Is there an explanation for the unexpected increase in activity of Nuclide A?

[songoku]

Homework Statement

Nuclide A decays to nuclide B. Initially, there are $1.29 \times10^9$ nuclei of A and after some time the activity of A is 10 000 Bq. If the half life of A and B is 10 years and 10 hours respectively, find activity of B

Relevant Equations

$A=\lambda N$

$t_{\frac 1 2}=\frac{ln~2}{\lambda}$

I found something I think does not make sense.

Decay constant of A:
$$\lambda_{A}=\frac{ln~2}{t_{\frac 1 2}}$$
$$=\frac{ln~2}{10\times 365 \times 24 \times 3600}$$
$$=2.2\times 10^{-9} / s$$

Initial activity of A = $\lambda_{A} N_{\text{initial}}$ = 2.2 x 10^-9 x 1.29 x 10⁹ = 2.84 Bq

Then after some time the activity becomes 10 000 Bq. How can the activity increase instead of decrease?

Is there something wrong with the question or something wrong with me?

Thanks

 

[Steve4Physics]

Is there something wrong with the question or something wrong with me?

There's nothing wrong with you! The question appears to have one or more mistakes.

Some possibilities are:
- the half-lives of A and B are the wrong way round;
- $1.29 \times10^9$ is a very small number for a number of nuclei in this context; maybe it should be $1.29 \times10^{19}$ for example.

 

[haruspex]

You could at least obtain the general form of the solution.

 

[songoku]

Thank you very much Steve4Physics and haruspex

 

[Astronuc]

Homework Statement:: Nuclide A decays to nuclide B. Initially, there are $1.29 \times10^9$ nuclei of A and after some time the activity of A is 10 000 Bq. If the half life of A and B is 10 years and 10 hours respectively, find activity of B
Relevant Equations:: $A=\lambda N$

$t_{\frac 1 2}=\frac{ln~2}{\lambda}$

Then after some time the activity becomes 10 000 Bq. How can the activity increase instead of decrease?

One should research "Transient Equilibrium", where t_1/2(parent) > t_1/2(daughter), or λ(parent) < λ(daughter). This is observed for the natural decay series of radionuclides ²³²Th, ²³⁵U, ²³⁸U and others.

https://en.wikipedia.org/wiki/Transient_equilibrium
Also see related Secular equilibrium.

 

[haruspex]

One should research "Transient Equilibrium", where t_1/2(parent) > t_1/2(daughter), or λ(parent) < λ(daughter). This is observed for the natural decay series of radionuclides ²³²Th, ²³⁵U, ²³⁸U and others.

https://en.wikipedia.org/wiki/Transient_equilibrium
Also see related Secular equilibrium.

At this stage it is not clear from @songoku's posts whether he has any difficulty in solving a correctly posed version of the question. The thread centres on the impossible combination of given facts.