Question

A cube that has a volume of 1.00 m³ contains N distinguishable particles.

1. Determine the probability that all the particles are in a smaller volume V of the cube if N = 1 and V = 0.500 m³.
2. Determine the probability that all the particles are in a smaller volume V of the cube if N = 1 and V = 0.300m³.
3. Determine the probability that all the particles are in a smaller volume V of the cube if N = 1 and V = 0.0100³.

Answer 1

1 P = 0.5

2 P = 0.3

3 P = 0.01

Step-by-step explanation:

The probability formula is

`P =V^N`

Where P is the probability V is the volume while N is the number of distinguishing particles

So for N = 1 and
`V = 0.500m^3`

`P = (0.500m^3)^1\\`

= 0.5

For N = 1 and
`V = 0.300m^3`

`P = (0.300m^3)^1`

= 0.3

For N = 1 and
`V = 0.0100m^3`

`P =(0.0100m^3)^1`

= 0.01