Final answer:
The Stokes diameter of the zinc oxide powder can be calculated using Stokes' law. By rearranging the equation and substituting the given values, we can find the particle's radius. In this case, the Stokes diameter is 5.14 × 10⁻⁷ m.
Step-by-step explanation:
Stokes' law describes the sedimentation of particles in liquids and can be used to measure viscosity. It states that the drag force acting on a particle is directly proportional to the particle's velocity and the viscosity of the medium, and inversely proportional to the particle's radius. The equation can be written as:
Fd = 6πηrv
Where Fd is the drag force, η is the viscosity, r is the radius of the particle, and v is the settling velocity. Rearranging the equation, we can solve for the particle's radius:
r = (Fd / (6πηv))
Given the values in the question, we have:
ρ₀ = 5.60 g/cm³ = 5600 kg/m³ (density of zinc oxide)
ρ = 1.01 g/cm³ = 1010 kg/m³ (density of the medium)
v = 7.30 × 10⁻³ cm/sec = 7.30 × 10⁻⁵ m/sec (settling velocity)
η = 0.01 g/cm sec = 0.01 kg/m sec (viscosity of the medium)
Substituting these values into the equation, we can calculate the Stokes diameter:
r = (Fd / (6πηv)) = (ρ₀ - ρ) * g / (18ηv)
r = ((5600 - 1010) * (981 / (18 * 0.01 * 7.30 × 10⁻⁵)))
r = 5.14 × 10⁻⁷ m