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.....