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 : 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 :

Now we have to calculate the time passed.

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

where,

k = rate constant  =

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

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

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