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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.

User Jay Shukla
by
8.1k points

1 Answer

6 votes

Answer:


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

User Vajapravin
by
8.4k points

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