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NCERT Physics Class 12 Exemplar Ch 13 Nuclei Part 3
Long Answer
21 Sometimes a radioactive nucleus decays into a nucleus which itself is radioactive. An example is:
Assume that we start with snuclei at time . The number of is of count zero at and will again be zero at . At what value of t, would the number of counts be a maximum?
Ans:
At time t, Let have active nuclei and have active nuclei.
But
Multiplying by and rearranging
Integrating both sides.
Since at
For maximum count,
On solving,
22 Deuteron is a bound state of a neutron and a proton with a binding energy . A -ray of energy E is aimed at a deuteron nucleus to try to break it into a (neutron + proton) such that the n and p move in the direction of the incident -ray. If , show that this cannot happen. Hence calculate how much bigger than B E must be for such a process to happen.
Ans:
- From conservation of energy
- From conservation of momentum
- If , the first equation gives and hence the second equation cannot be satisfied, and the process cannot take place.
- For the process to take place, Let , where Ξ» would be .
- Then: substituting for pn from Equation (2) into Equation (1) ,
- Since the determinant must be positive for to be real:
Or