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

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

(b) What is the expected ratio of plates $\left(N_{120kv}/N_{28}kv\right)$in the two experiments?

(c) What is the expected ratio of bandwidths$\left({\sigma }_{120\mathrm{kv}}/{\sigma }_{28}\mathrm{kv}\right)$?

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

The effect on resolution of increasing voltage from 28 to 120kV

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

(a)

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

$$\begin{gathered} {\mathrm{migrationtime}}_1=211.3\min (28\mathrm{kV}) \\ {\mathrm{migrationtime}}_2=54.36\min (120\mathrm{kV}) \end{gathered}$$

The ratio of the two is,

$211.3\min /54.36\min =3.9$

(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.

$\mathrm{N}=\frac{{\mathrm{\mu }}_{\mathrm{app}}{\mathrm{VL}}_{\mathrm{d}}}{2{\mathrm{DL}}_{\mathrm{t}}}$

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

(c)

Calculate the predicted bandwidth ratio ${\sigma }_{120}/{\sigma }_{28}$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 48% percent more than bandwidth of 28.

(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.