Q.5.33 - An Introduction to General, Organic, and Biological Chemistry

Question

Strontium-85, used for bone scans, has a half-life of 65 days.

a. How long will it take for the radiation level of strontium-85 to drop to one-fourth of its original level?

b. How long will it take for the radiation level of strontium- 85 to Radiation level to drop to one-eighth of its original level? 

Step-by-Step Solution

Answer

Part (a).$130$days

Part (b).$195$days 

Step 1: Given Information (Part a)

Half-life is the time expected for an amount to decrease to half of its underlying worth. The term is ordinarily utilized in atomic physical science to portray how rapidly unsteady particles go through radioactive rot or how long stable iotas get by.

Step 2: Explanation Part (a)

Given,

Strontium- $85$ has a half-life of $65$ days

Radiation level =$0.25$

Half-lives =${\left(\frac{1}{2}\right)}^{\mathrm{n}}=0.25$

$=\mathrm{n} \log 0.5=\log \left(0.25\right)$

$=n=2$

Time taken for the radiation level of strontium-$85$ to drop to one-fourth of its original level is,

$2\times 65=130$days

Step 3: Explanation Part (b)

Given,

Strontium-$85$ has a half-life of $65$days

The radiation levels drop to one-eighth of their original level = $\frac{1}{8}=0.125$

Half lifes = ${\left(\frac{1}{2}\right)}^{\mathrm{n}}=0.125=\log 0.5=\log \left(0.125\right)$

$n=3$

Time taken for the radiation level of strontium-$85$ to drop to one-eighth of its original level is,

$3\times 65=195$days