Question

Calculate the improvement in S/N in progressing from spectrum A to spectrum D in Figure 5-15

Short answer

The improvement in S/N in progressing from spectrum A to spectrum D in figure 5-15 is 8.77.

Step-by-step solution

Step 1. Given information

The number of spectra is n = 77

Step 2. Introduction

The signal-to-noise ratio (S/N) after repetition is can be calculated as below.

${\left(\frac{S}{N}\right)}_n=\sqrt{n}{\left(\frac{S}{N}\right)}_i$

Here, ${\left(\frac{S}{N}\right)}_n$=Signal-to-noise ratio after repetition, n = number of spectra

${\left(\frac{S}{N}\right)}_i$=Signal-to-noise ratio before repetition

Step 3, Explanation

The improvement in S/N in progressing from spectrum A to spectrum D

$\text{improvement}=\frac{\left[{\left(\frac{S}{N}\right)}_n\right]}{{\left(\frac{S}{N}\right)}_i}=\sqrt{n}$

$\text{improvement}=\sqrt{77}=8.77$