Question

The smallest unit of charge is − 1.6 × 10 − 19 C, which is the charge in coulombs of a single electron. Robert Millikan was able to measure the charge on small droplets of oil by suspending them between a pair of electrically charged plates. Which of the values are possible charges of those oil droplets? − 8.0 × 10 − 19 C − 3.2 × 10 − 19 C − 1.2 × 10 − 19 C − 5.6 × 10 − 19 C − 4.8 × 10 − 19 C − 9.4 × 10 − 19 C

Answer 1

`-8.0 * 10 ^(-19 )\ C,\ -3.2 * 10 ^(-19 )\ C, -4.8 * 10 ^(-19 )\ C`

Step-by-step explanation:

Charge of an Electron

Since Robert Millikan determined the charge of a single electron is

`q_e=-1.6\cdot 10^(-19)\ C`

Every possible charged particle must have a charge that is an exact multiple of that elemental charge. For example, if a particle has 5 electrons in excess, thus its charge is
`5* -1.6\cdot 10^(-19)\ C=-8 \cdot 10^(-19)\ C`

Let's test the possible charges listed in the question:

`-8.0 * 10 ^(-19 )`. We have just found it's a possible charge of a particle

`-3.2 * 10 ^(-19 )`. Since 3.2 is an exact multiple of 1.6, this is also a possible charge of the oil droplets

`-1.2 * 10 ^(-19 )` this is not a possible charge for an oil droplet since it's smaller than the charge of the electron, the smallest unit of charge

`-5.6 * 10 ^(-19 ),\ -9.4 * 10 ^(-19 )` cannot be a possible charge for an oil droplet because they are not exact multiples of 1.6

Finally, the charge
`-4.8 * 10 ^(-19 )\ C` is four times the charge of the electron, so it is a possible value for the charge of an oil droplet

Summarizing, the following are the possible values for the charge of an oil droplet:

`-8.0 * 10 ^(-19 )\ C,\ -3.2 * 10 ^(-19 )\ C, -4.8 * 10 ^(-19 )\ C`