Answer to Question #108496 in Atomic and Nuclear Physics for Gifty

Question

Half life period of U234 is 2.5×105 years. In how many years it will remain 25% of original amount?

Answer 1

$N_0$ - initial amount of U234

$N=0.25 \times N_0$ - final amount of U234

$T=2.5 \times 10^5 \text{ years}$ - half life period

We can use the fact that

$$N=N_0 \Big( {1\over 2}\Big)^{\frac{t}{T}}$$

$N=0.25\times N_0=N_0 \Big( {1\over 2}\Big)^{\frac{t}{T}} \ \Rightarrow 0.25= \Big( {1\over 2}\Big)^{\frac{t}{T}} , \ \Big( {1\over 2}\Big)^2=\Big( {1\over 2}\Big)^{\frac{t}{T}} \ \Rightarrow 2=\frac{t}{T}$

$t=2T=5.0 \times 10^5 \text{ years}$

Answer: in $5\times 10^5$ years it will remain 25% of original amount.