How long does it take a 100 g sample of au-1 98 to decay to 6.25?

Answer 1

The half-life of gold-198 is approximately 2.7 days.

The decay constant k, is 0.693/(half-life in days) or 0.2567 d-1 to use in the radio active decay equation:

log10(Xo/X) = k*t/2.30, where Xo is the amount initially & X is the amount after time, t. So substitute & solve for t:

log (100/6.25) = (0.2567*t)/2.30

t = 10.8 days

Answer 2

The decay of an isotope follows exponential decay law, which can be modeled using the equation N(t) = N0 * e^(-λt), where N(t) is the amount remaining at time t, N0 is the initial amount, λ is the decay constant, and e is Euler's number. Given the half-life of Au-198 (2.7 days), you can calculate the decay constant (λ). Then, you can solve for time (t) when N(t) = 6.25 g, starting from 100 g.