Q24.37 P - Chemistry: Molecular Nature Of Matter And Change

Question

If one-trillionth of the atoms of a radioactive isotope disintegrate each day, what is the decay constant of the process?

 

Step-by-Step Solution

Answer

The decay constant is $1\times {10}^{-12}{\text{ day }}^{-1}.$

 

Step 1: Definition of decay constant

The size of a population of radioactive atoms and the pace at which the population diminishes due to radioactive decay are proportionate.

 

Step 2: Calculation of the decay constant

A: represents the activity, the amount of particles that have degraded during time.

N: number of particles

k: decay constant

Every day, one trillionth of the atoms dissolve.

 $A=\frac{1}{1\times {10}^{12}}\text{ decays }/\text{ day .}N$

Now, using this equation, compute the decay constant.

 $\begin{array}{c}A=k\cdot N\\ k=\frac{A}{N}\\ =\frac{\frac{1}{1\times {10}^{12}}\text{ decays }/\text{ day }\cdot N}{ \text{N}}\\ =1\times {10}^{-12}{\text{ day }}^{-1}.\end{array}$

Therefore, the computed value is $1\times {10}^{-12}{\text{ day }}^{-1}.$