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 $\mathring{A}$.

$A$ parallel beam of electrons travelling in $x-$ direction falls on a slit of width $d$. If after passing the slit,an electron acquires momentum $P_y$ in the $y-$ direction,then for a majority of electrons passing through the slit ($h$ is Planck's constant):

In the Davisson-Germer experiment,an electron beam of energy $75 \ eV$ falls normally on the surface of a crystal. If the maximum intensity is obtained at an angle of $45^o$ to the direction of the incident beam,then the inter-atomic distance in the lattice plane of the crystal will be .............. $\mathring{A}$

This question has Statement-$1$ and Statement-$2$. Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement-$1$: Davisson-Germer experiment established the wave nature of electrons.
Statement-$2$: If electrons have wave nature,they can interfere and show diffraction.

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

According to Bohr's theory,the electron in orbits has definite energy values. Then,according to the uncertainty principle,the lifetime of an excited state will be: