The Davisson-Germer experiment that first demonstrated the wave nature of matter used electrons accelerated to $54 \ V$. Determine the wavelength of the electrons in the Davisson-Germer experiment in $\mathring{A}$.

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

The wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure).

In the Davisson-Germer experiment,for which value of accelerating voltage was the intensity of the electron beam found to be maximum (in $V$)?

Using the Heisenberg uncertainty principle,arrange the following particles in the order of increasing lowest energy possible.
$(I)$ An electron in $H_{2}$ molecule
$(II)$ $A$ hydrogen atom in a $H_{2}$ molecule
$(III)$ $A$ proton in the carbon nucleus
$(IV)$ $A$ $H_{2}$ molecule within a nanotube

State Heisenberg's uncertainty principle.