Law of Radioactive Disintegration — lesson. Science State Board, Class 10.

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The law states that ‘in any radioactive substance, the number of nuclei disintegrating per second is directly proportional to the number of nuclei present’.

$\begin{array}{l} \frac{Δ N}{Δ t} α N \\ \frac{Δ N}{Δ t} = - λ N \end{array}$

Where

$λ$ is the decay constant and

$N$ is the number of nuclei in an atom. The negative sign denotes that the number of nuclei decreases with time.

Half-life period:

The half-life period (

$T$ ) of a radioactive substance is defined as the time during which half the amount of the substance disintegrates.

A statement 'four atoms with a half-life period of

$2\ seconds$ ' means that exactly two atoms will disintegrate approximately after

$2\ seconds$ .

The half-life period (

$T$ ) varies for different substances. The disintegration of a particular atom in a radioactive element is unpredictable. Usually, a smaller value of

$T$ indicates a faster decay.

The decay constant is a characteristic property of a radioactive element. The formula is given as

$Decay constant (λ) = \frac{0.693}{T}$

The higher value of

$λ$ denotes a faster decay.

Let the initial number of radioactive nuclei be

$N_0$ . Consider the number of nuclei present as

$N_0$

$\times \frac{1}{2}$ after a half-life period.

After two half-lives, the number of nuclei would be

$\frac{1}{2} \times (N_{0} \times \frac{1}{2}) = N_{0} {(\frac{1}{2})}^{2}$

After '

$n$ ' half-lives, the number of nuclei would be

$N = N_{0} {(\frac{1}{2})}^{n}$

If '

$t$ ' is the given time period and '

$T$ ' is the half-life period of the radioactive substance, then the value of half-life is

$n = \frac{t}{T}$

If '

$m_o$ ' is the initial mass of the substance and '

$m$ ' the mass of un-decayed nuclei, then

$\frac{N}{N_{0}} = \frac{m}{m_{0}}$

The above equation can be re-written as

$m = m_{0} {(\frac{1}{2})}^{n}$

This equation helps to find the mass of un-decayed particles.

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10. Law of Radioactive Disintegration

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