Multiple Choice
The daughter nuclide of positron emission will differ from the parent nuclide by
21. Nuclear Chemistry
Intro to Radioactivity
Struggling with General Chemistry?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Determine the age of a bone that has a decay rate of 3.80 dis/min ⋅ g C if the ratio of 12C:14C in living organisms has a decay rate of 15.3 dis/min ⋅ g C. (t1/2 of 14C = 5730 years).
A
1.39 × 104 yr
B
1.15 × 104 yr
C
2.30 × 104 yr
D
1.39 yr
E
1.15 yr
Verified step by step guidance1
Understand that the problem involves radioactive decay, specifically the decay of carbon-14 (14C) in a bone sample. The decay rate is given in disintegrations per minute per gram of carbon (dis/min · g C).
Use the decay rate of 14C in living organisms (15.3 dis/min · g C) as the initial activity (A0) and the decay rate in the bone (3.80 dis/min · g C) as the current activity (A).
Apply the radioactive decay formula: A = A0 * e^(-λt), where λ is the decay constant and t is the time elapsed. Rearrange the formula to solve for t: t = (1/λ) * ln(A0/A).
Calculate the decay constant (λ) using the half-life formula: λ = ln(2) / t1/2, where t1/2 is the half-life of 14C (5730 years).
Substitute the values of A0, A, and λ into the rearranged decay formula to calculate the age of the bone (t).
2:29mWatch next
Master Intro to Radioactivity with a bite sized video explanation from Jules
Start learningRelated Videos
Related Practice
Intro to Radioactivity practice set
Problem sets built by lead tutorsExpert video explanations