Question

Would the answers be different if m/z 5 500 were an ion with a mass

of 1 000 Da and z 5 2?

Short answer

No the answer will be same.

Step-by-step solution

the resolved mass difference:

$\mathrm{Resolving}\mathrm{power}=\frac{\mathrm{m}}{(△\mathrm{m})}\Rightarrow △\mathrm{m}=\frac{\mathrm{m}}{\mathrm{resolvingpower}}=\frac{500}{50000}=0.01$

For m/z 5 500, two peaks separated by m/z 5 0.01 are resolved.

Solving further:

the velocity v of an ion with mass m and charge z after acceleration through a voltage V is $\mathrm{v}=\sqrt{2\mathrm{zeV}/\mathrm{m}}$, where e is the elementary charge, with the charge z=1 is

$\mathrm{v}=\frac{\sqrt{2\mathrm{zeV}/\mathrm{m}}}{\mathrm{m}}=\sqrt{\frac{2\left(1\right)\left(1.602\times {10}^{-19}\mathrm{C}\right)}{\left(5000\mathrm{Da}\right)\left(1.661\times {10}^{-27}\mathrm{kg}/\mathrm{Da}\right)}}=87.839819\mathrm{km}/\mathrm{s}$

The time to transit 2.000 m is t = distance/velocity =role="math" localid="1663660877051" $8.7839819\times {10}^4\mathrm{m}/\mathrm{s}$ =22.768717 .