Answer
$R = 2.79 \times 10^{9} s^{-1}$
Work Step by Step
The equation of rate of decay, $R = \lambda N = \frac{Nln2}{T_{1/2}}$
where
$N = 2.03 \times 10 ^{20}$
$T_{1/2} = 1600 y \times 3.15 \times 10^{7} s/y$
$T_{1/2} = 5.046 \times 10^{10} s$
So,
$R = \frac{(2.03 \times 10 ^{20})(0.693)}{ 5.046 \times 10^{10} s}$
$R = 2.79 \times 10^{9} s^{-1}$
