Question

Carbon-11 is used in medical imaging. The half-life of this radioisotope is 20.4 min. What percentage of a sample remains after 60.0 min?34.013.05.2871.22.94

Answer 1

Answer:

Percentage of a sample remains after 60.0 min is 13.03%.

Explanation:

• It is known that the decay of isotopes of C-11 obeys first order kinetics.

• Also, it is clear that in first order decay the half-life time is independent of the initial concentration.

• Half-life time (t1/2) in first order reaction = 0.693/k, where k is the rate constant.

∴ k = 0.693/(t1/2) = 0.693/(20.4 min) = 0.03397 min⁻¹.

• The integrated law for first order reaction is:

kt = ln[A₀]/[A],

where, k is the rate constant (k = 0.03397 min⁻¹).

t is the time of the reaction (t = 60.0 min).

[A₀] is the initial concentration of C-11 ([A₀] = 100.0 %).

[A] is the remaining concentration of C-11 ([A] = ???%).

∵ kt = ln[A₀]/[A]

∴ (0.03397 min⁻¹)(60.0 min) = ln(100%)/[A]

∴ 2.038 = ln(100%)/[A]

• Taking e for both sides:

∴ 7.677 = (100%)/[A]

∴ [A] = (100%)/(7.677) = 13.03%.

So, percentage of a sample remains after 60.0 min is 13.03%.