# Calculating Experimental Error of Braggs Equation

• Lemenks
In summary, the conversation discusses the writer's difficulty in finding an equation for calculating the error in a lab report for an X-ray diffraction experiment. The writer has tried several equations, including D = A/sin(x), but is unsure if it is the correct approach. They are seeking help and clarification on the error calculation and any relevant equations or links.
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

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.

Hello Lemenks, and welcome to PF :)

I don't see an attempt at solution under 3, only a repeat of D=A/sin(x).

From your account, I think what you are asking is: What is the error in D = A/sin(x), given the error in x. Correct ?

Your relevant equations are some examples of error propagation in functions of a single variable. Generally: ##df = {df\over dx} dx##, which in error analysis is extended to finite differences: ##\Delta f = {df\over dx} \Delta x##.
Do you know how to find the derivative of 1/sin(x) ?

And I am interested in the way you determine ##\Delta x## too. Is it really just a simple reading off of a single angle ?

## 1. What is the Braggs Equation and why is it important?

The Braggs Equation is a mathematical formula that relates the wavelength of X-rays to the spacing between atomic planes in a crystal. It is important because it allows scientists to determine the structure of crystals and understand their properties.

## 2. How is experimental error calculated in Braggs Equation?

Experimental error in Braggs Equation is calculated by comparing the experimental value of the spacing between atomic planes to the theoretical value predicted by the equation. The difference between these values is divided by the theoretical value and multiplied by 100 to get a percentage error.

## 3. What factors can contribute to experimental error in Braggs Equation?

Several factors can contribute to experimental error in Braggs Equation, such as instrumental errors in measuring the X-ray wavelength or the angle of diffraction, impurities in the crystal, or human error in reading measurements.

## 4. How can experimental error in Braggs Equation be minimized?

To minimize experimental error in Braggs Equation, it is important to use precise and accurate instruments, properly calibrate equipment, and carefully handle and prepare the crystal sample. It is also beneficial to repeat measurements multiple times and take an average to reduce the impact of random errors.

## 5. What is an acceptable range for experimental error in Braggs Equation?

An acceptable range for experimental error in Braggs Equation can vary depending on the specific experiment and the level of precision required. In general, a percentage error of 5% or less is considered acceptable, but this may differ for different applications and experiments.

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