Respuesta :
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 [tex] 1/2^{3} [/tex] = 1/8 mg= 0.125mg.
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 [tex] 1/2^{3} [/tex] = 1/8 mg= 0.125mg.
A 1 mg sample of americium becomes [tex]\boxed{0.125{\text{ mg}}}[/tex] 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:
[tex]{{\text{A}}_{\text{0}}} = {{\text{A}}_{\text{t}}}{\left( 2 \right)^{\text{n}}}[/tex] …… (1)
Here,
[tex]{{\text{A}}_{\text{t}}}[/tex] is the final amount of substance.
[tex]{{\text{A}}_{\text{0}}}[/tex] is the initial amount of substance.
n is the number of half-lives.
Rearrange equation (1) for [tex]{{\text{A}}_{\text{t}}}[/tex].
[tex]{{\text{A}}_{\text{t}}} = \left( {\dfrac{{\text{1}}}{{{{\left( 2 \right)}^{\text{n}}}}}} \right)\left( {{{\text{A}}_{\text{0}}}} \right)[/tex] …… (2)
The value of [tex]{{\text{A}}_{\text{0}}}[/tex] is 1 mg.
The value of n is 3.
Substitute 1 mg for [tex]{{\text{A}}_{\text{0}}}[/tex] and 3 for n in equation (2) to calculate the amount of americium.
[tex]\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}[/tex]
Therefore 0.125 mg of americium remains after 3 half-lives.
Learn more:
- Find the age of the fabric: https://brainly.com/question/8716136
- Which nuclear emission is negatively charged? https://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.
