# Laws of Radioactive Disintegration

Rutherford and his co-workers made experimental study of the radioactive decay of various radioactive substances and gave the following laws:

- Radioactivity is a spontaneous process which is not affected by physical factors such as temperature, pressure etc. It depends upon chances to occur.
- In a radioactive decay either α-particle or β-particle is emitted by an atom. Emission of both particles is not possible by a single atom simultaneously.
- The rate of decay is directly proportional to the number of atoms present in the sample. If N be the number of atoms present in a sample then,

$$\frac{dN}{dt} \propto N$$

$$or, \frac{dN}{dt} = -\lambda N$$

$$\frac{dN}{N} = -\lambda dt$$

Where ‘λ’ is the proportionality constant known as decay constant. The negative sign suggests that number of atom is decreasing with increase n time.

$$\text{On integration}, \int\frac{dN}{N}= \int -\lambda dt$$

$$or, Log_eN = -\lambda t + c……(i)$$

At t = 0, N = N_{0 }(initial number of atoms)

$$or, Log_eN_o = -\lambda \times 0 + c$$

$$\therefore C = Log_eN_o……(ii)$$

Putting this value of c in equation (i), we get:

$$Log_eN = -\lambda t + Log_eN_o$$

$$or, Log_eN – Log_eN_o = -\lambda t$$

$$or, Log_e\frac{N}{N_o} = -\lambda t$$

$$or, \frac{N}{N_o} = e^{-\lambda t}$$

$$N = N_oe^{-\lambda t}…..(iii)$$

Equation (iii) is called decay equation.

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## 2 Responses to “Laws of Radioactive Disintegration”

very good but brief.

should be elaborate to capture all areas in radioactivity.