Formula Used
- m/q = m / q (direct definition).
- m = (m/q) · q and q = m / (m/q) (rearrangements).
- Cyclotron motion: ω = qB/m so m/q = B/ω and m/q = B/(2πf).
- Magnetic bending: qvB = mv²/r so m/q = (Br)/v.
- Acceleration through voltage then bending: qV = ½mv² with r = mv/(qB) gives m/q = (B²r²)/(2V).
How to Use This Calculator
- Select the calculation mode that matches your available measurements.
- Enter values and pick the correct units for each field.
- Choose the charge sign to set the sign of the ratio.
- Press Calculate to show results above the form.
- Use Download CSV or Download PDF after a result appears.
Example Data Table
| Scenario | Inputs | Output m/q | Notes |
|---|---|---|---|
| Direct (ion) | m = 28 u, q = +1 e | 2.9020e-7 kg/C | Approx. nitrogen ion, singly charged. |
| Cyclotron | B = 1.0 T, f = 10 MHz, q positive | 1.591549e-8 kg/C | Uses m/q = B/(2πf). |
| Voltage + radius | B = 0.5 T, r = 0.20 m, V = 2 kV | 2.50000000e-6 kg/C | Common in simple sector analyzers. |
Notes and Practical Tips
- If you work in atomic units, prefer u and e inputs.
- For negative particles, set the charge sign to negative.
- At high energies, relativistic corrections can matter.
- Always keep units consistent; this tool converts to SI internally.
Mass-to-Charge Ratio Guide
1) Why the ratio matters
The mass-to-charge ratio (m/q) controls how a particle responds to electric and magnetic fields. Two ions with the same charge state but different masses separate cleanly in many analyzers because the heavier ion bends less in the same field. In SI units, m/q is measured in kg/C.
2) Typical reference values
For quick checks, common values help. A proton has m/q ≈ 1.04×10−8 kg/C, while an electron has m/q ≈ −5.69×10−12 kg/C. A singly charged 28 u ion gives m/q ≈ 2.90×10−7 kg/C. Multiply the charge state (2e, 3e, …) to reduce m/q proportionally.
3) Cyclotron frequency method
In a uniform magnetic field, a charged particle circles with angular frequency ω = qB/m. Rearranging gives m/q = B/ω, or m/q = B/(2πf). For example, at B = 1.0 T and f = 10 MHz, m/q ≈ 1.59×10−8 kg/C. Precision depends on measuring B and f accurately.
4) Bending radius method
In beamlines and spectrometers, the curvature radius r is often known from geometry. With velocity v, the balance qvB = mv²/r yields m/q = (Br)/v. If B = 0.5 T, r = 0.20 m, and v = 1.0×106 m/s, then m/q ≈ 1.0×10−7 kg/C.
5) Voltage plus radius method
If the particle is accelerated through voltage V, non-relativistic energy gives qV = ½mv². Combining with the bending relation leads to m/q = (B²r²)/(2V). For B = 0.5 T, r = 0.20 m, V = 2 kV, the ratio is ≈ 2.5×10−6 kg/C.
6) Unit choices that reduce mistakes
Many labs use atomic mass units and elementary charges. This calculator converts between u/e and kg/C using 1 u = 1.66053906660×10−27 kg and 1 e = 1.602176634×10−19 C. Keeping inputs in familiar units makes sanity checks faster.
7) Interpreting sign and charge state
The sign of m/q follows the sign of q. Negative particles (electrons, anions) produce negative ratios. Charge state is equally important: a 40 u ion at +2e has half the m/q of the same mass at +1e. Always record the assumed charge sign and magnitude.
8) Practical accuracy tips
Report uncertainties when possible. A 1% error in B usually becomes a 1% error in m/q in cyclotron modes. For radius-based methods, misalignment can dominate. If speeds approach a significant fraction of c, relativistic mass increase can shift results; treat the voltage method as an estimate then.
FAQs
1) What does a smaller m/q mean?
Smaller m/q means the particle bends more for the same magnetic field. This often corresponds to higher charge state, lower mass, or both, and it usually implies higher cyclotron frequency in a fixed field.
2) Why do you show both kg/C and u/e?
kg/C is the SI form used in physics equations, while u/e matches mass spectrometry conventions. Showing both helps you compare to reference tables and avoid unit conversion errors during analysis and reporting.
3) Can I use this for electrons?
Yes. Set the charge sign to negative, and input mass in kg or u and charge in C or e. The output will be negative m/q, which matches the direction reversal of magnetic bending for electrons.
4) When is the voltage-based mode inaccurate?
It becomes inaccurate at relativistic speeds or when energy losses and non-uniform fields are significant. For very high voltages, use relativistic beam dynamics or compare with measured frequency or radius data.
5) Why does charge state change the ratio so much?
Because m/q scales inversely with q. Doubling the charge from +1e to +2e halves m/q for the same mass. That directly changes cyclotron frequency and bending radius in magnetic analyzers.
6) What inputs are best for a cyclotron measurement?
Use a well-calibrated magnetic field B and a precise frequency measurement f or ω. Frequency counters are often more accurate than velocity estimates, so cyclotron modes can produce stable ratios when B is known well.
7) How do I export my results?
Run a calculation first. Then use the Download CSV or Download PDF buttons in the results panel above the form. Exports include your inputs and the computed ratio in both unit systems.