Question

How much of a 1.00 mg sample of americium remains after 3 half-lives?

Answer 1

Answer: 0.125mg americium

Half-lives is a set of duration when a sample will become half of their original mass. In this case, the initial mass is 1mg and the sample is going for 3 times half-lives. Then the calculation would be: 1mg $1/2^{3}$ = 1/8 mg= 0.125mg.

Answer 2

A 1 mg sample of americium becomes $\boxed{0.125{\text{ mg}}}$ after 3 half-lives.

Further Explanation:

The process in which an unstable nucleus releases energy in the form of different particles like alpha particles, beta particles, and gamma particles is termed as radioactivity.

Half-life

As is evident from its name, it is the time after which the amount of radioactive substances becomes half of its original amount. It is represented by  .

The expression to calculate the amount of substance is as follows:

${{\text{A}}_{\text{0}}} = {{\text{A}}_{\text{t}}}{\left( 2 \right)^{\text{n}}}$                                                                               …… (1)

Here,

${{\text{A}}_{\text{t}}}$ is the final amount of substance.

${{\text{A}}_{\text{0}}}$ is the initial amount of substance.

n is the number of half-lives.

Rearrange equation (1) for ${{\text{A}}_{\text{t}}}$.

${{\text{A}}_{\text{t}}} = \left( {\dfrac{{\text{1}}}{{{{\left( 2 \right)}^{\text{n}}}}}} \right)\left( {{{\text{A}}_{\text{0}}}} \right)$     …… (2)                                                                                

The value of ${{\text{A}}_{\text{0}}}$ is 1 mg.

The value of n is 3.

Substitute 1 mg for ${{\text{A}}_{\text{0}}}$ and 3 for n in equation (2) to calculate the amount of americium.

$\begin{aligned}{{\text{A}}_{\text{t}}}&= \left( {\frac{{\text{1}}}{{{{\left( 2\right)}^{\text{3}}}}}} \right)\left( {{\text{1 mg}}} \right)\\&=\left( {\frac{1}{8}} \right)\left( {1{\text{ mg}}} \right)\\&= 0.125{\text{ mg}}\\\end{aligned}$  

Therefore 0.125 mg of americium remains after 3 half-lives.

Learn more:

1. Find the age of the fabric: brainly.com/question/8716136
2. Which nuclear emission is negatively charged? brainly.com/question/2261727

Answer details:

Grade: Senior School

Chapter: Nuclear chemistry

Subject: Chemistry

Keywords: half-life, 1 mg, 0.125 mg, americium, n, 3 half-lives, radioactivity, unstable nucleus, t1/2, substance, initial amount, final amount, number of half-lives, alpha particles, beta particles, gamma particles, energy, half, amount of substance, original amount.