# 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?

** ** EDIT ** ** 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!

• We don't answer homework like questions. You are required to attempt to find the solution and ask where you need help. – LDC3 Apr 12 '14 at 2:32
• Okay, fair enough. But would it be acceptable to give some guidance on the problem so I can know where to start? – user2205763 Apr 12 '14 at 2:48
• You are given B, r, and m/z. The unknowns are $e$ and V. Isn't $e$ a constant? Which means you can solve for V. – LDC3 Apr 12 '14 at 2:52
• Separation involves somehow the use of a slit, with a slit width, so the question is probably misformulated. You could consider the infinitely thin slit limit (i.e. find V for both m/z values), but it will not mean that they are separated, as all the dispersion factors would have to be taken into account. – PLD May 6 '14 at 14:59

## 1 Answer

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.