Question

The half-life of nickel-63 is 100 years. If a sample of nickel-63 decays until 6.25% of the original sample remains, how much time has passed? *

6.25 years
100 years
400 years
1600 years

Answer 1

400 years

Step-by-step explanation:

The equation that describes the decay of a radioactive sample is:

`m(t)=m_0 ((1)/(2))^{t/t_(1/2)}` (1)

where

m(t) is the amount of sample left at time t

`m_0` is the initial amount of the sample

`t_(1/2)` is the half-life, which is the time taken for the sample to halve

In this problem we have:

`t_(1/2)=100 y` is the half-life of Nickel-63

After a time t, the amount of sample left is 6.25% of the original one, which means that

`(m(t))/(m_0)=(6.25)/(100)`

So we can rewrite the equation (1) and solving for t to find the time:

`(6.25)/(100)=((1)/(2))^{t/t_(1/2)}\\\rightarrow (t)/(t_(1/2))=4\\t=4t_(1/2)=4(100)=400 y`