on which frequency electronic ballast is work? and what is value of inductor used in that?

The "electronic ballast" like in compact F-light, not only an inductor. It contains a small half-bridge SMPS (similar to PC supply), the working frequency from 40 to 100kHz. Need a ferrit-core output transformer, driver transformer (for push-pull driving and isolation), EMI-filter.On the output (serial with F-tube) also need a small inductor as ballast, but sometimes here You can find a capacitor.

The ballast uses the tube as a load to for the oscillator. When the tube is cold the oscillator provides usually 40kHz, while when the tube is already hot it delivers round about 20kHz. That is because of the change of the tube's impedance as a function of time and gas presure.

Here is a diagram of a ballast.