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