define decay constant of a radioactive element

Radioactivity is a spontaneous process which does not depend upon external factors like temperature, pressure etc i.e radioactive element is in a state of disintegration which depends upon law of chance. It means it is impossible to predict which particular atom of the radioactive element will disintegrate in a given time interval.

During disintegration of an atom either an, alpha particle or a beta particle is emitted. Both these particles are never emitted simultaneously. Also at a time, an atom will not emit more than one alpha particle or more than one beta particle.

The emission of an alpha particle from an atom will change it into a new atom whose charge number is reduced by 2 and mass number is reduced by 4.

The emission of a beta particle from an atom will change it into a new atom whose charge number is raised by 1,without any change in its mass number.

RADIOACTIVE DECAY LAW:-

The number of atoms disintegrated per second ( ie rate of disintegration of radioactive atom) at any instant is directly proportional to the number of radioactive atoms actually present in the sample at that instant.

Let N0=total number of atoms present originally at time (t)=0.

N=total number of atoms left undecayed at time t.

dN=small number of atoms that disintegrate in small interval of time dt.

Rate of disintegration R =-dN/dt=λN

We get the radioactive decay law as :

N = N0e-λt.....

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