No, an atom with a large atomic number does not necessarily have a small atomic radius. Atomic radius generally tends to decrease as you move from left to right across a period (horizontal row) of the periodic table. This trend is due to the increasing effective nuclear charge, which is the net positive charge experienced by the outermost electrons.
However, when you consider atoms in the same group (vertical column) of the periodic table, the atomic radius generally increases as you move down the group. This increase occurs because each subsequent period adds a new energy level (shell) to the electron configuration, resulting in an increase in the distance between the nucleus and the outermost electrons.
Therefore, while atomic radius can vary depending on the specific element and its position in the periodic table, it is not solely determined by the atomic number. The atomic radius is influenced by factors such as effective nuclear charge, electron configuration, and the number of energy levels or shells occupied by electrons.