Question

The half-life for the α decay of uranium is 4.47 × 109 yr. Determine the age (in years) of a rock specimen that contains 55.5% of its original number of atoms.

Answer 1

Answer:
`3.80* 10^9years`

Step-by-step explanation:

Half-life of uranium =
`4.47* 10^9` years

First we have to calculate the rate constant, we use the formula :

`k=\frac{0.693}{4.47* 10^9\text{years}}`

`k=0.155* 10^(-9)\text{years}^(-1)`

Now we have to calculate the age of the sample:

Expression for rate law for first order kinetics is given by:

`t=(2.303)/(k)\log(a)/(a-x)`

where,

k = rate constant =
`0.155* 10^(-9)\text{years}^(-1)`

t = age of sample = ?

a = let initial amount of the reactant = 100

a - x = amount left after decay process =
`(55.5)/(100)* 100=55.5`

Now put all the given values in above equation, we get

`t==(2.303)/(0.155* 10^(-9))\log(100)/(55.5)`

`t=3.80* 10^9years`

Thus the age of a rock specimen that contains 55.5% of its original number of atoms is
`3.80* 10^9years`