Oil drop experiment electron charge

[omega500]

The problem is based on the experiment conducted by Millikan to find the elementary charge.
In the experiment, charged oil droplets are suspended between two charged plates with a known electric field between them. In this way, the charge of each droplet can be calculated (the mass is known). The distance between the plates is given.
A graph of the voltage needed to bring each charge to equilibrium (to cancel out the gravitational force) as a function of the droplet's mass is attached.
graph b: y=1.47x
graph c: y=1.96x
graph d: y=2.94x

Homework Equations

When each charge is in equilibrium, the upward electric force equals the gravitational force.

F=mg
Eq=mg
Vq/d=mg
V=m*gd/q

The Attempt at a Solution

In this way, I can find the charge on each series of droplets. It is evident from the graph that the charge is a quantum value. I am now asked to find the elementary charge from the data given. How do I do so? I have no idea how many excess electrons are on the droplets (The question states that the elementary charge is the charge of one electron).

 

[Simon Bridge]

... but you do know that the total charge must be some integer value of the elementary charge, and the elementary charge has to be the same for every oil drop.

It may help to think of it in terms of q_e/m_e instead of just q.

 

[omega500]

Yes, but I have no idea what multiple of the elementary charge each charge is. The difference between the charge on the droplets that fall on line b and the charge on the droplets on c is 1.7E-19 C, and so is the difference between charge c and charge d. I imagine that this is the elementary charge for the purposes of this question, but finding it this way is just guesswork and I have no way of knowing that the difference is the elementary charge.

 

[omega500]

Actually, I think in this scenario I can assume that the difference equals the elementary charge. Thank you for all the help.

 

[haruspex]

Actually, I think in this scenario I can assume that the difference equals the elementary charge. Thank you for all the help.

You could be unlucky: if it just happens that all charges on the sampled drops are multiples of the same number, like 2 or 3, then you will deduce an electron charge too large by that factor. In practice, the idea is to collect enough samples that this is most unlikely to happen.
If you take the difference between b and c as one electron, can you determine the differences for all sequences? In particular, check a.

 

[Simon Bridge]

Actually, I think in this scenario I can assume that the difference equals the elementary charge.

Yah - welcome to experimental work. Don't be scared to play around when looking for a pattern.
You don't need to produce the actual elementary charge, just what the data supports.

Nice to compare with an accepted value though.

 

[omega500]

You could be unlucky: if it just happens that all charges on the sampled drops are multiples of the same number, like 2 or 3, then you will deduce an electron charge too large by that factor. In practice, the idea is to collect enough samples that this is most unlikely to happen.
If you take the difference between b and c as one electron, can you determine the differences for all sequences? In particular, check a.

Yes, but given what data I have here, I think that the parameters of the problem permit me to assume that the measurements given all are of consecutive number multiples of e. For a high school physics problem, I imagine that is permissible. In practice, it really would be necessary to conduct a large number of measurements.

 

[haruspex]

Yes, but given what data I have here, I think that the parameters of the problem permit me to assume that the measurements given all are of consecutive number multiples of e. For a high school physics problem, I imagine that is permissible. In practice, it really would be necessary to conduct a large number of measurements.

Yes, you can assume the data you have been given are adequate, but not that all, or indeed any, consecutive pairs of slopes differ by one electron. In particular, I don't see anywhere you have made use of the (a) line. As far as I can judge, its slope is 1.2. Compare that with the (b) slope.

More generally, you might have been given data in which consecutive steps were, say, 3e, 2e, 5e, 4e. Although every step is more than 1e, there's enough information to take a stab at e.