The effective mass of free carriers can be measured using cyclotron resonance. The resonance frequency (also known as the cyclotron frequency) of a charged particle in a magnetic field is, in MKS units,

where q is the charge and m is the effective mass of the particle. If a material is placed in a DC magnetic field and then a small oscillating field is applied, the free carriers will resonate at the cyclotron frequency. Knowing the magnitude of B then allows one to deduce the value of m from the resonance frequency.

Calculate the cyclotron frequency of an electron with effective mass 0.1 m₀ in the presence of a magnetic field B = 1 T, where m₀ is the mass of the free electron in vacuum. Some convenient unit conversions to remember are 1 T = 1 V-s/m² and m₀ = 0.5 × 10⁶ eV/c².

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Ос = |q|B m (2.2.6)