The mean lifetime of + mesons in their own rest frame (the “proper mean lifetime

Question

The mean lifetime of + mesons in their own rest frame (the “proper mean lifetime”) is 0 = 26ns. They are travelling at = u/c = 0.92 in the laboratory frame.

(a) What is the mean lifetime, , of + mesons in the laboratory frame? {2}

(b) What distance is travelled at this velocity during one mean lifetime? {2}

(c) What distance would be travelled in the absence of time dilation? {2}

(d) How long would the laboratory-frame distance calculated in part (b) appear to be in the rest frame of the + mesons? {2}

(e) In the experiment of Alva¨ger and co-workers in 1964, gamma ray photons from the decay of neutral 0 mesons travelling at 0.99975c were found to travel at a speed c in the same direction as the mesons, in the Earth’s frame of reference. What was the speed of the photons in the rest frame of the 0 mesons? {2}

Explanation / Answer

(a) t= L*t0 ; l-lorentz transfomation= 1/sqrt(1-B2)

   t= 26*1/sqrt(1-0.922) =66.34 ns

(b) Apply s=ut;

distance travelled(s)= 3*108*66.34*10-9 = 19.902 m

(c) Apply s=ut ; now t=t0=26ns;

s= 7.8 m

(d) Apply c=s/t ; t=t0

s= 7.8 m

(e) speed of light=3*108 {since according to special relativity speed of light is independent of the frame)

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