Question

The initial mass of a radioactive substance becomes $1/16$th in $80$minutes. Find the half-life.

Answer 1

Radioactive substance

• Explanation: Carbanions are derived formally from neutral organic molecules by removing positively charged atoms or groups of atoms, and they are important primarily as chemical intermediates or substances used in the preparation of other substances. The primary difference between a carbocation and a carbanion is that a carbocation has a positively charged carbon atom, whereas a carbanion has a negatively charged carbon atom.
• ${\left[\mathrm{A}\right]}_t={\left[\mathrm{A}\right]}_0/2^{\mathrm{n}}$
• ${\left[\mathrm{A}\right]}_t$ is the concentration at the time $\mathrm{t}.$
• ${\left[\mathrm{A}\right]}_0$ is the initial concentration
• $\mathrm{n}$ is the number of half-lives

Given:

${\left[\mathrm{A}\right]}_t=\frac{{\left[A\right]}_0}{16}$

$\frac{1}{2^{\mathrm{n}}}=\frac{1}{16}$

$\mathrm{n}=4$

• It takes$80$ minutes to complete $4$half-lives.
• The time required for one half-life is$80/4\min$. or $20\min .$
• So, the half-life is$20\mathrm{minutes}.$