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Question
0 3. The ºlifetime has been determined by studying the decy.om rest of the K+ meson in the mode K+ →° ++. The average distance travelled by the Tºin a block of photographic emulsion before it decays in the easily observable mode nº→ е+ + e +y is measured, and from the calculated velocity of flight of the its lifetime is obtained. Given that its lifetime is 0.8x10-¹6 sec, predict the average distance travelled by a zºbefore it decays. (Hint: you may assume that the pions have an average mass of 137 MeV;
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Transcribed Image Text:0 3. The ºlifetime has been determined by studying the decy.om rest of the K+ meson in the mode K+ →° ++. The average distance travelled by the Tºin a block of photographic emulsion before it decays in the easily observable mode nº→ е+ + e +y is measured, and from the calculated velocity of flight of the its lifetime is obtained. Given that its lifetime is 0.8x10-¹6 sec, predict the average distance travelled by a zºbefore it decays. (Hint: you may assume that the pions have an average mass of 137 MeV;
Expert Solution
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Step 1: The average distance

Given,

The lifetime, pi to the power of 0 equals 0.8 cross times 10 to the power of negative 16 end exponent s

Let the straight pi to the power of 0is moving with velocity 0.99 c.

The time before decay,

t equals gamma t subscript 0 t equals fraction numerator t subscript 0 over denominator square root of 1 minus v squared over c squared end root end fraction t equals fraction numerator 0.8 cross times 10 to the power of negative 16 end exponent over denominator square root of 1 minus open parentheses 0.99 c close parentheses squared over c squared end root end fraction t equals 5.671 cross times 10 to the power of negative 16 end exponent s

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Where has 0.99 come from for the velocity?

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