Assume diameter of a neutral helium atom is 1.40x10^2pm. Suppose that we could line up helium atoms side by side in contact with one another. How many atoms would it take to complete the distance of 6.70cm from end to end?
140 pm/atom x #atoms = 6.70E10 pm
6.70 X 10^8
To find out how many helium atoms it would take to complete a distance of 6.70 cm, we need to calculate the number of atoms that fit within this distance when they are lined up side by side in contact with one another.
Given:
Diameter of a helium atom = 1.40x10^2 pm (picometers)
Distance to be covered = 6.70 cm
First, convert the distance to picometers:
1 cm = 10^10 pm
Therefore, 6.70 cm = 6.70 x 10^10 pm
To determine how many atoms can fit within this distance, we need to calculate the number of atoms that fit in one picometer and then multiply it by the total number of picometers in 6.70 cm.
To ensure accuracy, we need to convert the diameter of the helium atom to an appropriate unit. Let's convert the diameter from picometers (pm) to centimeters (cm):
1 pm = 10^-12 cm
Therefore, the diameter of a helium atom is 1.40x10^2 pm * (10^-12 cm/pm) = 1.40x10^-10 cm
Next, we'll calculate the radius of a helium atom:
Radius = (Diameter) / 2 = 1.40x10^-10 cm / 2 = 7.00x10^-11 cm
Now, calculate the number of helium atoms that can fit within one picometer along a straight line:
Number of atoms in one picometer = 1 picometer / (2 * radius of a helium atom)
= 1 pm / (2 * 7.00x10^-11 cm) = 7.14x10^9 atoms/cm
Finally, multiply the number of atoms in one picometer by the total number of picometers in 6.70 cm to find the total number of atoms needed:
Number of atoms = (Number of atoms in one picometer) * (Total picometers in 6.70 cm)
= (7.14x10^9 atoms/cm) * (6.70x10^10 pm) = 477.78x10^19 atoms
Therefore, it would take approximately 4.78x10^21 atoms (or 478 sextillion atoms) to complete the distance of 6.70 cm from end to end when the helium atoms are lined up side by side in contact with one another.
To find out how many helium atoms would be needed to complete a distance of 6.70 cm from end to end, we first need to calculate the length of a single helium atom.
Given that the diameter of a neutral helium atom is 1.40 × 10^2 pm (picometers), we can divide this value by 2 to get the radius of the atom.
Radius = 1.40 × 10^2 pm / 2 = 7.00 × 10^1 pm
Now, we need to convert the radius from picometers to centimeters since the given distance is in centimeters.
1 pm = 1 × 10^(-12) cm
Radius = 7.00 × 10^1 pm × 1 × 10^(-12) cm/pm = 7.00 × 10^(-11) cm
Next, we divide the total distance of 6.70 cm by the length of a single helium atom (represented by its diameter, which is twice the radius) to determine the number of atoms needed.
Number of atoms = Total distance / Length of a single atom
Number of atoms = 6.70 cm / (2 × radius)
Number of atoms = 6.70 cm / (2 × 7.00 × 10^(-11) cm)
Evaluating this calculation:
Number of atoms = 6.70 cm / 1.40 × 10^(-10) cm
Number of atoms = 4.79 × 10^10
Therefore, it would take approximately 4.79 × 10^10 helium atoms lined up side by side to complete a distance of 6.70 cm from end to end.