Laws of Radioactive Disintegration

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The number of atoms disintegrated per second at any instant is directly proportional to the number of radioactive atoms actually present in the sample at that instant.

If N_o be the total number of atoms at t = 0, N be the total number of atoms left in the sample at time t then dN/dt will be the rate of disintegration.

(-ve sign indicates that the number of atoms left undecayed decreases with time).

(l is decay constant)

Half - Life

Half-life is the time period during which half the number of atoms present initially in the sample of radioactive element decays.

When t = T_½ ; N = N_o/2

The radioactive decay of radium is 1,620 years. The time required to reduce a given quantity of that element by half is 16,200 years. If the initial quantity is 226 grams (which corresponds to 6.02 x 10^-11 atoms), after 129,600 years only one atom will remain.

Average Life or Mean Life

Not all atoms of a given sample disintegrate together. Some atoms disintegrate right in the beginning for which the lifetime is zero. Therefore the lifetime of atoms, which disintegrate in between, ranges from zero to infinity.

Definition -Average Life or Mean Life

The total lifetime of all the atoms of the element divided by the total number of atoms present initially in the sample of the element.

Alpha, Beta and Gamma Decay

Radioactive nuclei being unstable, emit radiations to achieve states of greater stability.

Alpha Decay

Alpha decay is the phenomenon of emission of an a-particle from radioactive nucleus.

The result of alpha decay is that a new element is produced with proton number of two below its parent in the periodic table.

Beta Decay

A phenomenon of emission of an electron from a radioactive nucleus.

Experiments show that energy of emitted electron varies continuously from zero to maximum value, which was contrary to a-decay, whose energy was fixed. To account for this Wolf Gang Pauli postulated the existence of an uncharged particle antineutrino, along with b-particle and the whole energy Q is shared by b-particle and antineutrino. This explained why the energy of the electron was not fixed.

Gamma Decay

Gamma decay is the phenomenon of emission of gamma ray photon from a radioactive nucleus.

When an excited nucleus makes a transition to a state of lower energy, photons are emitted by nuclei, which have very large energies (about Me) and correspondingly short wavelength. There is no change in the charge number or mass number unlike in a and b-decay.

e.g., b decay of ₂₇Co⁶⁰ transforms to an excited state of ₂₈Ni⁶⁰. It reaches the ground state by emission of two g rays as shown

Applications

(i) Radioactive dating

This gives us an approximate age of the rock or material containing the radioactive atoms. For e.g., A measurement of a fraction of uranium atom which have decayed into lead (by knowing the half life of uranium) tells us how old the rock is.

(ii) Radiation from space converts nitrogen in the atmosphere into radioactive nuclide of carbon C-14. This tells us how long ago something died.

(iii) There are many radioactive isotopes which can be prepared artificially in a nuclear reactor. These radio isotopes find many uses in medicine to diagnose as well as to treat diseases.

(iv) Industries use radioactive isotopes as tracers which when added to a fluid in a pipeline can measure the flow rate in the pipeline and detect leaks. This is because of the gamma radiation passing through the pipeline which can be detected.

(v) Tracers are used in agriculture to measure the uptake of nutrients by plants from the fertilizers in the soil.

(vi) Sheets of plastic, paper and metal of accurate thickness are manufactured by sending radiation from a radio isotope. By measuring the intensity of radiation passing through the sheets with the help of a detector the variation in the sheet thickness can be checked and adjusted.