Radioactive Decay Kinetics

Question

Radioactive decay obeys first order kinetics; if a sample has a half-life of 5 years, what percentage remains after 15 years approximately?

RankGuru · Accepted Answer

Radioactive decay follows first order kinetics, so the half-life is constant and each half-life reduces the remaining sample to half of its previous amount. The number of half-lives in 15 years is 15/5 = 3. After each half-life the surviving fraction is multiplied by one-half, so after three half-lives the fraction remaining is (1/2)^3 = 1/8, which equals 12.5 percent of the original sample. The option 50 percent corresponds to one half-life only. The option 25 percent corresponds to two half-lives. The option 6.25 percent would require four half-lives, or 20 years. The first order nature of nuclear decay, with its characteristic constant half-life, is highlighted in NCERT kinetics. Understanding radioactive decay kinetics in this way ties directly into the wider study of chemical kinetics, where the same reasoning recurs across many problems. Plausibility check: starting at 100 percent and halving three times gives 100 → 50 → 25 → 12.5 percent, confirming that 12.5 percent remains after 15 years.

Radioactive Decay Kinetics

Select the correct option:

🔒 Solution Hidden from View

More chemical kinetics Practice Questions

The rate constant of a reaction increases by a factor of one hundred when temperature rises from 300...

How is the instantaneous rate of a reaction obtained from a graph of concentration plotted against t...

Define how the threshold energy of a reaction is related to the activation energy and the average en...

Why does the rate of a zero order reaction remain unchanged even when the concentration of the react...

When the temperature of a reaction is raised from 300 K to 310 K, the rate roughly doubles; what doe...

How does a positive catalyst increase the rate of a chemical reaction without itself being consumed ...

Distinguish between order and molecularity by deciding which quantity can be fractional for a multis...

What are the units of the rate constant for a reaction that is found experimentally to be second ord...

Acid-catalysed hydrolysis of an ester in a large excess of water follows first order kinetics; why i...

A plot of the natural logarithm of reactant concentration against time gives a straight line with ne...

According to collision theory, why do only a small fraction of molecular collisions actually result ...

The rate of a typical reaction approximately doubles for every ten degree rise in temperature; what ...

About This Question

Solution