Question

The half-life of strontium-90 is 29 years. Find the mass remaining after 18 years if a 100-g sample is left to decay.

Required: please find me a solution other that the solution attached.

Answer 1

To calculate the remaining mass of strontium-90 after 18 years, we use the half-life formula and find that approximately 75 grams of the initial 100-gram sample would remain.

Step-by-step explanation:

To find the mass of strontium-90 remaining after 18 years, we can use the concept of half-lives. Since the half-life of strontium-90 is 29 years, we can determine the fraction of the original sample that will remain after 18 years.

The formula to calculate the remaining mass (M) after time (t) is given by:

M = M0 × (1/2)t/T1/2

Where:

• M0 is the initial mass (100 g in this case)
• T1/2 is the half-life of the substance (29 years)
• t is the elapsed time (18 years)

Substituting the known values into the formula, we get:

M = 100 g × (1/2)18/29

Now, we calculate the exponent:

(1/2)18/29 ≈ 0.7496

Therefore, the remaining mass of strontium-90 after 18 years is:

M = 100 g × 0.7496

≈ 75 g

So, approximately 75 grams of the original 100-gram sample of strontium-90 would remain after 18 years.