The nucleus of 
is unstable against 
-decay with a half-life of 
years. Write down the equation of the decay and estimate the kinetic energy of the emitted 
-particle from the following data: 
amu and 
amu.
Text Solution
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).
The equation of the decay is
The energy 
is given by
Using the given data and 
amu , we get 
. This energy is shared by Ra and He. If the original nucleus Th is at rest, i.e. if the momentum of the system before 
-decay is zero, the total momentum after the decay will also be zero. Thus Ra and He will have equal and opposite linear momenta.
Now 
[Using (i)]
i.e. the kinertic energy of He is 56.5 times that of Ra , the total energy being
From eqs (ii) and (iii)
We have K.E. (Ra) 
and K.E. (He) 9.25 MeV .
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