Analysis of Experimental Errors on Wavelength and Angle Measurements

[bayan]

This is my report on an experiment that I have done and I really needed the latex codes to generate the equations. I have done the other parts of the report on other PC.

Do they seem to be ok? (the errors, like the max possible value and min possible value)

no help is really needed, rather I want to know what you think of it, any where I can improve or anything I should drop (unnecesary things)

Thank you!

for $$\lambda$$
$$\lambda =\frac{18.5}{6.5}$$
$$\lambda = 2.85 cm$$


This indicates that the apprxmiate wavelength is $$2.85 cm$$ with a error margin of $$^+_-0.03$$

now to find the spacing between the ball bearings we can use the first angle and $$Bragg's$$ $$equation$$ to find the other angles.

$$n1$$

$$1\lambda =2dSin14^o$$

$$d=\frac {2.85}{2Sin14^o}$$

$$d= 5.89 cm$$


Now we can find values for other angles that correspond to this equation.

$$n2$$

$$\theta=Sin^{-1} \frac {5.7}{11.78}$$

$$\theta = 28.9^o$$

for $$n3$$

$$\theta= Sin^{-1} \frac {8.55}{11.78}$$

$$\theta = 46.5^o$$

for $$n4$$

$$\theta = Sin^-1 \frac {11.4}{11.78}$$

$$\theta = 75.4^o$$

there is no $$n5$$ as the equation makes no scence and there is no value for $$sin$$ grater than $$1$$





Now we come to the errors that were involved in this experiment!

The wavelength was within a error range of $$^+_-0.03 cm$$.

the angle was read to the nearest degree so it was really $$14^o ^+_-1^o$$ which then makes the d value lower and higher.

For example the maximum d is when angle was $$14^o-1^o=13^o$$

Now we get the new $$d=\frac {2.88}{2sin13^o}$$ which is $$6.4 cm$$

The minimum value obtainable from these sets of result are as followed.

$$d=\frac {2.82}{2sin14^o}$$ which is $$5.82 cm$$

For $$n2$$ the angle was $$28.9^o$$ which could have been altered such that maximum is $$\theta = sin^-^1 \frac {5.76}{11.64}$$ which is about $$29.7^o$$ and the minimum value could have been
$$\theta = Sin^-^1 \frac {5.64}{12.8}$$ in which the angle is about $$26.1^o$$

This just repeats until the last value of reflection angle.

I will show that the last angle would still exist even with the big error probability.

For Max $\theta$ the $\theta=2.88$ which results $\theta = sin^{-1} \frac {11.52}{11.64}$ which is $81.8^o$ and for Min the angle is $\theta = sin^{-1} \frac {11.28}{12.8}$ which happens to be about $61.8^o$

So infact the errors did not have a huge impact on the resultst that we were really interested (which is to find how many ball bearings there is!) but if we were to have a diffrent aim those errors would have made it really hard (for example if we wanted to see what exactly the crystall looks like)

 

[quantumdude]

Sorry for the late reply. This thread got lost in the hustle and bustle of our recent upgrade. In case you're still interested, here's what I think of your report.

for $$\lambda$$
$$\lambda =\frac{18.5}{6.5}$$
$$\lambda = 2.85 cm$$

That second line needs units.

This indicates that the apprxmiate wavelength is $$2.85 cm$$ with a error margin of $$^+_-0.03$$

The error margin needs units.

now to find the spacing between the ball bearings we can use the first angle and $$Bragg's$$ $$equation$$ to find the other angles.

If you want LaTeX to line up with regular HTML text, then you should use the itex tags (inline LaTeX).

$$n1$$
$$1\lambda =2dSin14^o$$
$$d=\frac {2.85}{2Sin14^o}$$
$$d= 5.89 cm$$

In the first line it looks like it should be $n_1$, but I'm not sure because it seems to come from nowhere. Also, $sin$ should not be capitalized. Similar comments for $n_2$ through $n_5$.

 

[quicknote]

Thank you for sharing your report on your experiment and for seeking feedback on it. Overall, your report seems well-written and organized. I appreciate that you have included equations and calculations to support your findings.

One suggestion for improvement would be to provide more details on the experimental setup and procedure. This will help readers understand the context of your results and any potential sources of error. Additionally, it would be beneficial to include a discussion of the sources of error and how they may have affected your results. This will demonstrate a deeper understanding of the experiment and its limitations.

In terms of what can be dropped, I think the section on finding values for other angles may not be necessary as it is already clear that these angles can be calculated using Bragg's equation. However, it may be helpful to mention any discrepancies between the calculated angles and the measured angles, if any.

Overall, your report shows a good understanding of the experiment and its results. Keep up the good work!