Respuesta :

[tex]\bf \textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\to &80\\ t=\textit{elapsed time}\to &140\\ h=\textit{half-life}\to &35 \end{cases} \\\\\\ A=80\left( \frac{1}{2} \right)^{\frac{140}{35}}\implies A=80\left( \frac{1}{2} \right)^4[/tex]

At the end of 140 hours, 3.151mL of the sample will remain in the flask.

Data;

  • Half-Life = 35 hours
  • Initial volume = 80mL
  • Time = 140 hours

Half-Life

To solve this problem, we need to find the disintegration constant which we can use the formula of half-life to do so.

[tex]T_\frac{1}{2} = \frac{\ln2}{\lambda}[/tex]

Let's substitute the values and solve.

[tex]T_\frac{1}{2} = \frac{\ln2}{\lambda}\\\lambda = \frac{\ln2}{t_\frac{1}{2} }\\ \lambda = \frac{0.693}{35} \\\lambda = 0.0231 hr^-^1[/tex]

The formula of radioactivity is given as

[tex]N = N_0 e^-^\lambda^*^t\\[/tex]

Let's substitute the values and solve.

[tex]N = N_0 e^-^\lambda^*^t\\\\N = 80 * e^-^(^0^.^0^2^3^1^*^1^4^0^)\\N = 80 * e^-^3^.^2^3^4\\N = 80 * 0.039399\\N = 3.151[/tex]

At the end of 140 hours, 3.151mL of the sample will remain in the flask.

Learn more on radioactivity here;

https://brainly.com/question/1748389

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