The half-life is the time for half the atoms to decay. In 3240 years (2 half-lives: 3240/1620=2), the number of undecayed atoms left is given by the decay formula: $N=N_0{\left(\frac{1}{2}\right)}^{\frac{t}{T_{1/2}}}$. Substituting t=3240 and T_1/2=1620, we get $N=2.68\times {10}^{18}{\left(\frac{1}{2}\right)}^2=6.7\times {10}^{17}$. The number of atoms disintegrated is the initial minus the remaining: $2.68\times {10}^{18}-6.7\times {10}^{17}=2.01\times {10}^{18}$.

Final Answer:

2.01 × 10¹⁸