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Unstable pions are produced as a beam in...

Unstable pions are produced as a beam in a nuclear reaction experiment . The pions leave the target at a speed of 0.995c. The intensity of the beam reduces to half its original value as the beam travels a distance of 39 m . Find the half - life of pions (a) in the laboratory frame, (b) in their rest frame.

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To solve the problem step by step, we will break it down into two parts: (a) finding the half-life of pions in the laboratory frame and (b) finding the half-life in their rest frame. ### Part (a): Half-life in the Laboratory Frame 1. **Identify the given values:** - Speed of pions, \( v = 0.995c \) - Distance traveled, \( d = 39 \, \text{m} \) - Speed of light, \( c = 3 \times 10^8 \, \text{m/s} \) ...
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