Name the noble gas which has (i) highest first ionization energy (ii) highest boiling point.

i) In noble gas helium has the highest first ionization energy.
This is beause smaller the size greater will be the force of attraction and thus required more energy to remove an electron from a helium atom.
As we move down the group the first ionization energy become smaller. The force of attraction of the positively charged nucleus for electrons decrease as the square of the distance between them increase.

ii) Xenon has highest boiling point. In noble gases only london dispersion force take place between them.
These dispersion forces are momentary i.e, they develop only for a fraction of time and the strength of these forces depend on the distortion of electron cloud of the atom by another atom.
Now, greater the size of the atom greater will be the distoration of electron cloud of the atom and stronger will be the dispersion force which will in turn increase boiling point.