You have synthesized a new radioactive material which you have named OHarium (OH

Question

You have synthesized a new radioactive material which you have named OHarium (OHa) in honor of the professor that wrote your favorite undergraduate textbook on materials kinetics. You measure the rate of radioactive emission from 1 mol of OHa immediately after synthesis to be 6000 disintegrations/s. Exactly five days later, the rate has decreased to 5800 disintegrations/s. Based on this information, calculate the first-order reaction rate constant (s^_l) for the nuclear disintegration of OHa. What is the half-life of OHa (in years)?

Explanation / Answer

No = 6000

N = 5800

t = 5 days

k = 1/t * ln (Ao / A)

k = 1/5 * ln (6000/5800)

k = 0.00678 day-1

k = 7.85 x 10^-8 sec-1

half life = 0.693 / k

= 0.693 / 0.00678

= 102 days

= 102 (1/ 365 year)

= 0.279 years

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