two rays of different wavelength will generate the same electric current ?

It will depend on the electro-optic conversion efficiency of the photodiode for that particular wavelength. That is, if the photodiode is more efficient in the green wavelength then the electric current generated will be greater. Take a look at the photodiode curves supplied by the manufacture to determine the output current v.s. wavelength.

There should be a linear relationship between the frequency of light and the energy measured:

Measuring Planck's constant using Light Emitting Diodes (LEDs)

There is, but diodes don't actually measure energy when current is being generated.

Not so good a paper.

A much better one there.

But did you read them? It isn't at all about the OP's question (which I think is just homework, anyway.)

Jon

Probably different. Each photodiode type has a response versus wavelength curve, probably on its datasheet.

John