Final answer:
To determine how long it takes a 90 mg sample of strontium-90 to decay to 50.4 mg, the half-life of 29 years is used in an exponential decay formula. By inputting the initial and final amounts into the formula and solving for time, we can find the required time rounded to the nearest year.
Step-by-step explanation:
To find out how long it will take a 90-milligram sample of strontium-90 to decay to a mass of 50.4 mg, we can use the concept of half-life. The half-life of strontium-90 is given as 29 years, which means every 29 years, the mass of strontium-90 will reduce to half its initial quantity.
Let's use the formula for exponential decay: N = N0(1/2)^(t/T), where N is the remaining amount, N0 is the initial amount, t is the time, and T is the half-life.
In this problem:
- N0 = 90 mg (initial mass)
- N = 50.4 mg (final mass)
- T = 29 years (half-life)
- t is the unknown time we need to find
Arranging the formula to find t, we have:
t = T(log(N/N0)/log(1/2))
Plugging in our values, we calculate t tme t. After rounding to the nearest whole number, we obtain the answer.