Question

Radioactive elements such as radon (Radon 222), thoron (Radon 220) and their by-products

formed by the decay of radium (Radium 226) and thorium present in many sorts of rocks,

other building materials and in the soil. Prove that product formed by these elements follow

λt = ln (No/N) equation and their half-life independent of concentration.

Answer 1

The equation $\lambda\>t=In(\frac{N_0}{N})$ is an integrated rate law and is used for determining the reaction order.

Rearranging the equation

$In(N)=-\lambda\>t+In(N_0)$

A plot of In (N) versus time is a linear graph with a negative slope

The reaction must be a first-order reaction .The reaction rate depend on the number of undecayed nuclei present.

The half life of radioactivity is a constant and is independent of concentration of parent nuclide.

Half life t_½ is when $N= \frac{N_0}{2}$

$\lambda t_{½}=In\frac{N_O}{\frac{N_0}{2}}=In 2$

Therefore t_½ is independent of N but it is a constant.

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