Respuesta :
The decay of this radioactive unknown compound is a first-order process.
We can express the time dependence of its mass m using a first-order integrated rate law, where k is the rate constant:
[tex]m_t=m_0xe^{-kxt}[/tex]mt = mass at time t
m0 = initial mass
t = time
-----------------------------------------------------------------------------------------------------
Procedure:
1) We need to find "k":
From the first-order rate law we clear k,
[tex]\begin{gathered} \frac{m_t}{m_0}=\text{ }e^{-kxt} \\ \ln (\frac{m_t}{m_0})=\text{ -kxt} \\ \frac{\ln (\frac{m_t}{m_0})}{-t}=\text{ k} \end{gathered}[/tex][tex]k\text{ = }\frac{\ln (\frac{86.96ng}{695.7ng})}{-47}=0.044days^{-1}\text{ }[/tex]----------------------------------------------------------------------------------------------
2) We find the half-life from the value of k we have just calculated:
[tex]t_{\frac{1}{2}}=\text{ }\frac{\ln 2}{k}=\text{ }15.7\text{ days}[/tex]-----------------------------------------------------------------------------------------------
3) The number of half-lives of the unknown sample is:
Number of Half-lives = 47 days / 15.7 days = 3 (approx.)
Answer: Number of half-lives = 3
