The radius of a aluminum atom is 143 pm. How many aluminum atoms would have to be laid side by side to span a distance of 4.90 mm?

To determine the number of aluminum atoms laid side by side to span a distance of 4.90 mm, we need to first calculate the diameter of an aluminum atom (since they will be laid side by side).

The radius of the aluminum atom is given as 143 pm (picometers). To find the diameter, we can multiply the radius by 2:
Diameter = 2 * Radius = 2 * 143 pm = 286 pm

Converting picometers to meters:
1 pm = 1 x 10^-12 m
Therefore, 286 pm = 286 x 10^-12 m

To find the number of atoms required to span a distance of 4.90 mm, we need to divide the distance by the diameter of a single atom:

Number of atoms = (Total distance) / (Diameter of one atom)
Number of atoms = (4.90 mm) / (286 x 10^-12 m)

Now, let's convert 4.90 mm to meters:
1 mm = 10^-3 m
Therefore, 4.90 mm = 4.90 x 10^-3 m

Substituting the values into the equation:
Number of atoms = (4.90 x 10^-3 m) / (286 x 10^-12 m)

Dividing the values:
Number of atoms ≈ 1.71 x 10^7 atoms

Therefore, it would take approximately 1.71 x 10^7 aluminum atoms laid side by side to span a distance of 4.90 mm.

To solve this problem, we need to first calculate the length of a single aluminum atom. We can then divide the total distance by the length of a single atom to find the number of atoms required.

Given:
Radius of an aluminum atom = 143 pm
Distance to be spanned = 4.90 mm

1. Convert the radius of the aluminum atom to meters:
143 pm = 143 × 10^(-12) m

2. Convert the distance to be spanned to meters:
4.90 mm = 4.90 × 10^(-3) m

3. Calculate the length of a single aluminum atom by multiplying the radius by 2:
Length of a single aluminum atom = 2 × 143 × 10^(-12) m

4. Divide the total distance by the length of a single aluminum atom to find the number of atoms required:
Number of aluminum atoms required = (4.90 × 10^(-3) m) / (2 × 143 × 10^(-12) m)

Now, let's calculate the solution using the given values:

Step 1: Convert the radius of the aluminum atom to meters:
143 pm = 143 × 10^(-12) m = 1.43 × 10^(-10) m

Step 2: Convert the distance to be spanned to meters:
4.90 mm = 4.90 × 10^(-3) m

Step 3: Calculate the length of a single aluminum atom by multiplying the radius by 2:
Length of a single aluminum atom = 2 × 1.43 × 10^(-10) m = 2.86 × 10^(-10) m

Step 4: Divide the total distance by the length of a single aluminum atom to find the number of atoms required:
Number of aluminum atoms required = (4.90 × 10^(-3) m) / (2.86 × 10^(-10) m)

Calculating this division, we find that approximately 1.71 × 10^7 aluminum atoms would have to be laid side by side to span a distance of 4.90 mm.

I would convert 4.90 mm to pm. I'll call that Y, then the diameter of an Al atom is 286 so

286 pm diameter x ? Al atoms = Y
Solve for ? Al atoms.