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

Answer:

number of atom = 33816747099 atoms

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 = $\frac{mass}{molar mass}$

number of moles = $\frac{1.365022008*10^{-12}}{24.312}$

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