Worked example: Compare electron mobility in GaAs (m* = 0.067 m_e) and Si (m* = 0.26 m_e) if the scattering time τ is similar, and find the cyclotron frequency in GaAs at B = 1 T. Step 1: Mobility μ = eτ/m*, so μ_GaAs/μ_Si = m*_Si/m*_GaAs = 0.26/0.067 ≈ 3.9. Step 2: GaAs electrons are ~4× more mobile — the reason GaAs is used in high-frequency amplifiers. Step 3: Cyclotron frequency ω_c = eB/m* = 1.602×10⁻¹⁹ × 1 / (0.067 × 9.11×10⁻³¹). Step 4: m* = 6.10×10⁻³² kg; ω_c = 2.63×10¹² rad/s → f = ω/2π ≈ 4.2×10¹¹ Hz = 420 GHz. Conclusion: light effective mass means fast devices — m* is the number that decides transistor speed, measured directly by cyclotron resonance.