Who was the first to verify that electrons are wave-like in nature?

Match List $-I$ (Experiment performed) with List $-II$ (Phenomena discovered/associated) and select the correct option from the options given below:

List $-I$	List $-II$
$(1)$ Davisson and Germer	$(i)$ Wave nature of electrons
$(2)$ Millikan's oil drop experiment	$(ii)$ Charge of an electron
$(3)$ Rutherford experiment	$(iii)$ Quantisation of energy levels
$(4)$ Franck-Hertz experiment	$(iv)$ Existence of nucleus

Which phenomenon best supports the theory that matter has a wave nature?

The Davisson and Germer experiment proved:

$A$ sodium atom is in one of the states labeled 'Lowest excited levels'. It remains in that state for an average time of $10^{-8} \, s$,before it makes a transition back to a ground state. What is the uncertainty in energy of that excited state?

Consider two separate ideal gases of electrons and protons having the same number of particles. The temperature of both gases is the same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to :-