Question

After four half-lives of decay, what is the ratio of radioactive parent isotope to stable daughter isotope?

Answer 1

1:15 is the ratio of radioactive parent isotope to stable daughter isotope,

after four half-lives of decay.

Let:

• 'A' be the initial concentration of the radioactive parent isotope
• 'n' be the number of corresponding half-lives
• 'A/2ⁿ ' be the final concentration of the radioactive parent isotope

Using the Exponential Decay Relation:

                  A → A/2ⁿ ( after 'n' half-lives )

                  A⁴ → A/2⁴

                  A⁴ → A/16

∵The final concentration of the radioactive parent isotope is A/16.

∴The initial concentration of the stable daughter isotope will be 15A/16.

1:15 is the ratio of radioactive parent isotope to stable daughter isotope,

after four half-lives of decay.

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