Question

Rutherford experiment: why did he have to use wavelengths smaller than the subatomic particles to detect the location of it?

Answer 1

Could you elaborate on your question? By "detecting it", I assume you mean the positive nucleus coherent with his "planetary-model". The alpha particles that were fired at the gold plate (I assume this is what you refer to as wavelengths) were essentially the size of your normal He atom. Not the small wavelengths you refer to.

Answer 2

Its because of diffraction. Diffraction is the property by which when a wave having a wavelength lamda passes through a slit or hole of width d made in an object then the slit would act as a source of the wave if d<lamda and if lamda is greater than d then the waves would pass normally like a light beam would pass through a slit. Its because of this phenomenon low wavelength beams are used in certain elements as the space between the subatomic particles acts as a slit in general. I hope you understand this :)

Answer 3

i think ccause a waves gets scattered by a subatomic particle when it is smaller than that particle like in tyndal effect ! not sure though