Question

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

kg, how much will remain after 420 days.

Answer 1

`0.625kg`

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