Consider a collision between two particles one of which is at rest and the other strikes it head on with momentum `P_(1)`. Calculate the energy of reaction `Q` in terms of the kinetic energy of the particles before and they collide.

Explanation

To solve the problem of calculating the energy of reaction \( Q \) in terms of the kinetic energy of the particles before they collide, we can follow these steps:

### Step 1: Define the Initial Conditions
Let particle 1 with mass \( m_1 \) be moving with momentum \( P_1 \) and particle 2 with mass \( m_2 \) be at rest. The initial kinetic energy \( KE_1 \) of particle 1 can be expressed as:
\[ KE_1 = \frac{P_1^2}{2m_1} \]
The kinetic energy of particle 2 is zero since it is at rest:
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