Final answer:
The resonance frequency of a free electron in a 0.35 T magnetic field with a g-factor of 2.0023 can be calculated using the formula for electron spin resonance, which involves the Bohr magneton, Planck's constant, and the magnetic field strength.
Step-by-step explanation:
To calculate the resonance frequency of a free electron in a magnetic field of 0.35 T with a given g-factor of 2.0023, we use the formula for electron spin resonance (ESR), which is ν = (ge⋅μ_B⋅B)/h, where ν is the frequency, ge is the g-factor, μ_B is the Bohr magneton (approximately 9.274 x 10^-24 J/T), B is the magnetic field strength, and h is Planck's constant (approximately 6.626 x 10^-34 J⋅s). Plugging in the given values:
ν = (2.0023 x 9.274 x 10^-24 J/T x 0.35 T) / (6.626 x 10^-34 J⋅s)
After performing the calculation, we'll find the resonance frequency. Since it requires precision in calculation and unit conversions, which are not shown here, you'll need a calculator to obtain the exact value. Once you have the frequency in hertz (Hz), convert it to gigahertz (GHz) by dividing by 1 x 10^9 (since 1 GHz = 1 x 10^9 Hz).