Unmanned Aerial Vehicle (UAV) networks require successful mission execution, which is dependent on task planning and control. In this paper, we propose a distributed task allocation algorithm for a multi-UAV sensor network for sensing thorium intensities in the coastal areas of India. A power-aware coordination and planning approach is used to coordinate the activities of multiple UAVs. Depending on the availability of resources in each sensing UAV unit, each UAV initiates a task-scheduling algorithm and distributes its remaining tasks dynamically to other UAVs. The control station sends control information to the UAVs and receives the sensed parameters along with the location information from each UAV. The task allocation algorithm was simulated successfully using a network of static motes. The network was more effective and efficient with the use of this task allocation algorithm, thus contributing to improved mission execution in UAV networks.