How Long Will it Take for a 90-milligram Sample of Strontium-90 to Decay?

Calculating the Decay Time of Strontium-90

The half-life of strontium-90 is 29 years. In this scenario, we have a 90-milligram sample of strontium-90 that will decay to a mass of 50.4 mg. We need to determine how long it will take for this decay to occur.

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.

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. After rounding to the nearest whole number, we obtain the answer.