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# Radioactive decay single parent to daughter product

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Q1)
If a radioactive parent isotope decays to produce a stable daughter isotope, what will be the daughter to parent ratio (D/P) after 9 half-lives? You should give your answer as a single number.

Q2)
What is the product of the beta minus decay shown below? Fill in the atomic number, mass number and symbol for the resulting nucleus

14 ?
C ---> ? + e- + antineutrino
6 ?

#### Solution Preview

Please also open up the attachment.

(1)

Finding amount of stable Daughter product from radio-active decay of parent isotope....methodology

We do not know the decay constant Lamdain the Question so we need to effectively eliminate it

So we need to determine and answer the Question What is half life in terms of decay constant?

Consider a radio-active isotope source with decay constant lamda

Also consider that the isotope starts with (No) atoms at time t = 0

The number of atoms at any time t is defined by the decay law namely

N(t) = No.exp(-lamda*t) (1)

Now the time taken for a radio-active isotope to decay to half its mass (N/2) is given by solving (1) with N(t) replaced by N/2 and t the time replaced by the half life T(1/2)

Thus to ...

#### Solution Summary

Analysing the decay of a single radioactive parent nuclide to a single daughter product nuclide and determining the ration of Daughter to Parent (D/P) after 9 half lifes of the parent species.

The second part of the question shows how to look at beta - decay of Carbon 14 with the emmision of an electron and antineutrino and how to determine the resultant Nucleus, its mass number, atomic munber and species type

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