1) In an experiment similar to Perrin's, 120 particles per unit volume are counted at the bottom of a container. 80 particles per unit volume are counted at a height of 5.00 cm above this. At what height above the bottom of the container will there be 40 particles per unit volume? Correct answer: 14 cm

2) In an experiment similar to Perrin's, 100 particles per unit volume were counted close to the bottom of the column, and 1.0 um above this, 50 particles were counted in a similar volume. How many particles per unit volume would be expected at a height of 5.0 um above the bottom? Correct answer: 33

3) In an experiment similar to Perrin's, the number density of particles at a height of 10.0 um compared to the number density at the bottom is 1.0 x 10^-4 to 1. What is the ratio of the number density at height 5.0 um to the number density at the bottom?

Correct answer: 0.01 to 1

4) In an experiment similar to Perrin's, 100 particles per unit volume were counted close to the bottom of a column, and 1.0 cm above this, 50 particles were counted in a similar volume. If the experiment could be repeated on the moon where g= 1.6 m/s^2, how many would you expect to find 1.0 cm up (assuming there were still 100 particles per unit volume near the bottom as there were on Earth)? Correct answer: 89

Please provide detailed explanations of how to obtain these answers.