A nucleus at rest undergoes a decay emitting an a particle of de - Broglie wavelength ` lambda = 5.76 xx 10^(-15)m ` if the mass of the daughter nucleus is 223.610 amu and that of alpha particle is `4.002amu` , determine the total kinetic energy in the final state Hence , obtain the mass of the parent nucleus in amu (1 amu = 931.470 `MeV//e^(2)`)

Explanation

To solve the problem step-by-step, we will first determine the total kinetic energy of the final state after the decay of the parent nucleus and then calculate the mass of the parent nucleus.

### Step 1: Calculate the momentum of the alpha particle
The de Broglie wavelength \(\lambda\) of the alpha particle is given as:
\[ \lambda = 5.76 \times 10^{-15} \, \text{m} \]
Using the de Broglie relation:
...