# Nuclear decay of a mixture of P and S. (2009 USAPhO Question A2)

**1. The problem statement, all variables and given/known data**

A mixture of [itex]^{32}P[/itex] and [itex]^{35}S[/itex] (two beta emitters widely used in biochemical research) is placed next to a detector and allowed to decay, resulting in the data (attached) below. The detector has equal sensitivity to the beta particles emitted by each isotope, and both isotopes decay into stable daughters.

You should analyze the data graphically. Error estimates are not required.

a.Determine the half-life of each isotope.

[itex]^{35}S[/itex] has a signicantly longer half-life than [itex]^{32}P[/itex].

b.Determine the ratio of the number of [itex]^{32}P[/itex] atoms to the number of [itex]^{35}S[/itex] atoms in the original sample.

**2. Relevant equations**

[itex]\frac{dN}{dt}=-λΝ[/itex]

**3. The attempt at a solution**

[itex]|\frac{dN}{dt}|=N_P λ_P+N_S λ_S (1)[/itex]

[itex]T_{\frac{1}{2}S} \gg T_{\frac{1}{2}P}⇔λ_S \ll λ_P(2)[/itex]

[itex]N=N_0 e^{-λt} (3)[/itex]

But I can’t figure out how to use them in order to get a result.

http://ift.tt/1jGKVLQ

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