# Ratio of Electron's Charge to Mass

• Soaring Crane
In summary, the conversation discusses the results of an experiment measuring the e/m ratio for an electron. The experimental average e/m value is 2.055*10^11 C/kg with a standard deviation of 2.003*10^10 C/kg. The theoretical e/m ratio value is 1.759*10^11 C/kg. There is a difference between the experimental and theoretical values, with the difference being 2.960*10^10 C/kg. The discussion also considers the significance of the standard deviation and the error in the theoretical value. The conclusion is that the experimental results are close enough to the theoretical value, but more measurements could potentially improve the accuracy.

## Homework Statement

I think my inquiry is mostly geared at statistics, but physics is involved, too.

In measuring the e/m ratio for an electron, the experimental average e/m value of the data points is 2.055*10^11 C/kg.

The standard deviation for the data points is 2.003*10^10 C/kg using sqrt[(1/n)*sigma(x – mean)^2].

The theoretical e/m ratio value is 1.759*10^11 C/kg.

In taking the difference between the experimental value and the theoretical value, it is

|2.055*10^11 C/kg - 1.759*10^11 C/kg| = 2.960*10^10 C/kg.

Are the standard deviation and the difference between the theoretical/experimental values supposed to be the same?

If they do not match each other (2.003*10^10 C/kg and 2.960*10^10 C/kg), is it because the standard deviation focuses on the difference in relation to the mean while 2.960*10^10 C/kg actually reflects a comparison with the true e/m value? I'm confused at what these two values reveal about the error in the experiment.

See above.

## The Attempt at a Solution

See above.

Thanks.

Your experimental results can be formulated in the form

(2.1 +- 0.2)*10^11 C/kg

this means that there are a 68% (the std dev assumes a gaussian distribution around the average) probability that your experimental em ratio will fall within the indicated interval.

The theoretical value falls just outside of this interval. More measurements might enlarge the std dev and bring it within the interval. But really, it is close enough.

@Soaring Crane:

As andrevdh already wrote you can write:
(2.1 +- 0.2)*10^11 C/kg
Why doesn't it make sense to write
(2.055 +- 0.2003)*10^11 C/kg

Ideally your mean value lies within the standard deviation. What could be the reason that your mean value lies outside the standard deviation?

You measured a mean value of 2.1*10^11 C/kg with a standard deviation of 0.2*10^11 C/kg.
Is this a good result if you compare the standard deviation to your mean value?

The theoretical value is given as 1.759*10^11 C/kg. What is the error of this value and compare this error to yours.