The radius of a gold atom is 144 pm. How many gold atoms would have to be laid side by side to span a distance of 4.97 mm

2.18 × 10⁷ Au atoms

Explanation:

Step 1: Calculate the diameter of a gold atom

The diameter is twice the radius.

d = 2 × r = 2 × 144 pm = 228 pm

Step 2: Convert "d" to meters

We will use the conversion factor 1 m = 10¹² pm.

228 pm × 1 m/10¹² pm = 2.28 × 10⁻¹⁰ m

Step 3: Convert the total distance to be covered (D) to meters

We will use the conversion factor 1 m = 10³ mm.

4.97 mm × 1 m/10³ mm = 4.97 mm × 10⁻³ m

Step 4: Calculate the number of atoms of gold required

We will divide the total distance by the diameter of 1 atom of gold.

D/d = 4.97 mm × 10⁻³ m/2.28 × 10⁻¹⁰ m = 2.18 × 10⁷

number of molecules / avogadro's number * molecule molecular = mass

explanation:

we define a gram-molecular weight as the mass of one mole of any element or compound. a mole contains avogadro's number of units (molecules) –  

6.022

x

10

23

. so, dividing the number of molecules by avogadro's number gives us the number of moles. multiplying that by the molecular weight gives us the mass. from the periodic table we find the gram-molecular weight of u to be238 and of f to be19. so,  

u

f

6

will have a gram-molecular weight of 352g.