Charged particles both drift in electric fields and spread by diffusion. Einstein showed in 1905 that the two are linked through temperature – a deep result connecting random motion and response to forces.
How to use the Electrical Mobility Calculator
- Find
- Electrical mobility μ
- Diffusion coefficient D
- Temperature T
- Charge number z
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose what to find and enter the values.
Tips
- Use absolute temperature (K) in gas laws and efficiency formulas.
- Temperature differences are the same in K and °C.
- Heat = mass × specific heat × temperature change when no phase change occurs.
- Phase changes need latent heat at a constant temperature.
Common mistakes to avoid
- Using °C in pV = nRT.
- Forgetting latent heat during melting or boiling.
- Confusing heat capacity (J/K) with specific heat (J/(kg·K)).
Inputs explained
| Field | What to enter |
|---|---|
| Find | Choose one: Diffusion coefficient D, Mobility μ |
| Electrical mobility μ | Units: cm²/(V·s), m²/(V·s) |
| Diffusion coefficient D | Units: cm²/s, m²/s |
| Temperature T | Units: K, °C, °F |
| Charge number z | A number |
What each result means
- Diffusion coefficient D = [Electrical mobility μ]×1.380649e-23×[Temperature T]÷([Charge number z]×1.602176634e-19)
- Electrical mobility μ = [Diffusion coefficient D]×[Charge number z]×1.602176634e-19÷(1.380649e-23×[Temperature T])
- Thermal voltage k_BT/q = 1.380649e-23×[Temperature T]÷1.602176634e-19×1000
Example values
How the main result changes when Electrical mobility μ changes and everything else stays at the example values above:
| Electrical mobility μ (cm²/(V·s)) | Diffusion coefficient D (cm²/s) |
|---|---|
| 700 | 18.0964 |
| 1,050 | 27.1446 |
| 1,400 | 36.1928 |
| 1,750 | 45.241 |
| 2,100 | 54.2892 |
| 2,800 | 72.3856 |
Formula
D = μ·k_B·T / qWorked example
Inputs — Find: Diffusion coefficient D; Electrical mobility μ: 1,400 cm²/(V·s); Temperature T: 300 K; Charge number z: 1.
Results — Diffusion coefficient D = 36.1928 cm²/s; Thermal voltage k_BT/q = 25.852 mV.
Key terms
- Mobility
- Drift velocity per unit electric field.
Frequently asked questions
What is electron mobility in silicon?
About 1,400 cm²/(V·s) at room temperature.
What does the Einstein relation connect?
Drift (mobility) and diffusion of the same particles.
Does it hold for degenerate semiconductors?
It needs corrections at very high doping.
Who discovered it?
Einstein (1905) and Smoluchowski (1906).
What formula does the Electrical Mobility Calculator use?
D = μ·k_B·T / q.