Question

2) The mass of a radioactive element decays at rate given by m(t) = m0e^-rt, where m(t) is the mass at any time t, m0 is the initial mass, and r is the rate of decay.Uranium-240 has a rate of decay of .0491593745. What is the mass of U-240 left after 10 hours, if the initial mass is 50 grams? (Use e = 2.71828.]A) 28.54387 gB) 30.58254 gC) 32.14286 gD) 32.68034 g

Answer 1

Solution

- We are given the following formula:

$\begin{gathered} m(t)=m_0e^{-rt} \\ \text{where,} \\ r=\text{decay rate} \\ t=\text{time} \\ m_0=\text{ Initial mass} \\ m=\text{mass after time t} \end{gathered}$

- We are told that the Initial mass is 50g, the decay rate is .0491593745, time (t) is 10 hours, and e = 2.71828.

- With the above information, we can proceed to substitute the values given into the formula and get the mass of Uranium after 10 hours.

- This is done below:

$\begin{gathered} m=50\times2.71828^{-(0.0491593745)\times10} \\ \\ m=50\times0.611651003817 \\ \\ \therefore m=30.5825\ldots\approx30.58254g \end{gathered}$

Final Answer

The answer is 30.58254g (OPTION B)