A neutron with kinetic energy K=10 MeV activates a nuclear recation,`n+ ^(12)C rarr ^(9)Be +alpha` whose threshold `E_(th)=6.17 MeV` .Find the kinetic energy of the alpha particles outgoing at right angles to the direction of the incoming neutron.[Take `mu=931.1 MeV`]

Explanation

To solve the problem step by step, we will use the principles of conservation of energy and conservation of momentum.

### Step 1: Understand the Reaction and Given Data
We have a neutron (n) with kinetic energy \( K = 10 \, \text{MeV} \) colliding with a carbon-12 nucleus \( ^{12}\text{C} \) at rest. The reaction is:
\[ n + ^{12}\text{C} \rightarrow ^{9}\text{Be} + \alpha \]
The threshold energy for this reaction is given as \( E_{th} = 6.17 \, \text{MeV} \).

### Step 2: Calculate the Q-value of the Reaction
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