NCERT Physics Class 12 Exemplar Ch 13 Nuclei Part 3
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Long Answer
21 Sometimes a radioactive nucleus decays into a nucleus which itself is radioactive. An example is:
Assume that we start with nuclei 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 λ would be .

Then: substituting for pn from Equation (2) into Equation (1),
Since the determinant must be positive for to be real:
Or