24.138 CP - Chemistry: Molecular Nature Of Matter And Change

Question

Assuming that many radioactive nuclides can be considered safe after 20 half-lives, how long will it take for each of the following nuclides to be safe: 

(a) ²⁴²cm(t_1/2=163 days); 

(b) ²¹⁴Po_o($t_{\frac{1}{2}}=1.6\times {10}^{-4}\sec$); 

(c) ²³²Th($t_{\frac{1}{2}}=1.39\times {10}^{10}yr$)?

Step-by-Step Solution

Answer

(a) The time taken by ²⁴²cm nuclide to be safe is 3260 days.

(b) The time taken by ²¹⁴Po_o nuclide to be safe is $3.2\times {10}^{-3} \sec$.

(c) The time taken by ²³²Th nuclide to be safe is $2.78\times {10}^{11} yr$.

Step 1: Definition of Radioactive Nuclide

A radionuclide (radioactive nuclide, radioisotope, or radioactive isotope) is an unstable nuclide with too much nuclear energy.

This extra energy can be expelled as gamma radiation from the nucleus, transferred to one of its electrons, released as a conversion electron, or used to build and emit a new particle (alpha or beta particle) from the nucleus.

Step 2: Explanation for determining the time each nucleus takes.

To determine the time, it takes for each of the following nuclides to be safe, we will multiply the given half-lives by 20.

a. ²⁴²cm 

$$\begin{gathered} t_{\frac{1}{2}}=163days \\ 163days\left(20\right)=3260days \end{gathered}$$

 

b. ²¹⁴Po_o 

$$\begin{gathered} t_{\frac{1}{2}}=1.6x{10}^{-4}\sec \\ 1.6x{10}^{-4}\sec \left(20\right)=3.2\times {10}^{-3}\sec \end{gathered}$$

c. ²³²Th

$$\begin{gathered} t_{\frac{1}{2}}=1.39x{10}^{10}yr \\ 1.39x{10}^{10}yr\left(20\right)=2.78\times {10}^{11} yr \end{gathered}$$