Introduction:
The Millikan oil drop experiment is a classic experiment that helped to determine the charge of an electron. One of the key components of this experiment is the characteristic times of the tiny oil droplets.

Calculation:
To calculate the characteristic times of the oil droplet, we can use the following formula:

t = m/(6πηrV)

Where, t is the characteristic time, m is the mass of the oil droplet, η is the viscosity of air, r is the radius of the oil droplet, and V is the terminal velocity.

We are given the terminal velocity of the oil droplet as 1.6*10^-5. We can use this value along with the other parameters to calculate the characteristic time.

Parameters:
m = mass of the oil droplet
η = viscosity of air
r = radius of the oil droplet
V = terminal velocity

Calculation Steps:
1. Determine the mass of the oil droplet: This can be done by measuring the density of the oil used in the experiment and the volume of the droplet. Let's assume that the mass of the oil droplet is 2.0*10^-15 kg.
2. Determine the viscosity of air: The viscosity of air at room temperature is approximately 1.8*10^-5 Pa s.
3. Determine the radius of the oil droplet: This can be done by measuring the diameter of the droplet using a microscope. Let's assume that the radius of the droplet is 5.0*10^-7 m.
4. Use the formula to calculate the characteristic time:

t = m/(6πηrV)
t = (2.0*10^-15)/(6π*(1.8*10^-5)*(5.0*10^-7)*(1.6*10^-5))
t ≈ 1.2*10^-10 s

Conclusion:
The characteristic time of the tiny oil droplet in the Millikan oil drop experiment is approximately 1.2*10^-10 s when its terminal speed is 1.6*10^-5. This characteristic time is important because it helps to determine the charge of the electron.

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