Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Element X is a radioactive isotope such that every 22 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 1200 grams, how long would it be until the mass of the sample reached 800 grams, to the nearest tenth of a year?

Sagot :

reinhard10158

Step-by-step explanation:

s1 = 1200 g

s2 = 1200×2^(-1/22)

s3 = 1200×2^(-2/22)

...

s23 (22 years later) = 1200×2^-22/22 ≈ 1200×2^-1 = 1200/2

sn = 1200×2^(-(n-1)/22)

what is the n, so that the result is 800 g ?

800 = 1200×2^(-(n-1)/22)

800/1200 = 2^(-(n-1)/22)

2/3 = 2^(-(n-1)/22)

log2(2/3) = -(n-1)/22

22×log2(2/3) = -(n - 1) = -n + 1

n = -22×log2(2/3) + 1 = 13.86917502...

since we stared counting with n=1 for the starting quantity, the number of years is truly 1 less than n (s2 is after 1 year, s3 after 2 years ...).

so, we know for n = 13.86917502..., that in fact

12.86917502... ≈ 12.9 years have passed until the mass of the sample reached 800g.

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.