Under the same reaction conditions, initial concentration of 1.386 mol dm$$^{-3}$$ of a substance becomes half in 40 seconds and 20 seconds through first order and zero order kinetics, respectively. Ratio $$\left( {{{{k_1}} \over {{k_0}}}} \right)$$ of the rate constants for first order ($$k_1$$) and zero order ($$k_0$$) of the reactions is:

Carbon-14 is used to determine the age of organic material. The procedure is based on the formation of ${ }^{14} \mathrm{C}$ by neutron capture in the upper atmosphere.

$$ { }^{14} \mathrm{~N}+{ }_0^1 n \rightarrow{ }_6{ }^{14} \mathrm{C}+{ }_1^1 \mathrm{H} $$

${ }^{14} \mathrm{C}$ is absorbed by living organisms during photosynthesis. The ${ }^{14} \mathrm{C}$ content is constant in living organism once the plant or animal dies, the uptake of carbon dioxide by it ceases and the level of ${ }^{14} \mathrm{C}$ in the dead being, falls due to decay which ${ }^{14} \mathrm{C}$ undergoes.

$$ { }_6^{14} \mathrm{C} \rightarrow{ }_7^{14} \mathrm{~N}+\beta^{-} $$

The half-life period of ${ }^{14} \mathrm{C}$ is 5770 years. The decay constant ( $\lambda$ ) be calculated by using the following formula $\lambda=\frac{0.693}{t_{1 / 2}}$.

The comparison of the $\beta^{-}$activity of the dead matter with that of the carbon still in circulation enables measurement of the period of the isolation of the material from the living cycle. The method however, ceases to be accurate over periods longer than 30,000 years. The proportion of ${ }^{14} \mathrm{C}$ to ${ }^{12} \mathrm{C}$ in living matter is $1: 10^{12}$.

Which of the following option is correct?

Carbon-14 is used to determine the age of organic material. The procedure is based on the formation of ${ }^{14} \mathrm{C}$ by neutron capture in the upper atmosphere.

$$ { }^{14} \mathrm{~N}+{ }_0^1 n \rightarrow{ }_6{ }^{14} \mathrm{C}+{ }_1^1 \mathrm{H} $$

${ }^{14} \mathrm{C}$ is absorbed by living organisms during photosynthesis. The ${ }^{14} \mathrm{C}$ content is constant in living organism once the plant or animal dies, the uptake of carbon dioxide by it ceases and the level of ${ }^{14} \mathrm{C}$ in the dead being, falls due to decay which ${ }^{14} \mathrm{C}$ undergoes.

$$ { }_6^{14} \mathrm{C} \rightarrow{ }_7^{14} \mathrm{~N}+\beta^{-} $$

The half-life period of ${ }^{14} \mathrm{C}$ is 5770 years. The decay constant ( $\lambda$ ) be calculated by using the following formula $\lambda=\frac{0.693}{t_{1 / 2}}$.

The comparison of the $\beta^{-}$activity of the dead matter with that of the carbon still in circulation enables measurement of the period of the isolation of the material from the living cycle. The method however, ceases to be accurate over periods longer than 30,000 years. The proportion of ${ }^{14} \mathrm{C}$ to ${ }^{12} \mathrm{C}$ in living matter is $1: 10^{12}$.

What should be the age of fossil for meaningful determination of its age?