The element having the smallest atomic size is
Helium
The explanation for correct options
Option B; Helium
As we move along from the left to right of the periodic table, the nuclear charge increases, as a result, atomic size decreases.
Thus Helium is a member of group 18 which is at the extreme right of the periodic table and has the least atomic size.
The explanation for incorrect options
Option A; Hydrogen is present at the extreme left in the periodic table and has a greater atomic size.
Option C; Lithium is a member of group 1 which have the largest atomic size.
Option D, Gold is a metal that has more atomic size than noble gases like Helium.
Thus, Option B, Helium is the correct option.