My Report on Experiment & Error Analysis

[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)

 

[Moonbear]

Please only post your question once. Locking this one.

 

[quicknote]

Dear researcher,

Thank you for sharing your report on your experiment and error analysis. It seems that you have conducted a thorough and detailed experiment, and I appreciate your efforts in generating the equations using latex codes. It is always important to have precise and accurate equations in scientific reports.

From my initial review, your results seem to be reasonable and within the expected range. However, I would suggest including more details about the materials and methods used in your experiment. This will help readers understand the context of your experiment and replicate it if needed.

In terms of the errors, it is good that you have identified and discussed them in your report. It is important to acknowledge and address potential sources of error in any experiment. In the future, you can also include a section on error analysis where you discuss the impact of these errors on your results and how they could be minimized in future experiments.

Overall, I think your report is well-written and organized. However, if you want to improve it, you can consider adding some graphs or figures to visually represent your results. This can make it easier for readers to understand your findings.

I hope my feedback is helpful to you. Keep up the good work in your scientific endeavors!