Answer:
a) 7.9×10⁻¹¹ g (rounded to 2 significant figures)
b) 1.3×10⁻¹⁷ g (rounded to 2 significant figures)
Explanation:
A) Mass of dust in the room
[tex]Volume=length\times width\times height=20m\times 15m\times 8m=2,400m^3[/tex]
[tex]Number\text{ }of\text{ }particles=density\text{ }of\text{ }particles\times Volume[/tex]
[tex]Number\text{ }of\text{ }particles=2.6\times 10^9particles/m^3\times 2,400m^3= 6.24\times 10^{12}particles[/tex]
[tex]Volume\text{ }of\text{ }a\text{ }spehere=4/3\pi r^3=4/3\pi (2\times10^{-6}/2m)^3=4.1889\times 10^{-18}m^3[/tex]
[tex]Volume=6.24\times 10^{12}particles\times 4.1889\times10{-18}m^3/particle=2.61\times 10^{-5}m^3[/tex]
Density = 1.00 g/cm³ × sp gr = 1.00 g/cm³ × 3 = 3.00 g/cm³
Density = 3.00 g/cm³ × (1m/100cm)³ = 3.00×10⁻⁶ g/m³
[tex]Mass=density\times volume=3.00\times 10^{-6}g/m^3\times 2.61\times10^{-5}m^3=7.84\times10^{-11}g[/tex]
B) Mass of dust in each average breath of 400cm³
[tex]Mass\text{ }in\text{ }a\text{ }room/2,400m^3=Mass\text{ }in\text{ }a\text{ }breath/4\times 10^{-4}m^3[/tex]
[tex]Mass\text{ }in\text{ }a\text{ }breath=4\times10^{-4}m^3\times 7.84\times 10^{-11}g/2,400m^3=1.31\times 10^{-11}g[/tex]
