\(^{60}_{27}Co\rightarrow^{60}_{28}Ni+^0_{-1}e\)
\(^{60}_{28}Ni\rightarrow^{58}_{28}Ni+^2_0e\)
Sau t(s) \(\dfrac{m_{Ni}}{m_{Co}}=0,9\)
\(H_0=\dfrac{ln\left(2\right)}{T}.\dfrac{m_0}{60}.6,02.10^{23}\Leftrightarrow3,7.10^{11}=\dfrac{ln\left(2\right)}{5,33.365.24.60.60}.\dfrac{m_0}{60}.6,02.10^{23}\\ \Rightarrow m_0=8,9.10^{-3}\left(kg\right)=8,9\left(g\right)\)
\(m_{Co}=m_0.e^{-kt}\)
Số nguyên tử Ni sinh ra bằng số nguyên tử Co phân rã.
\(m_{Ni}=\dfrac{N_{Ni}}{N_A}.60=\dfrac{N_0}{N_A}.\left(1-e^{-kt}\right).60\\ m_{Co}=\dfrac{N_0}{N_A}.e^{-kt}.60\)
\(\Rightarrow\dfrac{1-e^{-kt}}{e^{-kt}}=0,9\Rightarrow\dfrac{1-e^{-5,33t}}{e^{-5,33t}}=0,9\\ \Rightarrow t=0,12\left(năm\right)\)
