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

Answer:

400 years

Explanation:

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

$m(t)=m_0 (\frac{1}{2})^{t/t_{1/2}}$ (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

$\frac{m(t)}{m_0}=\frac{6.25}{100}$

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

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