Financial Calculations

Question

Please step by step instructions.

Solve the problem.

The half-life of silicon-32 is 710 years. If 100 grams is present now, how much will be present in 600 years? (Round your answer to three decimal places.)

A) 94.311
B) 0
C) 0.286
D) 55.668

Answer 1

The half-life of an element is how long it takes for half of the amount of that element to decay.
So here the amount is 100 grams. Since 710 years is the half-life, it takes 710 years for 50 grams of it to decay and that will leave another 50 to go. So if the time passed is 600 years, the answer (most likely) will be 55.668 grams. 

Answer 2

This problem is about radioactive decay of an isotope, which is an exponential decay process. In terms of the half-life T, the formula for the amount N present at time t is

 

N = N₀ 2^-t/T

where N₀ is the amount present at t=0.

In your case,

N = 100 g *2^-600/710 = 55.7 g.