- #1

Athenian

- 143

- 33

- Homework Statement:
- How would I go about calculating a realistic uncertainty value in my given equation? For more information, please refer below.

- Relevant Equations:
- Refer below.

**Background Information:**

I am working on a pulsed NMR lab project that involves graphing out a semi-log graph of free induction decay amplitude as a function of time. After graphing out the semi-log graph, I am to determine the apparent spin-spin relaxation time (##{T_2}^*##) through the numerical values that corresponds to the linear line my data points go along.

For example, one linear equation I got from my data points is as shown below.

$$y = mt+b$$

##m=-0.008344 \pm 0.0004948## mV/##\mu##s

##b=2.931 \pm 0.07160## mV

To acquire ##{T_2}^*## (i.e. the apparent spin-spin relaxation time), I decided to calculate the value by using the below equation.

$${T_2}^*=\frac{\big(\frac{b}{e} - b\big)}{m}$$

For the above case, I got the numerical answer of ##{T_2}^*= 222.05## ##\mu##s.

**Problem:**

Using the equation for ##{T_2}^*## as shown above, I can calculate for my uncertainty value as well. Therefore, rather than inserting the value of 2.931 for ##b##, I used 0.07160 (the uncertainty value) instead.

Using uncertainty values only, I acquired the uncertainty answer of ##{T_2}^*= \pm 91.47## ##\mu##s.

*As the uncertainty value is incredibly large (when compared to the actual value of 222 ##\mu##s), I believe I must have done something wrong here.*

While I am unable to come up with a fix to the problem, I believe either I managed to approach calculating for my uncertainty value in a wrong manner or I somehow got the equation to acquire the value for ##{T_2}^*## incorrectly.

Ultimately, any assistance on this question would be greatly appreciated. Thank you very much for reading through this.