find the diameter of one atom in nanometers, we need to convert the length from centimeters to nanometers first.
Given:
1 nanometer (nm) = 10^-9 meters (m)
1 centimeter (cm) = 0.01 meters (m)
First, let's convert the length of the row from centimeters to meters:
Length in meters = 1 cm * 0.01 m/cm = 0.01 meters
Since we know that 100 million atoms make a row 1 cm in length, we can find the length of one atom by dividing the length of the row by the number of atoms:
Length of one atom = Length of row / Number of atoms
Length of one atom = 0.01 meters / 100,000,000 atoms
Now, let's convert the length of one atom from meters to nanometers:
Length of one atom in nanometers = Length of one atom * (1 nm/10^-9 m)
Length of one atom in nanometers = 0.01 meters / 100,000,000 atoms * (1 nm/10^-9 m)
Simplifying the expression:
Length of one atom in nanometers = (0.01 / 100,000,000) * (10^9 / 1) nm
Finally, we can calculate the diameter of one atom by doubling the length of one atom.
Diameter of one atom in nanometers = 2 * Length of one atom in nanometers
By plugging in the values, we get:
Diameter of one atom in nanometers = 2 * (0.01 / 100,000,000) * (10^9 / 1) nm
Simplifying further:
Diameter of one atom in nanometers = 20 nm
Therefore, the diameter of one atom is 20 nanometers.
To find the diameter of a single atom in nanometers, we can calculate the length of a single atom in centimeters and then convert it to nanometers using the given conversion factor.
First, let's determine the length of a single atom. We know that 100 million atoms make a row 1 cm in length. Therefore, to find the length of a single atom in centimeters, we need to divide the length of the row (1 cm) by the number of atoms in the row (100 million).
Length of a single atom in centimeters = (1 cm) / (100 million)
Length of a single atom in centimeters = 1 × 10^-8 cm
Now, we can convert the length of a single atom from centimeters to nanometers using the conversion factor given (1 nm = 10^-9 m).
Length of a single atom in nanometers = (1 × 10^-8 cm) × (10^-7 m / 1 cm) × (10^9 nm / 1 m)
Length of a single atom in nanometers = 1 × 10^-8 × 10^-7 × 10^9 nm
Length of a single atom in nanometers = 10^-8 × 10^-7 × 10^9 nm
Length of a single atom in nanometers = 10^-8 × 10^2 nm
Length of a single atom in nanometers = 10^-6 nm
Therefore, the diameter of a single atom is 10^-6 nm.