Low concentration replicate samples of Pb-EDTA gave the following counts in a mass spectral measurement: 188.3, 145.9, 159.7, 174.7, 143.7, 213.1, 164.7, 169.3, 158.7, 176.3. Ten measurements of a blank had a mean of 27.3 counts. A sample containing 1.00 ìM Pb-EDTA gave 1877 counts. Estimate the signal and concentration detection limits for Pb-EDTA.
goteem
To estimate the signal and concentration detection limits for Pb-EDTA, we need to calculate the average count and standard deviation for the blank measurements, and then use that information to calculate the signal-to-noise ratio (SNR).
Let's start by calculating the average count and standard deviation for the blank measurements:
1. Average count for the blank measurements:
- Add up all the counts for the blank measurements: 27.3 + 27.3 + ... (ten times).
- Divide the sum by the number of measurements (ten in this case).
Next, we can calculate the standard deviation of the blank measurements:
1. Calculate the variance of the blank measurements:
- For each blank measurement, subtract the average count calculated previously.
- Square the result obtained above for each blank measurement.
- Add up all the squared values.
- Divide the sum by the number of blank measurements minus one.
2. Calculate the standard deviation:
- Take the square root of the variance calculated above.
Now that we have the average count and standard deviation for the blank measurements, we can calculate the SNR for the low concentration replicate samples and the sample containing 1.00 ìM Pb-EDTA:
1. Calculate the average count for the low concentration replicate samples using the given counts.
2. Calculate the SNR for the low concentration replicate samples:
- Subtract the average count of the blank from the average count of the low concentration samples.
- Divide the result by the standard deviation of the blank.
3. Calculate the SNR for the sample containing 1.00 ìM Pb-EDTA:
- Subtract the average count of the blank from the count of the sample containing 1.00 ìM Pb-EDTA.
- Divide the result by the standard deviation of the blank.
Finally, the signal detection limit corresponds to the lowest concentration that produces an SNR greater than a defined threshold, typically 3. The concentration detection limit can be estimated by dividing the signal detection limit by the slope of the calibration curve.
To summarize, follow these steps to estimate the signal and concentration detection limits for Pb-EDTA:
1. Calculate the average count and standard deviation for the blank measurements.
2. Calculate the average count for the low concentration replicate samples.
3. Calculate the SNR for the low concentration replicate samples.
4. Calculate the SNR for the sample containing 1.00 ìM Pb-EDTA.
5. Determine the signal detection limit by finding the lowest concentration that produces an SNR greater than the threshold (usually 3).
6. Calculate the concentration detection limit by dividing the signal detection limit by the slope of the calibration curve.