Question

Hydrogen-3 has a half-life of 12.32 years. A sample of H-3 weighing 3.02 grams is left for 15.0 years. What will the final weight of the H-3 sample be?

Answer 1

Answer: n = 1.30g

Step-by-step explanation:

Answer 2

`\large \boxed{\text{1.38 g}}`

Step-by-step explanation:

Two important formulas in radioactive decay are

`(1) \qquad t_{(1)/(2)} = (\ln 2)/(k)\\\\(2) \qquad \ln \left((N_(0))/(N)\right) = kt`

1. Calculate the decay constant k

`\begin{array}{rcl}t_{(1)/(2)} &=& (\ln 2)/(k)\\\\\text{12.32 yr} &= &(\ln 2)/(k)\\\\k & = & \frac{\ln 2}{\text{12.32 yr}}\\\\& = & \text{0.056 26 yr}^(-1)\\\end{array}`

2. Calculate the mass remaining

`\begin{array}{rcl}\ln \left((A_(0))/(A)\right) &= &kt \\\\\ln \left(\frac{\text{3.20 g}}{A}\right) &= &\text{0.056 26 yr}^(-1)* \text{15 yr} \\\\\ln \left(\frac{\text{3.20 g}}{A}\right) &= &0.8439 \\\\\frac{\text{3.20 g}}{A} &= &e^(0.8439) \\\\\frac{\text{3.20 g}}{A}&= &2.325 \\\\A &= &\frac{\text{3.20 g}}{2.325}\\\\&= & \textbf{1.38 g}\\\end{array}\\\text{The final mass of the sample will be $\large \boxed{\textbf{1.38 g}}$}`