Question

Half-life of Po-210 is 140 days. If the initial mass of the sample is 5

Answer 1

Answer:

$0.625kg$

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

$\displaystyle f(t) = a {0.5}^{t/T}$

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:

$\displaystyle f(420)=5\cdot{0.5}^{420/140}$

reduce fraction:

$\displaystyle f(420)=5\cdot{0.5}^{3}$

By using calculator we acquire:

$\displaystyle f(420)=0.625$

hence, the remaining sample after 420 days is 0.625 kg