Question

Uranium-238 decays very slowly.its half-life is 4.47 billion years.

What percentage of a sample of Uranium-238 will remain after 13.4 billion years?


i have to test after 3 days!!!!!

Answer 1

13.4 billion years is 3 times of the half-life, 4.47 billion years. So the Uranium-238 will go through three times of half decay. So the remain percentage will be 50%*50%*50%=12.5%.

Answer 2

12.53 % of a sample of Uranium-238 will remain after 13.4 billion years.

Step-by-step explanation:

The half life of the uranium-238 =
`t_{(1)/(2)}`=4.47 billion years

All the radioactive reaction are of first order kinetics. The rate constant and t half of the reaction are related as:

`k=\frac{0.693}{t_{(1)/(2)}}=\frac{0.693}{4.47 \text{billion years}}=0.1550 (\text{billion years})^(-1)`

`k=(2.303)/(t)\log([A_o])/([A])`

where,

k = rate constant =
`0.1550 (\text{billion years})^(-1)`

t = time taken during radio decay = 4.47 billion years

`[A_o]` = initial amount of the reactant =
`1.45* 10^(-6)mol/L`

[A] = amount left left after time t.

`\log ([A])/([A_o])=-(kt)/(2.303)`

`([A])/([A_o])=0.1253=(12.53)/(100)=12.53\%`

12.53 % of a sample of Uranium-238 will remain after 13.4 billion years.