Determine the amount of time for polonium-210 to decay to one fourth its original quantity. The half-life of polonium-210 is 138 days.

Question

asked Nov 28, 2020 130k views

1 Answer

Lars Skaug · Answer 1 · 2020-12-04T02:42:42+0000

Answer: 276 days

Step-by-step explanation:

This problem can be solved using the Radioactive Half Life Formula:

$A=A_(o).2^{(-t)/(h)}$ (1)

Where:

A=(1)/(4)A_(o) is the final amount of the material

A_(o) is the initial amount of the material

is the time elapsed

h=138 days is the half life of polonium-210

Knowing this, let's substitute the values and find
from (1):

$(1)/(4)A_(o)=A_(o)2^{(-t)/(138 days)}$ (2)

$(A_(o))/(4A_(o))=2^{(-t)/(138 days)}$ (3)

$(1)/(4)=2^{(-t)/(138 days)}$ (4)

Applying natural logarithm in both sides:

$ln((1)/(4))=ln(2^{(-t)/(138 days)})$ (5)

-1.386=-(t)/(138days)ln(2) (6)

Clearing
:

t=276days (7)