Answer:
a) Two half lives, b) [tex]m(276) = 6.526\,g[/tex]
Step-by-step explanation:
a) The polonium-210 has a half life of 138.4 days. Therefore, 1.994 half lives have past.
b) Mass decay is described by the following exponential model:
[tex]m(t)=m_{o}\cdot e^{-\frac{t}{\tau} }[/tex]
The time constant for the isotope is:
[tex]\tau = \frac{138.4\,days}{\ln 2}[/tex]
[tex]\tau = 199.669\,days[/tex]
The mass of the isotope after 276 days is:
[tex]m(276) = (26\,g)\cdot e^{-\frac{276\,days}{199.669\,days} }[/tex]
[tex]m(276) = 6.526\,g[/tex]
Answer:
Step-by-step explanation:
Given:
t1/2 = 138 days
t = 276 days
No = 26 g
t/t1/2 = 276/138
= 2 half-lifes
N(t) = No × (1/2)^(t/t1/2)
= 26 × (1/2)^2
N(276 days) = 6.5 g
