D

Step 1: Determine the number of decays per second (activity) for the sample. The activity can be calculated using the formula \( A = N \cdot \lambda \), where \( N \) is the number of atoms and \( \lambda \) is the decay constant.

Step 2: Find the decay constant using \( \lambda = \frac{0.693}{T_{1/2}} \). Given the mean life \( \tau = T_{1/2}/0.693 \), rearranging gives us \( T_{1/2} = \tau \cdot 0.693 \). Given \( \tau = 9.8 \) seconds, \( T_{1/2} \) can be calculated.

Step 3: Calculate \( N \) for \( 10^{13} \) atoms. This is directly given in the question.

Step 4: Calculate power output using the energy released per decay and multiply by the number of decays per second: \( Power = A \cdot E_{decay} \)), where \( E_{decay} = 200 \) MeV, convert this value into Joules (1 MeV = 1.6 \times 10^{-13} J).

Step 5: Finally, calculate the total power output of the sample and round it appropriately to find the correct answer, leading to option D.