That depends what assumptions you make about what the 5 grams of matter is made of.
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The quantity supplied the house for forty years.
The decay of plutonium-240 follows exponential decay kinetics, where the amount remaining is given by 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 the base of the natural logarithm. The decay constant for plutonium-240 is 0.0106 years^-1. By rearranging the equation to solve for time (t) when N(t) = 9 grams and N0 = 27 grams, you can calculate the time it will take for 27 grams of plutonium-240 to decay to 9 grams. The calculated time will be approximately 20.5 years.
(2,000 years) times (1,000 years) = 2 million square yearsThat quantity has no physical significance.
You would have to wait 2,000 years for this to occur. Half of 2,000 is 1,000. Half of 1,000 is 500. This process happens twice. 1,000 years * 2 processes = 2,000 years.
The amount of material left in radioactive decay is an exponential function. Therefore, the way you solve this is to write it as an exponential function; for example: f = e-kt, where "f" is the fraction remaining after a certain time, "t" is the time in any unit you choose (for example, years), and "k" is a constant you have to find out. Replace the numbers you know (for t = 1600 years, f = 1/2, since 1/2 of the original remains), and solve for "k". Then, write the equation again, this time with the constant "k" you figured out before, and the time (365 years). This will give you the fraction left after that amount of time.