Statement I: Atomic radius increases down a group.
Statement II: The higher the atomic number within a group, the smaller the atom.
(A) Both statement I and statement II are correct and statement II is the correct explanation for statement I.
(B) Both statement I and statement II are correct and statement II is not the correct explanation for statement I.
(C) Statement I is correct but statement II is incorrect.
(D) Statement I is incorrect but statement II is correct.
(E) Both statement I and statement II are incorrect.

Hint: An atom is considered to be spherical in size and the size of an atom is measured in terms of its radius. The atomic radius is the most probable distance from the centre of the nucleus to the outermost shell containing electrons. The factors on which the atomic size depends are nuclear charge and the number of orbits.

Complete step by step answer:
With the increase in nuclear charge, the force of attraction between the nucleus and electron cloud increases. Thus, the electron cloud will move closer to the nucleus and hence atomic size decreases.
With the increase in the number of orbits, the distance between the last orbit and nucleus also increases. Hence, atomic size also increases.
As we move down a group, the nuclear charge goes on decreasing. The electrons get added in new shells which will screen the nucleus. This screening effect due to the addition of new electrons goes on increasing. So, the attraction of the nucleus for the outermost shell electron also goes on decreasing. Thus, the distance between the nucleus and the last electron will increase and hence, the atomic radius increases down a group. Hence, statement I is correct.
As the atomic number increases from top to bottom in a group, the addition of electrons takes place to new energy levels which lie very far away from the nucleus. Hence, the atomic size increases down a group. Hence, statement II is incorrect.

So, the correct option is C.

Note: Across a period, the atomic number or the nuclear charge goes on increasing but the electrons are added in the same shell. So, they do not screen the nucleus that much. The attraction of the nucleus for the outermost electrons goes on increasing. Hence, the atomic radius decreases across a period.