1. (a) A sample of Ca₃(PO₄)₂ containing phosphorus-32 has an activity of 3.35 × 10³ dpm Exactly 2 days later, the activity is 3.18 × 10³ dpm. Calculate the half-life of phosphorus-32
2. (b) A highly radioactive sample of nuclear waste products with a half-life of 200, years is stored in an underground tank. How long will it take for the activity to diminish from an initial activity of 6.50 × 10¹² dpm to a fairly harmless activity of 3.00 x 10³ dpm?

Interpretation:

Exactly 2 days later, the activity is 3.18×103dpm the half-life of phosphorus-32 has to be calculated.

Concept Introduction:

Radiocarbon dating: The dynamic equilibrium exists in all living organism by exhaling or inhaling, maintain the same ratio of 12C and 14C that takes in. when the living organism dies, the intake of 14C stops and it’s the ratio no longer exhibits equilibrium; undergoes radioactive decay.

Half-life period: The time required to reduce to half of its initial value.

Formula used to calculate half-life:

t1/2= 0.693kwhere, k is rate constant.                     (or)ln[N]t- ln[N]0= -kt

The rate constant in radioactive decay series for Phosphorous-32 is,

Using first order integrated rate law,

ln[AAo] =  - Kt

Here, A = activity

A_o initial activity, k is constant.

By substituting activity value and initial activity in this equation,

ln(3.35×1033.18×103) = k ( 2 days)ln (1

Interpretation:

The time required for the activity to diminish from given initial activity to final  has to be calculated.

Concept Introduction:

Radiocarbon dating: The dynamic equilibrium exists in all living organism by exhaling or inhaling, maintain the same ratio of 12C and 14C that takes in. when the living organism dies, the intake of 14C stops and it’s the ratio no longer exhibits equilibrium; undergoes radioactive decay.

Half-life period: The time required to reduce to half of its initial value.

Formula used to calculate half-life:

t1/2= 0.693kwhere, k is rate constant.                     (or)ln[N]t- ln[N]0= -kt