Calculating Experimental Error

[Lemenks]

Homework Statement

I am writing a lab report for an X-ray diffraction. I have been attempting to come up with an equation for the error using formulas some people from college gave me and also some I found on wikipedia but I am quite sure I am doing it wrong. The only variable is the angle where the maximum intensities are found. I am using Bragg's law to calculate the spacing between the atoms.

Homework Equations

D = (N*wavelength)/(2*sin(x))

As there is no error in N, wavelength, or "2", we can let that equal A.

D = A/sin(x)

Some equations I was given:

Z = aX
dZ = adX

Z = X^a
dZ/z = |a|dx/x

Z = SinX
dZ = dX CosX

The Attempt at a Solution

D = Z = A/sin(x) = A (sin(x))^-1 = A f(y)^-1

I have tried loads of ways of calculating this but I keep getting silly answers. Any help, ideas or links would be really appreciated.

 

[vela]

Take it one step at a time. You might find it helpful to introduce new variables. For example, let w=1/sin(x). Then you have $D = Aw$, so applying your first rule, you have $\delta D = A \delta w$. (I'm using deltas instead of d because dD looks weird.) Now your job is to find $\delta w$. If you let $v=\sin x$, then $w=1/v = v^{-1}$. Using the second rule, you can find $\delta w$ in terms of $\delta v$. Then you need to find $\delta v$ in terms of $\delta x$, and then put it all together.

 

[Lemenks]

Hey thanks for the reply, it is very concise and logical, I actually tried that but assumed I must have made a mistake as the value I was getting for the error seemed to large ~80%.

The final equation I have is:

dD = A (dx cosx)/(sinx)^2

This equation seems to give a value for error of about 80%. x ranges from 3 to 35 and dx was 0.1. ie the beam angle ranged from 3 to 35 degree in 0.1 degree steps.

 

[vela]

You need to use radians, not degrees. That's probably where the issue lies.

 

[HalfLostAndSearching]

Dear writer,

Thank you for sharing your question about calculating experimental error in your lab report for X-ray diffraction. It is important to accurately calculate experimental error in order to determine the reliability and precision of your results.

Firstly, it is important to understand the concept of experimental error. Experimental error refers to the difference between the measured value and the true value. It can arise from a variety of sources such as equipment limitations, human error, or external factors. In order to calculate experimental error, you will need to have multiple measurements of the same quantity and compare them to the true value.

In your case, you are using Bragg's law to calculate the spacing between atoms. The equation you have provided, D = (N*wavelength)/(2*sin(x)), is correct. However, in order to calculate experimental error, you will need to have multiple measurements of the angle x and compare them to the expected value. The expected value can be obtained from a reference source or from previous experiments.

Once you have multiple measurements of x, you can calculate the average value and the standard deviation. The average value will give you an estimate of the true value, while the standard deviation will give you an indication of the precision of your measurements. The standard deviation can be used to calculate the experimental error using the following formula:

Experimental error = (measured value - expected value)/expected value * 100%

It is important to note that the standard deviation should be calculated using the formula for a sample, not the population. Also, the percentage error should be reported with the correct number of significant figures.

In terms of the equations you were given, they may be useful for calculating experimental error in different situations but may not be applicable in this specific case. I would recommend discussing with your instructor or a colleague to ensure you are using the correct equations and methods for your experiment.

I hope this helps and I wish you all the best with your lab report. Keep up the good work as a scientist!