Question

Radium decays according to the functionQC) - Qewhere Q represents the quantity remaining after tyears and kis the decayconstant 0.00043. How long will take for 40g of radium to decay to 10g?A. Approx. 93 yearsB. Approx 3224 yearsC. Approx 8579 yearsD. Approox. 2144 years

Answer 1

First, we have the next data:

Q(t) = final mass at time t = 10 g

Qo = initial mass = 40 g

v = decay constan = 0.00043 1/years

This kind of process like decay, follow a first-order reaction, and the formula used for this:

`\begin{gathered} Q(t)=Qoxe^(-vxt) \\ \text{Clearing t:} \\ (Q(t))/(Qo)=e^(-vxt) \\ \ln ((Q(t))/(Qo))=-\text{vxt} \\ \frac{\ln ((Q(t))/(Qo))}{-\text{v}}=t \end{gathered}`
`\begin{gathered} \frac{\ln ((10)/(40))}{-0.00043\text{ 1/years}}=\text{ t} \\ \end{gathered}`

Answer: t = 3224 years