Natural carbon consists almost exclusively of^12C and^13C, but cosmic rays high

Question

Natural carbon consists almost exclusively of^12C and^13C, but cosmic rays high in Earth's atmosphere produce^14C, such that atmospheric carbon dioxide contains about 1.35e-12 atoms of^14C per carbon atom. Plants (and the animals that eat them) obtain their carbon from the atmosphere, and therefore their composition tends to be similar to the atmosphere. Suppose a living plant has 5.10 g of carbon. How many atoms of^14C are in it? What is the decay constant lambda for^14C, in inverse years? How many decays per second will there be from the sample described in part (a)? Suppose the sample described in part (a) dies (stops absorbing carbon from the atmosphere). After 9330 y, what will be the decay rate from the sample? Suppose the sample described in part (a) is discovered to currently have a decay rate of 0.590 s^-1. How old is this sample?

Explanation / Answer

a) for 5.1 g of Carbon

Number of 14C = 5.1/(atomic mass of Carbon) * 1.35 *10^-12 * 6.022 *10^23

Number of 14C = 5.1/(12.01) * 1.35 *10^-12 * 6.022 *10^23

Number of 14C = 3.45 *10^11

b)

decay constant = ln(2)/half life

decay constant = ln(2)/5730

decay constant = 1.21 *10^-4 year^-1

c)

for decay per sec

Ro = No * decay constant

Ro = 3.45 *10^11 * 1.21 *10^-4/(365 * 3600 * 24)

Ro = 1.32 decays/s

d)

after 9330 years

R = 1.32 * (1/2)^(9330/5730)

R = 0.428 s^-1

e)

let the age is t

0.590 = 1.32 * (1/2)^(t/5730)
solving for t

t = 6656 years

the sample is 6656 years old

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.