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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.

2 Answers

2 votes
A and D is the answer
User HAK
by
8.7k points
5 votes

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.

User Eugene Talagrand
by
8.5k points
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