Question

Q) the half life a radioactive isotope x is 50 years. it decays to another element y which is stable . the two elements x and y were found to be in the ratio of 1:5 in a sample of a given rock. the age of the rock was estimated to be ?

Answer 1

Hello! Let me try to answer this :)

Nt = amount of compound after t years
No = start amount of compund
t1/2 = half life

Thanks and please correct if there are any mistakes ^ ^

Answer 2

Answer : The age of the rock was, 129 years

Solution :

As we know that the radioactive decay follow the first order kinetics.

Formula used :

$\frac{N}N_o}=\frac{1}{2}^{\frac{t}{t_{1/2}}}$

by taking 'log' on both side, we get

$\log (\frac{N}{N_o})=\frac{t}{t_{1/2}}\times \log (\frac{1}{2})$

where,

N = amount left after decay process = 1x

$N_o$ = initial amount = 1x + 5x = 6x

t = age of the rock = ?

$t_{1/2}$ = half life of the rock = 50 years

Now put all the given values in the above formula, we get the age of the rock.

$\log (\frac{1x}{6x})=\frac{t}{50years}\times \log (\frac{1}{2})$

$t=129years$

Therefore, the age of the rocks was, 129 years.