assume the diameer of a neutral helium atom is 1.40 x 10 to the second power pm. suppose that we could line up helium atoms side by side in contact with one another. how many atoms would it take to make the distance from end to end 9.00cm
1.4E2 pm = 140 pm
140 pm x (1 m/1E12 pm) x (100 cm/m) = ?? cm diameter.
?? cm x # atoms = 9 cm.
Solve for # atoms.
To calculate the number of atoms required to make a distance of 9.00 cm, we need to convert the given diameter of a helium atom into a length unit that matches the distance unit given (cm). Here's the step-by-step process to compute the number of atoms:
1. Convert the diameter of a helium atom from picometers (pm) to centimeters (cm):
- 1 pm = 1 x 10^-12 cm (1 picometer is equal to 10^(-12) centimeters)
- Given diameter = 1.40 x 10^2 pm
- Diameter in cm = (1.40 x 10^2 pm) x (1 x 10^-12 cm/pm) = 1.40 x 10^-10 cm
2. Calculate the number of atoms required to make the distance of 9.00 cm:
- Distance = 9.00 cm
- Number of atoms = Distance / Diameter
- Number of atoms = 9.00 cm / (1.40 x 10^-10 cm)
Now, let's calculate the value:
Number of atoms = 9.00 cm / (1.40 x 10^-10 cm)
= 6.42857143 x 10^10 atoms
Therefore, it would take approximately 6.43 x 10^10 helium atoms lined up side by side to make the distance from end to end 9.00 cm.