The Tully's fewest switches surface hopping algorithm is implemented within the framework of the time-dependent density functional based tight binding method (TD-DFTB) to simulate the energy relaxation following absorption of a UV photon by polycyclic aromatic hydrocarbons (PAHs). This approach is used to study the size effect on the ultrafast dynamics in excited states for a special class of PAH species called polyacenes. We determine the dynamical relaxation times and discuss the underlying mechanisms. Our results show that there is a striking alternation in decay times of the brightest singlet state for neutral polyacenes with 3 to 6 aromatic cycles. The alternation corresponds to an order-of-magnitude variation between roughly 10 and 100 fs and is correlated with a qualitatively similar alternation of energy gaps between the brightest state and the state lying just below in energy.