An isolated nucleus which was initially at rest, disintegrates into two nuclei due to internal nuclear forces and no `gamma` rays are produced. If the ratio of their kinetic energy is found to be `64/27`, then

Options

A. Ratio of their de-broglie wavelength is `(sqrt(64))/(sqrt(27))` respectively
B. Ratio of their speed is 64/27 respectively
C. Ratio of their nuclear radius is 5/4 respectively
D. None of these

Explanation

To solve the problem step by step, we will analyze the disintegration of the isolated nucleus into two smaller nuclei, taking into account the conservation of momentum and kinetic energy.

### Step 1: Understand the conservation of momentum
Since the nucleus is initially at rest, the total momentum before disintegration is zero. After disintegration, the momentum of the two nuclei must also sum to zero. If we denote the momenta of the two nuclei as \( P_1 \) and \( P_2 \), we can write:
\[ P_1 + P_2 = 0 \]
This implies:
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