Question

Calculate the number of atoms contained in a cylinder 1 um in diameter by 1 um deep of magnesium. Round off your answer to eleven significant figures.

Answer 1

number of atom = 33816747099 atoms

Step-by-step explanation:

given data

diameter = 1 μm

height = 1 μm

to find out

number of atoms

solution

we know here id diameter is 1μm then radius r = 0.5 μm

so volume will be

volume = π×r²×h

volume = π×0.5²×1 ×
`10^({-6})^3` m³

volume = 7.853981634 ×
`10^(-19)` m³

and

we know density of magnesium is = 1.738 g/cm³ = 1738 × 10³ g/m³

so mass will be = volume × density

mass = 7.853981634 ×
`10^(-19)` × 1738 × 10³

mass = 1.365022008 ×
`10^(-12)` g

so

number of moles =
`(mass)/(molar mass)`

number of moles =
`(1.365022008*10^(-12))/(24.312)`

number of moles = 5.614601876 ×
`10^(-14)` moles

we know 1 mole = 6.023 ×
`10^(23)` atoms

so

number of atom will be = 5.614601876 ×
`10^(-14)` × 6.023 ×
`10^(23)`

number of atom = 33816747099 atoms