Question

The half-life for beta decay of strontium-90 is 28.8 years. A milk sample is found to contain 10.3 ppm strontium-90. How many years would pass before the strontium-90 concentration would drop to 1.0 ppm? The half-life for beta decay of strontium-90 is 28.8 years. A milk sample is found to contain 10.3 ppm strontium-90. How many years would pass before the strontium-90 concentration would drop to 1.0 ppm? 131 96.9 0.112 92.3 186

Answer 1

96.9 years would pass before the strontium-90 concentration would drop to 1.0 ppm.

Step-by-step explanation:

Given that:

Half life = 28.8 years

`t_(1/2)=\frac {ln\ 2}{k}`

Where, k is rate constant

So,

`k=\frac {ln\ 2}{t_(1/2)}`

`k=\frac {ln\ 2}{28.8}\ years^(-1)`

The rate constant, k = 0.024067 years⁻¹

Using integrated rate law for first order kinetics as:

`[A_t]=[A_0]e^(-kt)`

Where,

`[A_t]` is the final concentration= 1.0 ppm

`[A_0]` is the initial concentration = 10.3 ppm

Time = ?

So,

`(1.0)/(10.3)=e^(-0.024067* t)`

`\ln \left((1)/(10.3)\right)=-0.024067t`

`t=(\ln \left(10.3\right))/(0.024067)\ years`

t = 96.9 years

96.9 years would pass before the strontium-90 concentration would drop to 1.0 ppm.