Answer:
[tex]0.625kg[/tex]
Step-by-step explanation:
we are given half-life of PO-210 and the initial mass
we want to figure out the remaining mass after 420 days
in order to solve so we can consider the half-life formula given by
[tex] \displaystyle f(t) = a {0.5}^{t/T} [/tex]
where:
- f(t) is the remaining quantity of a substance after time t has elapsed.
- a is the initial quantity of this substance.
- T is the half-life
since it halves every 140 days our T is 140 and t is 420. as the initial mass of the sample is 5 our a is 5
thus substitute:
[tex]\displaystyle f(420)=5\cdot{0.5}^{420/140}[/tex]
reduce fraction:
[tex]\displaystyle f(420)=5\cdot{0.5}^{3}[/tex]
By using calculator we acquire:
[tex]\displaystyle f(420)=0.625[/tex]
hence, the remaining sample after 420 days is 0.625 kg
