Question

Figure 26-24 shows the effect on resolution of increasing voltage from 28 to120kV.

(a) What is the expected ratio of migration times $\mathbf{(}{\mathbf{t}}_{\mathbf{120}}\mathbf{kV}\mathbf{/}{\mathbf{t}}_{\mathbf{28}}\mathbf{kV}\mathbf{)}$in the two experiments? Measure the migration times for peak 1 and find the observed ratio.

(b) What is the expected ratio of plates $\mathbf{(}{\mathbf{N}}_{\mathbf{120}\mathbf{kV}}\mathbf{/}{\mathbf{N}}_{\mathbf{28}}\mathbf{kV}\mathbf{)}$in the two experiments?

(c) What is the expected ratio of bandwidths$\mathbf{(}{\mathbf{\sigma }}_{\mathbf{120}\mathbf{kV}}\mathbf{/}{\mathbf{\sigma }}_{\mathbf{28}\mathbf{kV}}\mathbf{)}$?

(d) What is the physical reason why increasing voltage decreases bandwidth and increases resolution?

Short answer

1. The ratio of migrating times in the two tests - increasing the voltage by would raise the velocity by resulting in a decrease in migration time, assuming peak 1 has the 211.3min/54.36min = 3.9
2. The expected ratio of plates in the two experiments is 4.3
3. The expected ratio of bandwidths is 48%.
4. Bandwidth would be reduced while resolution would be raised.

Step-by-step solution

Concept used

The effect on resolution of increasing voltage from 28 to120kV.

In this work, you will be provided the figure which depicts the effect of increasing voltage on resolution.

Measure the migration times for peak 1:

(a)

Here's how we'll figure out what to expect ratio of migrating times in the two tests - increasing the voltage by 120kV / 28kV = 4.3 would raise the velocity by 4.3 resulting in a decrease in migration time, assuming peak 1 has the following:

$$\begin{gathered} migrationtim{e}_1=211.3\left(28\mathrm{kV}\right) \\ migrationtim{e}_2=54.36\min \left(120\mathrm{kV}\right) \end{gathered}$$

The ratio of the two is,

211.3min / 54.36min = 3.9

Define the expected ratio of plates

(b)

The predicted plate ratio $\left({\mathrm{N}}_{120}/{\mathrm{N}}_{28}\right)$will be determined next. Consider the following equation in the two experiments.

$N=\frac{{\upsilon }_{app}V{L}_d}{2D{L}_t}$

Since the number of plates (N) is proportional to the voltage (V) , increasing the voltage will increase the plate number by 4.3.

Define the expected ratio of bandwidths

(c)

Calculate the predicted bandwidth ratio ${\mathrm{\sigma }}_{120}/{\mathrm{\sigma }}_{28}$ below.

Take into account that bandwidth is proportional to $1/\sqrt{N}$where

$N=L_d^2/{\sigma }^2\Rightarrow \sigma =L_d/\sqrt{N}$

With increase in the voltage by 4.3 increases the N by 4.3, reducing the bandwidth by

$1/\sqrt{4.3}=0.48$.

Also, bandwidth of 120 is percent more than bandwidth of 28.

Reason for increase in voltage decreases bandwidth and increases resolution:

(d)

Determine the physical reason why raising voltage will reduce bandwidth and increase resolution –

higher voltage = faster ions

faster ions = less time for diffusion

As a result, bandwidth would be reduced while resolution would be raised.