3. En déduire le nombre et la masse de noyaux de polonium initiaux.
N(t) = N_0 \cdot \exp(-\lambda \cdot t)
N_0 = N(t) \cdot \exp(\lambda \cdot t)
N_0 = N(t) \cdot \exp \bigg(\dfrac{\ln(2) \cdot t}{t_{1/2}}\bigg)
AN : N_0 = {\color{red}\xcancel\color{black}{1{,}63 \times 10^8}} \times \exp \bigg(\dfrac{\ln(2) \times 72}{\color{red}\xcancel\color{black}{138{,}4}}\bigg)
N_0 = \color{red}\xcancel\color{black}{1{,}61 \times 10^8}
La masse initiale de polonium vaut :
m = \dfrac{N_0}{N_{\text{A}}} \cdot M
AN : m = \dfrac{\color{red}\xcancel\color{black}{1{,}61 \times 10^8}}{6{,}02 \times 10^{23}} \times 210 = \color{red}\xcancel\color{black}{5{,}61 \times 10^{23}} g