Question

The isotope radium-226 decays into radon-222, with a half-life of around 1,600 years. If a rock contained 6 grams of radium-226 when it reached its closure temperature but only 0.375 grams when it was discovered, which two statements about the rock are true?

A] The rock reached its closure temperature 6,400 years ago.
B] The rock reached its closure temperature 4,800 years ago.
C]The rock had 2.625 grams of radon-222 1,600 years ago.
D]When the rock was discovered, it had 5.625 grams of radon-222.
E]When the rock was discovered, it had 3.375 grams of radon-222.

Answer 1

A and D is the answer

Answer 2

Answer : The correct option is, (A) The rock reached its closure temperature 6,400 years ago.

Explanation :

Half-life = 1600 years

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

`k=(0.693)/(t_(1/2))`

`k=\frac{0.693}{1600\text{ years}}`

`k=4.33* 10^(-4)\text{ years}^(-1)`

Now we have to calculate the time passed.

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

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

where,

k = rate constant =
`4.33* 10^(-4)\text{ years}^(-1)`

t = time passed by the sample = ?

a = initial amount of the reactant = 6 g

a - x = amount left after decay process = 0.375 g

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

`t=(2.303)/(4.33* 10^(-4))\log(6)/(0.375)`

`t=6404.36\text{ years}\approx 6400\text{ years}`

Therefore, the correct option is, (A) The rock reached its closure temperature 6,400 years ago.