Question

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.

Answer 1

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

`t` is the time elapsed

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

Knowing this, let's substitute the values and find
`t` 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`:

`t=276days` (7)