How Do You Calculate Uncertainty δd in Bragg Scattering?

[UncertaintyMan]

My goal is to find the uncertainty δd in the following equation.

d=C_1 \frac{1}{\sqrt{V}} \frac{1}{D}

• C_1 is the collection of constants \frac{2Lhc}{\sqrt{2m_e c^2 }}
• D is a value measured in meters with an uncertainty δD = 0.001 m
• and V is a value measured in volts with an uncertainty δV = 100 V

My best guess on how to calculate δd is

\frac{δd}{d}=|C_1| \sqrt{(\frac{δV}{V})^2+(\frac{δD}{D})^2 }
... then plug in all the known values and solve for δd

...Unfortunately I have no resources to tell me if I'm doing this right. I appreciate any helpful pointers any of you may have, I'm a big time noob when it comes to error analysis.

For those of you who are curious, this is from a Bragg Scattering lab and d represents the distance between atoms in a polycrystalline graphite crystal.

 

[SammyS]

My goal is to find the uncertainty δd in the following equation.

d=C_1 \frac{1}{\sqrt{V}} \frac{1}{D}

• C_1 is the collection of constants \frac{2Lhc}{\sqrt{2m_e c^2 }}
• D is a value measured in meters with an uncertainty δD = 0.001 m
• and V is a value measured in volts with an uncertainty δV = 100 V

My best guess on how to calculate δd is

\frac{δd}{d}=|C_1| \sqrt{(\frac{δV}{V})^2+(\frac{δD}{D})^2 }
... then plug in all the known values and solve for δd

...Unfortunately I have no resources to tell me if I'm doing this right. I appreciate any helpful pointers any of you may have, I'm a big time noob when it comes to error analysis.

For those of you who are curious, this is from a Bragg Scattering lab and d represents the distance between atoms in a polycrystalline graphite crystal.

d is inversely prop. to √(V) , not V itself.

You should have something like:

\displaystyle \frac{δd}{d}=|C_1| \sqrt{\left(\frac{δ(\sqrt{V})}{\sqrt{V}}\right)^2+\left(\frac{δD}{D} \right)^2 }​

 

[UncertaintyMan]

Awesome, thank you!

Quick side question: is it true that both of these equations have the same δd formula?

Equation 1. d = \sqrt{V}D
Equation 2. d = \frac{1}{\sqrt{V}D}

Error for either equation:
\frac{δd}{d} = \sqrt{(\frac{δ(\sqrt{V})}{\sqrt{V}})^2 + (\frac{δD}{D})^2}

 

[SammyS]

Awesome, thank you!

Quick side question: is it true that both of these equations have the same δd formula?

Equation 1. d = \sqrt{V}D
Equation 2. d = \frac{1}{\sqrt{V}D}

Error for either equation:
\frac{δd}{d} = \sqrt{(\frac{δ(\sqrt{V})}{\sqrt{V}})^2 + (\frac{δD}{D})^2}

Yes, for reasonably small relative error.