Calculate accelerating voltage required to separate two particles in a magnetic sector analyser So, in mass spectrometry we have the following equation to describe a magnetic sector analyser,
$$\frac{m}{z}=\frac{B^2r^2e}{2V}.$$

Lets say that I have two particles with different mass/charge ratios,
$$\frac{m_1}{z_1} = 120.9,\quad \frac{m_2}{z_2} = 121.0,$$
and I have $B=2\text{T}$, $r=25\text{cm}$. For example, what accelerating voltage $V$ do I need to apply to separate these two particles? What criteria do I have to determine whether two particles are separated?

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I don't know where to start with this. So even though you don't generally answer homework-like questions on this forum, some pointers in the right direction would be greatly appreciated!
Baseline separating C-12 from C-13 from C-14 requires accelerator mass spectrometry,

http://en.wikipedia.org/wiki/Accelerator_mass_spectrometry

Your example requires 100 times the finesse.  I'm not optimistic for reduction to practice vs. a paper solution.  Your target could be a charge-coupled device or a channel plate amplifier.  Observe the spatial separation of signals above noise.  A Faraday cup works differently.  Time-of-flight is not optimistic.

You might diddle FT ion cyclotron resonance in a high-Q cavity.