A certain substance has a half-life of 5.0 hours. How many nuclei of the substance are required to give an initial activity of 6.0 ?Ci? (1 Ci = 3.7 × $10 ^ { 10 }$ Bq)

Question

Quizplus · Accepted Answer

The correct answer is A because the initial activity is 6.0 ?Ci, which is equal to 6.0 × 3.7 × $10 ^ { 10 }$ Bq = 2.22 × $10 ^ { 11 }$ Bq. The activity of a radioactive substance is given by the equation A = ?N, where A is the activity in Bq, ? is the decay constant in s?1, and N is the number of radioactive nuclei. The decay constant is related to the half-life by the equation ? = ln(2)/t1/2, where t1/2 is the half-life in seconds. Substituting the given values into these equations, we get:? = ln(2)/t1/2 = ln(2)/(5.0 × 3600 s) = 3.92 × $10 ^ {- 5 }$ s?1N = A/? = (2.22 × $10 ^ { 11 }$ Bq)/(3.92 × $10 ^ {- 5 }$ s?1) = 5.66 × $10 ^ { 15 }$ nucleiTherefore, the number of nuclei required to give an initial activity of 6.0 ?Ci is 5.66 × $10 ^ { 15 }$ nuclei, which is closest to choice A, 5.8 × $10 ^ { 9 }$ nuclei.

A Certain Substance Has a Half-Life of 5 101010 ^ { 10 }1010

A Certain Substance Has a Half-Life of 5 $10 ^ { 10 }$