The radius of a niobium atom is 131 pm. How many niobium atoms would have to be laid side by side to span a distance of 1.4 mm??
I know that 10^9 is pm or is it -9??
1 picometer (pm) is 10^-12 m and 1 millimeter (mm) = 10^-3 m. Thus, (1.4x10^-3)/(131x10^-12) = 1.07 x 10^7 atoms
To convert from picometers (pm) to meters (m), you need to divide by 10^12. Therefore, 131 pm would be written as 131 x 10^(-12) m.
To find out how many niobium atoms would have to be laid side by side to span a distance of 1.4 mm, you need to divide the distance by the diameter of a niobium atom.
The diameter of an atom is twice the radius. So, the diameter of a niobium atom would be 2 x 131 x 10^(-12) m = 262 x 10^(-12) m.
Now, we can divide the total distance of 1.4 mm by the diameter of a niobium atom. Let's convert 1.4 mm to meters by dividing it by 1000:
1.4 mm = 1.4 x 10^(-3) m
So, the number of niobium atoms required to span a distance of 1.4 mm would be:
(1.4 x 10^(-3) m) / (262 x 10^(-12) m)
Now we can simplify the expression by canceling units:
= (1.4 / 262) x 10^(-3 - (-12)) m
= 5.34 x 10^8
Therefore, approximately 5.34 x 10^8 niobium atoms would have to be laid side by side to span a distance of 1.4 mm.
The notation 10^9 is used to represent "10 raised to the power of 9," which means multiplying 10 by itself 9 times. In the context of distance measurements, pm stands for picometer, which is equal to 10^-12 meters.
To solve the problem, we need to convert the given distance of 1.4 mm to picometers to ensure consistency with the radius unit, which is given in picometers.
1 mm is equal to 10^-3 meters, so 1.4 mm is equal to 1.4 × 10^-3 meters.
To convert meters to picometers, we multiply by a conversion factor: 1 meter = 10^12 picometers.
Therefore, the distance of 1.4 mm can be converted to picometers as follows:
1.4 × 10^-3 meters × 10^12 picometers/1 meter = 1.4 × 10^9 picometers.
Now we can determine how many niobium atoms are needed to span the given distance.
To find out how many atoms would fit in the given distance, we divide the distance by the diameter of each atom. The diameter is twice the radius.
The given radius of a niobium atom is 131 picometers, which means the diameter is 2 × 131 picometers = 262 picometers.
Finally, to determine the number of niobium atoms needed to span the distance, we divide the distance by the diameter of each atom:
Number of atoms = (1.4 × 10^9 picometers) / (262 picometers).
Evaluating this expression, we find the number of niobium atoms that would need to be laid side by side to span a distance of 1.4 mm.
pm is a very small unit, smaller than a head lice. 1 m=10^9 pm, which is the same as 1pm is 10^-9 m
numberatoms*diatmeter atom=1.4mm
numberatoms*131pm=1.4mm
change both to m
numberatoms*131pm*1m/10^9pm)=1.4mm(1m/10^3mm)
number atoms= 1.4*10^9/(131*10^3)
number atoms=1.4 (10^6)/131=1.07*10^4
check that.